id	sid	tid	token	lemma	pos
cana-6127	1	1	communications	communication	NOUN
cana-6127	1	2	on	on	ADP
cana-6127	1	3	applied	apply	VERB
cana-6127	1	4	nonlinear	nonlinear	ADJ
cana-6127	1	5	analysis	analysis	NOUN
cana-6127	1	6	issn	issn	NOUN
cana-6127	1	7	:	:	PUNCT
cana-6127	1	8	1074	1074	NUM
cana-6127	1	9	-	-	PUNCT
cana-6127	1	10	133x	133x	NUM
cana-6127	1	11	vol	vol	VERB
cana-6127	1	12	32	32	NUM
cana-6127	1	13	no	no	NOUN
cana-6127	1	14	.	.	PUNCT
cana-6127	2	1	10s	10	NOUN
cana-6127	2	2	(	(	PUNCT
cana-6127	2	3	2025	2025	NUM
cana-6127	2	4	)	)	PUNCT
cana-6127	2	5	3460	3460	NUM
cana-6127	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	2	7	analysis	analysis	NOUN
cana-6127	2	8	of	of	ADP
cana-6127	2	9	three	three	NUM
cana-6127	2	10	-	-	PUNCT
cana-6127	2	11	dimensional	dimensional	ADJ
cana-6127	2	12	non	non	ADJ
cana-6127	2	13	-	-	ADJ
cana-6127	2	14	homogeneous	homogeneous	ADJ
cana-6127	2	15	fractional	fractional	ADJ
cana-6127	2	16	order	order	NOUN
cana-6127	2	17	thermoelastic	thermoelastic	ADJ
cana-6127	2	18	problem	problem	NOUN
cana-6127	2	19	of	of	ADP
cana-6127	2	20	thick	thick	ADJ
cana-6127	2	21	rectangular	rectangular	ADJ
cana-6127	2	22	plate	plate	NOUN
cana-6127	2	23	with	with	ADP
cana-6127	2	24	internal	internal	ADJ
cana-6127	2	25	heat	heat	NOUN
cana-6127	2	26	generation	generation	NOUN
cana-6127	2	27	yogesh	yogesh	PROPN
cana-6127	2	28	u.	u.	PROPN
cana-6127	2	29	naner𝟏	naner𝟏	PROPN
cana-6127	2	30	,	,	PUNCT
cana-6127	2	31	satish	satish	PROPN
cana-6127	2	32	g.	g.	PROPN
cana-6127	2	33	khavale𝟐	khavale𝟐	PROPN
cana-6127	2	34	,	,	PUNCT
cana-6127	2	35	kishor	kishor	PROPN
cana-6127	2	36	.	.	PUNCT
cana-6127	3	1	r.	r.	PROPN
cana-6127	3	2	gaikwad𝟑	gaikwad𝟑	PROPN
cana-6127	3	3	1department	1department	NUM
cana-6127	3	4	of	of	ADP
cana-6127	3	5	mathematics	mathematic	NOUN
cana-6127	4	1	,	,	PUNCT
cana-6127	4	2	shri	shri	PROPN
cana-6127	4	3	vitthal	vitthal	VERB
cana-6127	4	4	rukhmini	rukhmini	NOUN
cana-6127	4	5	arts	art	NOUN
cana-6127	4	6	,	,	PUNCT
cana-6127	4	7	commerce	commerce	NOUN
cana-6127	4	8	and	and	CCONJ
cana-6127	4	9	science	science	PROPN
cana-6127	4	10	college	college	PROPN
cana-6127	4	11	,	,	PUNCT
cana-6127	4	12	sawana	sawana	PROPN
cana-6127	4	13	,	,	PUNCT
cana-6127	4	14	yavatmal	yavatmal	PROPN
cana-6127	4	15	,	,	PUNCT
cana-6127	4	16	maharashtra	maharashtra	PROPN
cana-6127	4	17	,	,	PUNCT
cana-6127	4	18	india-445205	india-445205	NOUN
cana-6127	4	19	.	.	PUNCT
cana-6127	5	1	2department	2department	NUM
cana-6127	5	2	of	of	ADP
cana-6127	5	3	mathematics	mathematic	NOUN
cana-6127	5	4	,	,	PUNCT
cana-6127	5	5	statistics	statistic	NOUN
cana-6127	5	6	and	and	CCONJ
cana-6127	5	7	computer	computer	NOUN
cana-6127	5	8	science	science	NOUN
cana-6127	5	9	,	,	PUNCT
cana-6127	5	10	chetana	chetana	PROPN
cana-6127	5	11	’s	’s	PART
cana-6127	5	12	h.	h.	PROPN
cana-6127	5	13	s.	s.	PROPN
cana-6127	5	14	college	college	PROPN
cana-6127	5	15	of	of	ADP
cana-6127	5	16	commerce	commerce	PROPN
cana-6127	5	17	and	and	CCONJ
cana-6127	5	18	economics	economic	NOUN
cana-6127	5	19	,	,	PUNCT
cana-6127	5	20	smt	smt	PROPN
cana-6127	5	21	.	.	PUNCT
cana-6127	6	1	k.	k.	PROPN
cana-6127	6	2	c.	c.	PROPN
cana-6127	6	3	college	college	PROPN
cana-6127	6	4	of	of	ADP
cana-6127	6	5	art	art	PROPN
cana-6127	6	6	,	,	PUNCT
cana-6127	6	7	bandra	bandra	PROPN
cana-6127	6	8	(	(	PUNCT
cana-6127	6	9	east	east	PROPN
cana-6127	6	10	)	)	PUNCT
cana-6127	6	11	,	,	PUNCT
cana-6127	6	12	mumbai	mumbai	PROPN
cana-6127	6	13	,	,	PUNCT
cana-6127	6	14	maharashtra	maharashtra	PROPN
cana-6127	6	15	,	,	PUNCT
cana-6127	6	16	india	india	PROPN
cana-6127	6	17	400051	400051	NUM
cana-6127	6	18	.	.	PUNCT
cana-6127	7	1	3post	3post	NUM
cana-6127	7	2	graduate	graduate	NOUN
cana-6127	7	3	department	department	NOUN
cana-6127	7	4	of	of	ADP
cana-6127	7	5	mathematics	mathematic	NOUN
cana-6127	7	6	,	,	PUNCT
cana-6127	7	7	n.	n.	PROPN
cana-6127	7	8	e.	e.	PROPN
cana-6127	7	9	s.	s.	PROPN
cana-6127	7	10	,	,	PUNCT
cana-6127	7	11	science	science	PROPN
cana-6127	7	12	college	college	PROPN
cana-6127	7	13	,	,	PUNCT
cana-6127	7	14	nanded	nanded	PROPN
cana-6127	7	15	,	,	PUNCT
cana-6127	7	16	maharashtra	maharashtra	PROPN
cana-6127	7	17	,	,	PUNCT
cana-6127	7	18	india	india	PROPN
cana-6127	7	19	431605	431605	NUM
cana-6127	7	20	.	.	PUNCT
cana-6127	8	1	emailynaner@gmail.com	emailynaner@gmail.com	X
cana-6127	8	2	,	,	PUNCT
cana-6127	8	3	khavalesatish8@gmail.com	khavalesatish8@gmail.com	X
cana-6127	8	4	,	,	PUNCT
cana-6127	8	5	drkr.gaikwad@yahoo.in	drkr.gaikwad@yahoo.in	PROPN
cana-6127	8	6	,	,	PUNCT
cana-6127	8	7	satish.khavale@chetanacollege.in	satish.khavale@chetanacollege.in	NOUN
cana-6127	8	8	article	article	NOUN
cana-6127	8	9	history	history	NOUN
cana-6127	8	10	:	:	PUNCT
cana-6127	8	11	received	receive	VERB
cana-6127	8	12	:	:	PUNCT
cana-6127	8	13	19	19	NUM
cana-6127	8	14	-	-	SYM
cana-6127	8	15	08	08	NUM
cana-6127	8	16	-	-	PUNCT
cana-6127	8	17	2025	2025	NUM
cana-6127	8	18	revised	revise	VERB
cana-6127	8	19	:	:	PUNCT
cana-6127	8	20	24	24	NUM
cana-6127	8	21	-	-	PUNCT
cana-6127	8	22	09	09	NUM
cana-6127	8	23	-	-	PUNCT
cana-6127	8	24	2025	2025	NUM
cana-6127	8	25	accepted	accept	VERB
cana-6127	8	26	:	:	PUNCT
cana-6127	8	27	15	15	NUM
cana-6127	8	28	-	-	SYM
cana-6127	8	29	10	10	NUM
cana-6127	8	30	-	-	PUNCT
cana-6127	8	31	2025	2025	NUM
cana-6127	8	32	abstract	abstract	NOUN
cana-6127	8	33	:	:	PUNCT
cana-6127	8	34	this	this	DET
cana-6127	8	35	paper	paper	NOUN
cana-6127	8	36	investigates	investigate	VERB
cana-6127	8	37	the	the	DET
cana-6127	8	38	thermal	thermal	ADJ
cana-6127	8	39	behaviour	behaviour	NOUN
cana-6127	8	40	of	of	ADP
cana-6127	8	41	a	a	DET
cana-6127	8	42	three	three	NUM
cana-6127	8	43	-	-	PUNCT
cana-6127	8	44	dimensional	dimensional	ADJ
cana-6127	8	45	thick	thick	ADJ
cana-6127	8	46	rectangular	rectangular	ADJ
cana-6127	8	47	plate	plate	NOUN
cana-6127	8	48	governed	govern	VERB
cana-6127	8	49	by	by	ADP
cana-6127	8	50	a	a	DET
cana-6127	8	51	fractional	fractional	ADJ
cana-6127	8	52	-	-	PUNCT
cana-6127	8	53	order	order	NOUN
cana-6127	8	54	derivative	derivative	NOUN
cana-6127	8	55	.	.	PUNCT
cana-6127	9	1	the	the	DET
cana-6127	9	2	plate	plate	NOUN
cana-6127	9	3	,	,	PUNCT
cana-6127	9	4	occupying	occupy	VERB
cana-6127	9	5	the	the	DET
cana-6127	9	6	region	region	NOUN
cana-6127	9	7	𝐷	𝐷	PROPN
cana-6127	9	8	=	=	SYM
cana-6127	9	9	{	{	PUNCT
cana-6127	9	10	(	(	PUNCT
cana-6127	9	11	𝑥	𝑥	NOUN
cana-6127	9	12	,	,	PUNCT
cana-6127	9	13	𝑦	𝑦	NOUN
cana-6127	9	14	,	,	PUNCT
cana-6127	9	15	𝑧	𝑧	NOUN
cana-6127	9	16	)	)	PUNCT
cana-6127	9	17	∈	∈	PROPN
cana-6127	9	18	𝑅3	𝑅3	NOUN
cana-6127	9	19	:	:	PUNCT
cana-6127	9	20	0	0	NUM
cana-6127	9	21	≤	≤	NUM
cana-6127	9	22	𝑥	𝑥	PRON
cana-6127	9	23	≤	≤	NUM
cana-6127	9	24	𝑎	𝑎	ADJ
cana-6127	9	25	,	,	PUNCT
cana-6127	9	26	0	0	NUM
cana-6127	9	27	≤	≤	NUM
cana-6127	9	28	𝑦	𝑦	NOUN
cana-6127	9	29	≤	≤	NOUN
cana-6127	9	30	𝑏	𝑏	NOUN
cana-6127	9	31	,	,	PUNCT
cana-6127	9	32	0	0	NUM
cana-6127	9	33	≤	≤	NOUN
cana-6127	9	34	𝑧	𝑧	PRON
cana-6127	9	35	≤	≤	NUM
cana-6127	9	36	𝑐	𝑐	NOUN
cana-6127	9	37	}	}	PUNCT
cana-6127	9	38	,	,	PUNCT
cana-6127	9	39	is	be	AUX
cana-6127	9	40	initially	initially	ADV
cana-6127	9	41	at	at	ADP
cana-6127	9	42	an	an	DET
cana-6127	9	43	arbitrary	arbitrary	ADJ
cana-6127	9	44	temperature	temperature	NOUN
cana-6127	9	45	distribution	distribution	NOUN
cana-6127	9	46	𝑓(𝑥	𝑓(𝑥	NOUN
cana-6127	9	47	,	,	PUNCT
cana-6127	9	48	𝑦	𝑦	NOUN
cana-6127	9	49	,	,	PUNCT
cana-6127	9	50	𝑧	𝑧	NOUN
cana-6127	9	51	)	)	PUNCT
cana-6127	9	52	.	.	PUNCT
cana-6127	10	1	for	for	ADP
cana-6127	10	2	𝑡	𝑡	X
cana-6127	10	3	>	>	X
cana-6127	10	4	0	0	PROPN
cana-6127	10	5	,	,	PUNCT
cana-6127	10	6	the	the	DET
cana-6127	10	7	plate	plate	NOUN
cana-6127	10	8	experiences	experience	VERB
cana-6127	10	9	internal	internal	ADJ
cana-6127	10	10	heat	heat	NOUN
cana-6127	10	11	generation	generation	NOUN
cana-6127	10	12	represented	represent	VERB
cana-6127	10	13	by	by	ADP
cana-6127	10	14	𝑔(𝑥	𝑔(𝑥	PROPN
cana-6127	10	15	,	,	PUNCT
cana-6127	10	16	𝑦	𝑦	NOUN
cana-6127	10	17	,	,	PUNCT
cana-6127	10	18	𝑧	𝑧	NOUN
cana-6127	10	19	,	,	PUNCT
cana-6127	10	20	𝑡	𝑡	NOUN
cana-6127	10	21	)	)	PUNCT
cana-6127	10	22	btu	btu	PROPN
cana-6127	10	23	/	/	SYM
cana-6127	10	24	hr	hr	PROPN
cana-6127	10	25	ft3	ft3	NOUN
cana-6127	10	26	,	,	PUNCT
cana-6127	10	27	while	while	SCONJ
cana-6127	10	28	all	all	DET
cana-6127	10	29	boundary	boundary	ADJ
cana-6127	10	30	surfaces	surface	NOUN
cana-6127	10	31	are	be	AUX
cana-6127	10	32	maintained	maintain	VERB
cana-6127	10	33	at	at	ADP
cana-6127	10	34	zero	zero	NUM
cana-6127	10	35	temperature	temperature	NOUN
cana-6127	10	36	.	.	PUNCT
cana-6127	11	1	the	the	DET
cana-6127	11	2	governing	govern	VERB
cana-6127	11	3	model	model	NOUN
cana-6127	11	4	is	be	AUX
cana-6127	11	5	formulated	formulate	VERB
cana-6127	11	6	using	use	VERB
cana-6127	11	7	the	the	DET
cana-6127	11	8	caputo	caputo	PROPN
cana-6127	11	9	fractional	fractional	PROPN
cana-6127	11	10	derivative	derivative	PROPN
cana-6127	11	11	,	,	PUNCT
cana-6127	11	12	and	and	CCONJ
cana-6127	11	13	analytical	analytical	ADJ
cana-6127	11	14	solutions	solution	NOUN
cana-6127	11	15	for	for	ADP
cana-6127	11	16	temperature	temperature	NOUN
cana-6127	11	17	,	,	PUNCT
cana-6127	11	18	displacement	displacement	NOUN
cana-6127	11	19	,	,	PUNCT
cana-6127	11	20	and	and	CCONJ
cana-6127	11	21	thermal	thermal	ADJ
cana-6127	11	22	stresses	stress	NOUN
cana-6127	11	23	are	be	AUX
cana-6127	11	24	derived	derive	VERB
cana-6127	11	25	through	through	ADP
cana-6127	11	26	the	the	DET
cana-6127	11	27	integral	integral	ADJ
cana-6127	11	28	transform	transform	NOUN
cana-6127	11	29	technique	technique	NOUN
cana-6127	11	30	.	.	PUNCT
cana-6127	12	1	numerical	numerical	ADJ
cana-6127	12	2	simulations	simulation	NOUN
cana-6127	12	3	are	be	AUX
cana-6127	12	4	carried	carry	VERB
cana-6127	12	5	out	out	ADP
cana-6127	12	6	using	use	VERB
cana-6127	12	7	ptc	ptc	PROPN
cana-6127	12	8	mathcad	mathcad	PROPN
cana-6127	12	9	software	software	PROPN
cana-6127	12	10	,	,	PUNCT
cana-6127	12	11	and	and	CCONJ
cana-6127	12	12	the	the	DET
cana-6127	12	13	results	result	NOUN
cana-6127	12	14	are	be	AUX
cana-6127	12	15	illustrated	illustrate	VERB
cana-6127	12	16	graphically	graphically	ADV
cana-6127	12	17	.	.	PUNCT
cana-6127	13	1	the	the	DET
cana-6127	13	2	study	study	NOUN
cana-6127	13	3	highlights	highlight	VERB
cana-6127	13	4	the	the	DET
cana-6127	13	5	influence	influence	NOUN
cana-6127	13	6	of	of	ADP
cana-6127	13	7	the	the	DET
cana-6127	13	8	fractional	fractional	ADJ
cana-6127	13	9	-	-	PUNCT
cana-6127	13	10	order	order	NOUN
cana-6127	13	11	parameter	parameter	NOUN
cana-6127	13	12	on	on	ADP
cana-6127	13	13	heat	heat	NOUN
cana-6127	13	14	conduction	conduction	NOUN
cana-6127	13	15	,	,	PUNCT
cana-6127	13	16	displacement	displacement	NOUN
cana-6127	13	17	,	,	PUNCT
cana-6127	13	18	and	and	CCONJ
cana-6127	13	19	stress	stress	NOUN
cana-6127	13	20	distribution	distribution	NOUN
cana-6127	13	21	,	,	PUNCT
cana-6127	13	22	demonstrating	demonstrate	VERB
cana-6127	13	23	the	the	DET
cana-6127	13	24	effectiveness	effectiveness	NOUN
cana-6127	13	25	of	of	ADP
cana-6127	13	26	fractional	fractional	ADJ
cana-6127	13	27	-	-	PUNCT
cana-6127	13	28	order	order	NOUN
cana-6127	13	29	thermoelastic	thermoelastic	ADJ
cana-6127	13	30	models	model	NOUN
cana-6127	13	31	in	in	ADP
cana-6127	13	32	capturing	capture	VERB
cana-6127	13	33	nonlocal	nonlocal	ADJ
cana-6127	13	34	thermal	thermal	ADJ
cana-6127	13	35	effects	effect	NOUN
cana-6127	13	36	.	.	PUNCT
cana-6127	14	1	introduction	introduction	NOUN
cana-6127	14	2	:	:	PUNCT
cana-6127	14	3	the	the	DET
cana-6127	14	4	study	study	NOUN
cana-6127	14	5	of	of	ADP
cana-6127	14	6	thermoelastic	thermoelastic	ADJ
cana-6127	14	7	behaviour	behaviour	NOUN
cana-6127	14	8	in	in	ADP
cana-6127	14	9	solid	solid	ADJ
cana-6127	14	10	materials	material	NOUN
cana-6127	14	11	has	have	AUX
cana-6127	14	12	gained	gain	VERB
cana-6127	14	13	significant	significant	ADJ
cana-6127	14	14	importance	importance	NOUN
cana-6127	14	15	due	due	ADP
cana-6127	14	16	to	to	ADP
cana-6127	14	17	its	its	PRON
cana-6127	14	18	wide	wide	ADJ
cana-6127	14	19	applications	application	NOUN
cana-6127	14	20	in	in	ADP
cana-6127	14	21	aerospace	aerospace	NOUN
cana-6127	14	22	,	,	PUNCT
cana-6127	14	23	mechanical	mechanical	ADJ
cana-6127	14	24	,	,	PUNCT
cana-6127	14	25	and	and	CCONJ
cana-6127	14	26	civil	civil	ADJ
cana-6127	14	27	engineering	engineering	NOUN
cana-6127	14	28	.	.	PUNCT
cana-6127	15	1	classical	classical	ADJ
cana-6127	15	2	thermoelastic	thermoelastic	ADJ
cana-6127	15	3	theories	theory	NOUN
cana-6127	15	4	often	often	ADV
cana-6127	15	5	assume	assume	VERB
cana-6127	15	6	instantaneous	instantaneous	ADJ
cana-6127	15	7	heat	heat	NOUN
cana-6127	15	8	propagation	propagation	NOUN
cana-6127	15	9	,	,	PUNCT
cana-6127	15	10	which	which	PRON
cana-6127	15	11	contradicts	contradict	VERB
cana-6127	15	12	physical	physical	ADJ
cana-6127	15	13	reality	reality	NOUN
cana-6127	15	14	.	.	PUNCT
cana-6127	16	1	to	to	PART
cana-6127	16	2	overcome	overcome	VERB
cana-6127	16	3	this	this	DET
cana-6127	16	4	limitation	limitation	NOUN
cana-6127	16	5	,	,	PUNCT
cana-6127	16	6	fractionalorder	fractionalorder	ADJ
cana-6127	16	7	thermoelasticity	thermoelasticity	NOUN
cana-6127	16	8	has	have	AUX
cana-6127	16	9	been	be	AUX
cana-6127	16	10	introduced	introduce	VERB
cana-6127	16	11	as	as	ADP
cana-6127	16	12	an	an	DET
cana-6127	16	13	effective	effective	ADJ
cana-6127	16	14	approach	approach	NOUN
cana-6127	16	15	to	to	ADP
cana-6127	16	16	model	model	NOUN
cana-6127	16	17	heat	heat	NOUN
cana-6127	16	18	conduction	conduction	NOUN
cana-6127	16	19	with	with	ADP
cana-6127	16	20	memory	memory	NOUN
cana-6127	16	21	and	and	CCONJ
cana-6127	16	22	nonlocal	nonlocal	ADJ
cana-6127	16	23	effects	effect	NOUN
cana-6127	16	24	.	.	PUNCT
cana-6127	17	1	in	in	ADP
cana-6127	17	2	this	this	DET
cana-6127	17	3	paper	paper	NOUN
cana-6127	17	4	,	,	PUNCT
cana-6127	17	5	a	a	DET
cana-6127	17	6	three	three	NUM
cana-6127	17	7	-	-	PUNCT
cana-6127	17	8	dimensional	dimensional	ADJ
cana-6127	17	9	nonhomogeneous	nonhomogeneous	ADJ
cana-6127	17	10	thick	thick	ADJ
cana-6127	17	11	rectangular	rectangular	ADJ
cana-6127	17	12	plate	plate	NOUN
cana-6127	17	13	with	with	ADP
cana-6127	17	14	internal	internal	ADJ
cana-6127	17	15	heat	heat	NOUN
cana-6127	17	16	generation	generation	NOUN
cana-6127	17	17	is	be	AUX
cana-6127	17	18	analysed	analyse	VERB
cana-6127	17	19	using	use	VERB
cana-6127	17	20	the	the	DET
cana-6127	17	21	caputo	caputo	PROPN
cana-6127	17	22	fractional	fractional	PROPN
cana-6127	17	23	derivative	derivative	PROPN
cana-6127	17	24	.	.	PUNCT
cana-6127	18	1	the	the	DET
cana-6127	18	2	objective	objective	NOUN
cana-6127	18	3	is	be	AUX
cana-6127	18	4	to	to	PART
cana-6127	18	5	investigate	investigate	VERB
cana-6127	18	6	how	how	SCONJ
cana-6127	18	7	the	the	DET
cana-6127	18	8	fractional	fractional	ADJ
cana-6127	18	9	-	-	PUNCT
cana-6127	18	10	order	order	NOUN
cana-6127	18	11	parameter	parameter	NOUN
cana-6127	18	12	(	(	PUNCT
cana-6127	18	13	α	α	NOUN
cana-6127	18	14	)	)	PUNCT
cana-6127	18	15	influences	influence	VERB
cana-6127	18	16	temperature	temperature	NOUN
cana-6127	18	17	,	,	PUNCT
cana-6127	18	18	displacement	displacement	NOUN
cana-6127	18	19	,	,	PUNCT
cana-6127	18	20	and	and	CCONJ
cana-6127	18	21	stress	stress	NOUN
cana-6127	18	22	distributions	distribution	NOUN
cana-6127	18	23	.	.	PUNCT
cana-6127	19	1	the	the	DET
cana-6127	19	2	proposed	propose	VERB
cana-6127	19	3	model	model	NOUN
cana-6127	19	4	provides	provide	VERB
cana-6127	19	5	a	a	DET
cana-6127	19	6	more	more	ADV
cana-6127	19	7	generalized	generalized	ADJ
cana-6127	19	8	framework	framework	NOUN
cana-6127	19	9	that	that	PRON
cana-6127	19	10	includes	include	VERB
cana-6127	19	11	both	both	CCONJ
cana-6127	19	12	the	the	DET
cana-6127	19	13	classical	classical	ADJ
cana-6127	19	14	and	and	CCONJ
cana-6127	19	15	wave	wave	NOUN
cana-6127	19	16	-	-	PUNCT
cana-6127	19	17	type	type	NOUN
cana-6127	19	18	heat	heat	NOUN
cana-6127	19	19	conduction	conduction	NOUN
cana-6127	19	20	as	as	ADP
cana-6127	19	21	special	special	ADJ
cana-6127	19	22	cases	case	NOUN
cana-6127	19	23	,	,	PUNCT
cana-6127	19	24	thus	thus	ADV
cana-6127	19	25	offering	offer	VERB
cana-6127	19	26	a	a	DET
cana-6127	19	27	realistic	realistic	ADJ
cana-6127	19	28	representation	representation	NOUN
cana-6127	19	29	of	of	ADP
cana-6127	19	30	transient	transient	ADJ
cana-6127	19	31	thermal	thermal	ADJ
cana-6127	19	32	behaviour	behaviour	NOUN
cana-6127	19	33	in	in	ADP
cana-6127	19	34	thick	thick	ADJ
cana-6127	19	35	plates	plate	NOUN
cana-6127	19	36	.	.	PUNCT
cana-6127	20	1	objectives	objective	NOUN
cana-6127	20	2	:	:	PUNCT
cana-6127	20	3	1	1	X
cana-6127	20	4	.	.	X
cana-6127	20	5	to	to	PART
cana-6127	20	6	investigate	investigate	VERB
cana-6127	20	7	the	the	DET
cana-6127	20	8	thermal	thermal	ADJ
cana-6127	20	9	behaviour	behaviour	NOUN
cana-6127	20	10	of	of	ADP
cana-6127	20	11	a	a	DET
cana-6127	20	12	three	three	NUM
cana-6127	20	13	-	-	PUNCT
cana-6127	20	14	dimensional	dimensional	ADJ
cana-6127	20	15	thick	thick	ADJ
cana-6127	20	16	rectangular	rectangular	ADJ
cana-6127	20	17	plate	plate	NOUN
cana-6127	20	18	subjected	subject	VERB
cana-6127	20	19	to	to	ADP
cana-6127	20	20	internal	internal	ADJ
cana-6127	20	21	heat	heat	NOUN
cana-6127	20	22	generation	generation	NOUN
cana-6127	20	23	.	.	PUNCT
cana-6127	21	1	2	2	X
cana-6127	21	2	.	.	PUNCT
cana-6127	21	3	to	to	PART
cana-6127	21	4	analyse	analyse	VERB
cana-6127	21	5	the	the	DET
cana-6127	21	6	effect	effect	NOUN
cana-6127	21	7	of	of	ADP
cana-6127	21	8	the	the	DET
cana-6127	21	9	fractional	fractional	ADJ
cana-6127	21	10	-	-	PUNCT
cana-6127	21	11	order	order	NOUN
cana-6127	21	12	parameter	parameter	NOUN
cana-6127	21	13	(	(	PUNCT
cana-6127	21	14	α	α	NOUN
cana-6127	21	15	)	)	PUNCT
cana-6127	21	16	on	on	ADP
cana-6127	21	17	temperature	temperature	NOUN
cana-6127	21	18	,	,	PUNCT
cana-6127	21	19	displacement	displacement	NOUN
cana-6127	21	20	,	,	PUNCT
cana-6127	21	21	and	and	CCONJ
cana-6127	21	22	thermal	thermal	ADJ
cana-6127	21	23	stresses	stress	NOUN
cana-6127	21	24	.	.	PUNCT
cana-6127	22	1	3	3	X
cana-6127	22	2	.	.	X
cana-6127	22	3	to	to	PART
cana-6127	22	4	demonstrate	demonstrate	VERB
cana-6127	22	5	the	the	DET
cana-6127	22	6	usefulness	usefulness	NOUN
cana-6127	22	7	of	of	ADP
cana-6127	22	8	fractional	fractional	ADJ
cana-6127	22	9	-	-	PUNCT
cana-6127	22	10	order	order	NOUN
cana-6127	22	11	thermoelastic	thermoelastic	ADJ
cana-6127	22	12	models	model	NOUN
cana-6127	22	13	in	in	ADP
cana-6127	22	14	capturing	capture	VERB
cana-6127	22	15	nonlocal	nonlocal	ADJ
cana-6127	22	16	and	and	CCONJ
cana-6127	22	17	memory	memory	NOUN
cana-6127	22	18	effects	effect	NOUN
cana-6127	22	19	in	in	ADP
cana-6127	22	20	heat	heat	NOUN
cana-6127	22	21	conduction	conduction	NOUN
cana-6127	22	22	.	.	PUNCT
cana-6127	23	1	methods	method	NOUN
cana-6127	23	2	:	:	PUNCT
cana-6127	23	3	the	the	DET
cana-6127	23	4	governing	govern	VERB
cana-6127	23	5	equations	equation	NOUN
cana-6127	23	6	are	be	AUX
cana-6127	23	7	derived	derive	VERB
cana-6127	23	8	using	use	VERB
cana-6127	23	9	the	the	DET
cana-6127	23	10	caputo	caputo	PROPN
cana-6127	23	11	fractional	fractional	PROPN
cana-6127	23	12	derivative	derivative	NOUN
cana-6127	23	13	for	for	ADP
cana-6127	23	14	time	time	NOUN
cana-6127	23	15	-	-	PUNCT
cana-6127	23	16	fractional	fractional	ADJ
cana-6127	23	17	heat	heat	NOUN
cana-6127	23	18	conduction	conduction	NOUN
cana-6127	23	19	.	.	PUNCT
cana-6127	24	1	integral	integral	ADJ
cana-6127	24	2	transform	transform	NOUN
cana-6127	24	3	techniques	technique	NOUN
cana-6127	24	4	are	be	AUX
cana-6127	24	5	employed	employ	VERB
cana-6127	24	6	to	to	PART
cana-6127	24	7	obtain	obtain	VERB
cana-6127	24	8	analytical	analytical	ADJ
cana-6127	24	9	solutions	solution	NOUN
cana-6127	24	10	for	for	ADP
cana-6127	24	11	temperature	temperature	NOUN
cana-6127	24	12	,	,	PUNCT
cana-6127	24	13	displacement	displacement	NOUN
cana-6127	24	14	,	,	PUNCT
cana-6127	24	15	and	and	CCONJ
cana-6127	24	16	stress	stress	NOUN
cana-6127	24	17	fields	field	NOUN
cana-6127	24	18	.	.	PUNCT
cana-6127	25	1	mittagmailto:ynaner@gmail.com	mittagmailto:ynaner@gmail.com	X
cana-6127	26	1	mailto:khavalesatish8@gmail.com	mailto:khavalesatish8@gmail.com	X
cana-6127	26	2	mailto:drkr.gaikwad@yahoo.in	mailto:drkr.gaikwad@yahoo.in	PROPN
cana-6127	26	3	mailto:satish.khavale@chetanacollege.in	mailto:satish.khavale@chetanacollege.in	PROPN
cana-6127	26	4	communications	communication	NOUN
cana-6127	26	5	on	on	ADP
cana-6127	26	6	applied	apply	VERB
cana-6127	26	7	nonlinear	nonlinear	ADJ
cana-6127	26	8	analysis	analysis	NOUN
cana-6127	26	9	issn	issn	NOUN
cana-6127	26	10	:	:	PUNCT
cana-6127	26	11	1074	1074	NUM
cana-6127	26	12	-	-	PUNCT
cana-6127	26	13	133x	133x	NUM
cana-6127	26	14	vol	vol	VERB
cana-6127	26	15	32	32	NUM
cana-6127	26	16	no	no	NOUN
cana-6127	26	17	.	.	PUNCT
cana-6127	27	1	10s	10	NOUN
cana-6127	27	2	(	(	PUNCT
cana-6127	27	3	2025	2025	NUM
cana-6127	27	4	)	)	PUNCT
cana-6127	27	5	3461	3461	NUM
cana-6127	27	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	27	7	leffler	leffl	ADJ
cana-6127	27	8	functions	function	NOUN
cana-6127	27	9	are	be	AUX
cana-6127	27	10	used	use	VERB
cana-6127	27	11	in	in	ADP
cana-6127	27	12	the	the	DET
cana-6127	27	13	solutions	solution	NOUN
cana-6127	27	14	to	to	PART
cana-6127	27	15	describe	describe	VERB
cana-6127	27	16	the	the	DET
cana-6127	27	17	fractional	fractional	ADJ
cana-6127	27	18	behaviour	behaviour	NOUN
cana-6127	27	19	.	.	PUNCT
cana-6127	28	1	numerical	numerical	ADJ
cana-6127	28	2	simulations	simulation	NOUN
cana-6127	28	3	are	be	AUX
cana-6127	28	4	performed	perform	VERB
cana-6127	28	5	in	in	ADP
cana-6127	28	6	ptc	ptc	PROPN
cana-6127	28	7	mathcad	mathcad	PROPN
cana-6127	28	8	prime	prime	PROPN
cana-6127	28	9	for	for	ADP
cana-6127	28	10	a	a	DET
cana-6127	28	11	thick	thick	ADJ
cana-6127	28	12	rectangular	rectangular	ADJ
cana-6127	28	13	plate	plate	NOUN
cana-6127	28	14	using	use	VERB
cana-6127	28	15	physical	physical	ADJ
cana-6127	28	16	constants	constant	NOUN
cana-6127	28	17	.	.	PUNCT
cana-6127	29	1	results	result	NOUN
cana-6127	29	2	:	:	PUNCT
cana-6127	29	3	the	the	DET
cana-6127	29	4	temperature	temperature	NOUN
cana-6127	29	5	distribution	distribution	NOUN
cana-6127	29	6	decreases	decrease	VERB
cana-6127	29	7	with	with	ADP
cana-6127	29	8	increasing	increase	VERB
cana-6127	29	9	fractional	fractional	ADJ
cana-6127	29	10	order	order	NOUN
cana-6127	29	11	α	α	NOUN
cana-6127	29	12	and	and	CCONJ
cana-6127	29	13	is	be	AUX
cana-6127	29	14	maximum	maximum	ADJ
cana-6127	29	15	at	at	ADP
cana-6127	29	16	the	the	DET
cana-6127	29	17	centre	centre	NOUN
cana-6127	29	18	of	of	ADP
cana-6127	29	19	the	the	DET
cana-6127	29	20	plate	plate	NOUN
cana-6127	29	21	.	.	PUNCT
cana-6127	30	1	displacement	displacement	ADJ
cana-6127	30	2	components	component	NOUN
cana-6127	30	3	show	show	VERB
cana-6127	30	4	symmetrical	symmetrical	ADJ
cana-6127	30	5	behaviour	behaviour	NOUN
cana-6127	30	6	,	,	PUNCT
cana-6127	30	7	increasing	increase	VERB
cana-6127	30	8	from	from	ADP
cana-6127	30	9	the	the	DET
cana-6127	30	10	edges	edge	NOUN
cana-6127	30	11	and	and	CCONJ
cana-6127	30	12	vanishing	vanish	VERB
cana-6127	30	13	at	at	ADP
cana-6127	30	14	the	the	DET
cana-6127	30	15	centre	centre	NOUN
cana-6127	30	16	.	.	PUNCT
cana-6127	31	1	stress	stress	NOUN
cana-6127	31	2	components	component	NOUN
cana-6127	31	3	are	be	AUX
cana-6127	31	4	compressive	compressive	ADJ
cana-6127	31	5	,	,	PUNCT
cana-6127	31	6	peaking	peak	VERB
cana-6127	31	7	at	at	ADP
cana-6127	31	8	the	the	DET
cana-6127	31	9	middle	middle	NOUN
cana-6127	31	10	of	of	ADP
cana-6127	31	11	the	the	DET
cana-6127	31	12	plate	plate	NOUN
cana-6127	31	13	and	and	CCONJ
cana-6127	31	14	zero	zero	NUM
cana-6127	31	15	at	at	ADP
cana-6127	31	16	the	the	DET
cana-6127	31	17	edges	edge	NOUN
cana-6127	31	18	.	.	PUNCT
cana-6127	32	1	the	the	DET
cana-6127	32	2	fractional	fractional	ADJ
cana-6127	32	3	order	order	NOUN
cana-6127	32	4	parameter	parameter	NOUN
cana-6127	32	5	α	α	PROPN
cana-6127	32	6	significantly	significantly	ADV
cana-6127	32	7	affects	affect	VERB
cana-6127	32	8	heat	heat	NOUN
cana-6127	32	9	transfer	transfer	NOUN
cana-6127	32	10	.	.	PUNCT
cana-6127	33	1	graphs	graph	NOUN
cana-6127	33	2	demonstrate	demonstrate	VERB
cana-6127	33	3	clear	clear	ADJ
cana-6127	33	4	variation	variation	NOUN
cana-6127	33	5	between	between	ADP
cana-6127	33	6	classical	classical	ADJ
cana-6127	33	7	(	(	PUNCT
cana-6127	33	8	α	α	NOUN
cana-6127	33	9	=	=	SYM
cana-6127	33	10	1	1	NUM
cana-6127	33	11	)	)	PUNCT
cana-6127	33	12	and	and	CCONJ
cana-6127	33	13	fractional	fractional	ADJ
cana-6127	33	14	-	-	PUNCT
cana-6127	33	15	order	order	NOUN
cana-6127	33	16	(	(	PUNCT
cana-6127	33	17	α	α	NOUN
cana-6127	33	18	≠	≠	PROPN
cana-6127	33	19	1	1	NUM
cana-6127	33	20	)	)	PUNCT
cana-6127	33	21	thermoelastic	thermoelastic	ADJ
cana-6127	33	22	behaviour	behaviour	NOUN
cana-6127	33	23	.	.	PUNCT
cana-6127	34	1	conclusions	conclusion	NOUN
cana-6127	34	2	:	:	PUNCT
cana-6127	34	3	for	for	ADP
cana-6127	34	4	α	α	NOUN
cana-6127	34	5	=	=	SYM
cana-6127	34	6	1	1	NUM
cana-6127	34	7	,	,	PUNCT
cana-6127	34	8	the	the	DET
cana-6127	34	9	model	model	NOUN
cana-6127	34	10	reduces	reduce	VERB
cana-6127	34	11	to	to	ADP
cana-6127	34	12	the	the	DET
cana-6127	34	13	classical	classical	ADJ
cana-6127	34	14	heat	heat	NOUN
cana-6127	34	15	diffusion	diffusion	NOUN
cana-6127	34	16	equation	equation	NOUN
cana-6127	34	17	,	,	PUNCT
cana-6127	34	18	while	while	SCONJ
cana-6127	34	19	α	α	NOUN
cana-6127	34	20	=	=	SYM
cana-6127	34	21	2	2	NUM
cana-6127	34	22	corresponds	correspond	NOUN
cana-6127	34	23	to	to	ADP
cana-6127	34	24	the	the	DET
cana-6127	34	25	wave	wave	NOUN
cana-6127	34	26	equation	equation	NOUN
cana-6127	34	27	.	.	PUNCT
cana-6127	35	1	the	the	DET
cana-6127	35	2	fractional	fractional	ADJ
cana-6127	35	3	order	order	NOUN
cana-6127	35	4	0	0	PUNCT
cana-6127	35	5	<	<	X
cana-6127	35	6	α	α	X
cana-6127	35	7	<	<	X
cana-6127	35	8	1	1	NUM
cana-6127	35	9	,	,	PUNCT
cana-6127	35	10	α	α	NOUN
cana-6127	35	11	=	=	SYM
cana-6127	35	12	1	1	NUM
cana-6127	35	13	,	,	PUNCT
cana-6127	35	14	and	and	CCONJ
cana-6127	35	15	1	1	NUM
cana-6127	35	16	<	<	X
cana-6127	35	17	α	α	X
cana-6127	35	18	<	<	X
cana-6127	35	19	2	2	NUM
cana-6127	35	20	represent	represent	VERB
cana-6127	35	21	weak	weak	ADJ
cana-6127	35	22	,	,	PUNCT
cana-6127	35	23	normal	normal	ADJ
cana-6127	35	24	,	,	PUNCT
cana-6127	35	25	and	and	CCONJ
cana-6127	35	26	strong	strong	ADJ
cana-6127	35	27	conductivity	conductivity	NOUN
cana-6127	35	28	,	,	PUNCT
cana-6127	35	29	respectively	respectively	ADV
cana-6127	35	30	.	.	PUNCT
cana-6127	36	1	stress	stress	NOUN
cana-6127	36	2	distributions	distribution	NOUN
cana-6127	36	3	are	be	AUX
cana-6127	36	4	tensile	tensile	ADJ
cana-6127	36	5	/	/	SYM
cana-6127	36	6	compressive	compressive	ADJ
cana-6127	36	7	and	and	CCONJ
cana-6127	36	8	follow	follow	VERB
cana-6127	36	9	normal	normal	ADJ
cana-6127	36	10	curves	curve	NOUN
cana-6127	36	11	in	in	ADP
cana-6127	36	12	all	all	DET
cana-6127	36	13	directions	direction	NOUN
cana-6127	36	14	,	,	PUNCT
cana-6127	36	15	directly	directly	ADV
cana-6127	36	16	proportional	proportional	ADJ
cana-6127	36	17	to	to	ADP
cana-6127	36	18	α	α	PRON
cana-6127	36	19	.	.	PUNCT
cana-6127	37	1	the	the	DET
cana-6127	37	2	fractional	fractional	ADJ
cana-6127	37	3	order	order	NOUN
cana-6127	37	4	α	α	NOUN
cana-6127	37	5	governs	govern	VERB
cana-6127	37	6	nonlocal	nonlocal	ADJ
cana-6127	37	7	heat	heat	NOUN
cana-6127	37	8	transfer	transfer	NOUN
cana-6127	37	9	,	,	PUNCT
cana-6127	37	10	influencing	influence	VERB
cana-6127	37	11	both	both	DET
cana-6127	37	12	response	response	NOUN
cana-6127	37	13	time	time	NOUN
cana-6127	37	14	and	and	CCONJ
cana-6127	37	15	temperature	temperature	NOUN
cana-6127	37	16	overshoot	overshoot	NOUN
cana-6127	37	17	.	.	PUNCT
cana-6127	38	1	the	the	DET
cana-6127	38	2	model	model	NOUN
cana-6127	38	3	effectively	effectively	ADV
cana-6127	38	4	describes	describe	VERB
cana-6127	38	5	transient	transient	ADJ
cana-6127	38	6	thermoelastic	thermoelastic	ADJ
cana-6127	38	7	behavior	behavior	NOUN
cana-6127	38	8	in	in	ADP
cana-6127	38	9	thick	thick	ADJ
cana-6127	38	10	plates	plate	NOUN
cana-6127	38	11	and	and	CCONJ
cana-6127	38	12	can	can	AUX
cana-6127	38	13	be	be	AUX
cana-6127	38	14	applied	apply	VERB
cana-6127	38	15	to	to	ADP
cana-6127	38	16	other	other	ADJ
cana-6127	38	17	nonhomogeneous	nonhomogeneous	ADJ
cana-6127	38	18	materials	material	NOUN
cana-6127	38	19	.	.	PUNCT
cana-6127	39	1	keywords	keyword	NOUN
cana-6127	39	2	:	:	PUNCT
cana-6127	39	3	thermal	thermal	ADJ
cana-6127	39	4	behavior	behavior	NOUN
cana-6127	39	5	,	,	PUNCT
cana-6127	39	6	internal	internal	ADJ
cana-6127	39	7	heat	heat	NOUN
cana-6127	39	8	source	source	NOUN
cana-6127	39	9	,	,	PUNCT
cana-6127	39	10	caputo	caputo	PROPN
cana-6127	39	11	fractional	fractional	PROPN
cana-6127	39	12	derivative	derivative	PROPN
cana-6127	39	13	,	,	PUNCT
cana-6127	39	14	thick	thick	ADJ
cana-6127	39	15	rectangular	rectangular	ADJ
cana-6127	39	16	plate	plate	NOUN
cana-6127	39	17	,	,	PUNCT
cana-6127	39	18	mittag	mittag	ADJ
cana-6127	39	19	-	-	PUNCT
cana-6127	39	20	leffler	leffler	NOUN
cana-6127	39	21	functions	function	NOUN
cana-6127	39	22	.	.	PUNCT
cana-6127	40	1	1	1	X
cana-6127	40	2	.	.	X
cana-6127	40	3	introduction	introduction	NOUN
cana-6127	40	4	biot	biot	NOUN
cana-6127	40	5	[	[	X
cana-6127	40	6	1	1	NUM
cana-6127	40	7	]	]	PUNCT
cana-6127	40	8	formulated	formulate	VERB
cana-6127	40	9	the	the	DET
cana-6127	40	10	theory	theory	NOUN
cana-6127	40	11	of	of	ADP
cana-6127	40	12	coupled	couple	VERB
cana-6127	40	13	thermoelasticity	thermoelasticity	NOUN
cana-6127	40	14	to	to	PART
cana-6127	40	15	eliminate	eliminate	VERB
cana-6127	40	16	the	the	DET
cana-6127	40	17	paradox	paradox	ADJ
cana-6127	40	18	inherent	inherent	ADJ
cana-6127	40	19	in	in	ADP
cana-6127	40	20	the	the	DET
cana-6127	40	21	classical	classical	ADJ
cana-6127	40	22	uncoupled	uncoupled	ADJ
cana-6127	40	23	theory	theory	NOUN
cana-6127	40	24	that	that	SCONJ
cana-6127	40	25	elastic	elastic	ADJ
cana-6127	40	26	changes	change	NOUN
cana-6127	40	27	have	have	AUX
cana-6127	40	28	no	no	DET
cana-6127	40	29	effect	effect	NOUN
cana-6127	40	30	on	on	ADP
cana-6127	40	31	the	the	DET
cana-6127	40	32	temperature	temperature	NOUN
cana-6127	40	33	.	.	PUNCT
cana-6127	41	1	the	the	DET
cana-6127	41	2	heat	heat	NOUN
cana-6127	41	3	equations	equation	NOUN
cana-6127	41	4	for	for	ADP
cana-6127	41	5	both	both	DET
cana-6127	41	6	theories	theory	NOUN
cana-6127	41	7	are	be	AUX
cana-6127	41	8	of	of	ADP
cana-6127	41	9	the	the	DET
cana-6127	41	10	diffusion	diffusion	NOUN
cana-6127	41	11	type	type	NOUN
cana-6127	41	12	predicting	predict	VERB
cana-6127	41	13	infinite	infinite	ADJ
cana-6127	41	14	speeds	speed	NOUN
cana-6127	41	15	of	of	ADP
cana-6127	41	16	propagation	propagation	NOUN
cana-6127	41	17	for	for	ADP
cana-6127	41	18	heat	heat	NOUN
cana-6127	41	19	waves	wave	NOUN
cana-6127	41	20	contrary	contrary	ADJ
cana-6127	41	21	to	to	ADP
cana-6127	41	22	physical	physical	ADJ
cana-6127	41	23	observations	observation	NOUN
cana-6127	41	24	.	.	PUNCT
cana-6127	42	1	the	the	DET
cana-6127	42	2	generalised	generalise	VERB
cana-6127	42	3	thermoelastic	thermoelastic	ADJ
cana-6127	42	4	problem	problem	NOUN
cana-6127	42	5	of	of	ADP
cana-6127	42	6	a	a	DET
cana-6127	42	7	thick	thick	ADJ
cana-6127	42	8	plate	plate	NOUN
cana-6127	42	9	under	under	ADP
cana-6127	42	10	axisymmetric	axisymmetric	ADJ
cana-6127	42	11	heat	heat	NOUN
cana-6127	42	12	supply	supply	NOUN
cana-6127	42	13	was	be	AUX
cana-6127	42	14	resolved	resolve	VERB
cana-6127	42	15	by	by	ADP
cana-6127	42	16	sherief	sherief	NOUN
cana-6127	42	17	and	and	CCONJ
cana-6127	42	18	hamza	hamza	NOUN
cana-6127	43	1	[	[	X
cana-6127	43	2	2	2	NUM
cana-6127	43	3	]	]	PUNCT
cana-6127	43	4	.	.	PUNCT
cana-6127	44	1	the	the	DET
cana-6127	44	2	generalised	generalise	VERB
cana-6127	44	3	dynamical	dynamical	ADJ
cana-6127	44	4	theory	theory	NOUN
cana-6127	44	5	of	of	ADP
cana-6127	44	6	thermoelasticity	thermoelasticity	NOUN
cana-6127	44	7	with	with	ADP
cana-6127	44	8	one	one	NUM
cana-6127	44	9	relaxation	relaxation	NOUN
cana-6127	44	10	period	period	NOUN
cana-6127	44	11	,	,	PUNCT
cana-6127	44	12	for	for	ADP
cana-6127	44	13	the	the	DET
cana-6127	44	14	isotropic	isotropic	ADJ
cana-6127	44	15	body	body	NOUN
cana-6127	44	16	,	,	PUNCT
cana-6127	44	17	was	be	AUX
cana-6127	44	18	developed	develop	VERB
cana-6127	44	19	by	by	ADP
cana-6127	44	20	lord	lord	PROPN
cana-6127	44	21	and	and	CCONJ
cana-6127	44	22	shulman	shulman	PROPN
cana-6127	45	1	[	[	X
cana-6127	45	2	3	3	NUM
cana-6127	45	3	]	]	PUNCT
cana-6127	45	4	.	.	PUNCT
cana-6127	46	1	in	in	ADP
cana-6127	46	2	their	their	PRON
cana-6127	46	3	study	study	NOUN
cana-6127	46	4	of	of	ADP
cana-6127	46	5	the	the	DET
cana-6127	46	6	theoretical	theoretical	ADJ
cana-6127	46	7	analysis	analysis	NOUN
cana-6127	46	8	of	of	ADP
cana-6127	46	9	a	a	DET
cana-6127	46	10	rectangular	rectangular	ADJ
cana-6127	46	11	plate	plate	NOUN
cana-6127	46	12	in	in	ADP
cana-6127	46	13	a	a	DET
cana-6127	46	14	compressive	compressive	ADJ
cana-6127	46	15	stress	stress	NOUN
cana-6127	46	16	field	field	NOUN
cana-6127	46	17	and	and	CCONJ
cana-6127	46	18	associated	associate	VERB
cana-6127	46	19	thermal	thermal	ADJ
cana-6127	46	20	stresses	stress	NOUN
cana-6127	46	21	was	be	AUX
cana-6127	46	22	resolved	resolve	VERB
cana-6127	46	23	by	by	ADP
cana-6127	46	24	tanigawa	tanigawa	PROPN
cana-6127	46	25	and	and	CCONJ
cana-6127	46	26	komatsubara	komatsubara	NOUN
cana-6127	46	27	[	[	X
cana-6127	46	28	4	4	NUM
cana-6127	46	29	]	]	PUNCT
cana-6127	46	30	.	.	PUNCT
cana-6127	47	1	the	the	DET
cana-6127	47	2	solution	solution	NOUN
cana-6127	47	3	to	to	ADP
cana-6127	47	4	the	the	DET
cana-6127	47	5	plane	plane	NOUN
cana-6127	47	6	thermoelasticity	thermoelasticity	NOUN
cana-6127	47	7	problem	problem	NOUN
cana-6127	47	8	for	for	ADP
cana-6127	47	9	a	a	DET
cana-6127	47	10	rectangular	rectangular	ADJ
cana-6127	47	11	domain	domain	NOUN
cana-6127	47	12	is	be	AUX
cana-6127	47	13	discussed	discuss	VERB
cana-6127	47	14	in	in	ADP
cana-6127	47	15	vihak	vihak	PROPN
cana-6127	47	16	et	et	PROPN
cana-6127	47	17	al	al	PROPN
cana-6127	47	18	.	.	PROPN
cana-6127	47	19	,	,	PUNCT
cana-6127	48	1	[	[	X
cana-6127	48	2	5	5	NUM
cana-6127	48	3	]	]	PUNCT
cana-6127	48	4	.	.	PUNCT
cana-6127	49	1	a	a	DET
cana-6127	49	2	laminated	laminate	VERB
cana-6127	49	3	rectangular	rectangular	ADJ
cana-6127	49	4	plate	plate	NOUN
cana-6127	49	5	subjected	subject	VERB
cana-6127	49	6	to	to	ADP
cana-6127	49	7	a	a	DET
cana-6127	49	8	thermal	thermal	ADJ
cana-6127	49	9	shock	shock	NOUN
cana-6127	49	10	was	be	AUX
cana-6127	49	11	the	the	DET
cana-6127	49	12	focus	focus	NOUN
cana-6127	49	13	of	of	ADP
cana-6127	49	14	an	an	DET
cana-6127	49	15	investigation	investigation	NOUN
cana-6127	49	16	by	by	ADP
cana-6127	49	17	adam	adam	PROPN
cana-6127	49	18	and	and	CCONJ
cana-6127	49	19	best	good	ADJ
cana-6127	50	1	[	[	X
cana-6127	50	2	6	6	NUM
cana-6127	50	3	]	]	PUNCT
cana-6127	50	4	.	.	PUNCT
cana-6127	51	1	tanigawa	tanigawa	PROPN
cana-6127	51	2	et	et	PROPN
cana-6127	51	3	al	al	PROPN
cana-6127	51	4	.	.	PUNCT
cana-6127	52	1	[	[	X
cana-6127	52	2	7	7	NUM
cana-6127	52	3	8	8	NUM
cana-6127	52	4	]	]	PUNCT
cana-6127	52	5	.	.	PUNCT
cana-6127	53	1	investigate	investigate	VERB
cana-6127	53	2	the	the	DET
cana-6127	53	3	thermal	thermal	ADJ
cana-6127	53	4	analysis	analysis	NOUN
cana-6127	53	5	of	of	ADP
cana-6127	53	6	thermal	thermal	ADJ
cana-6127	53	7	buckling	buckling	NOUN
cana-6127	53	8	caused	cause	VERB
cana-6127	53	9	by	by	ADP
cana-6127	53	10	uniform	uniform	ADJ
cana-6127	53	11	heat	heat	NOUN
cana-6127	53	12	supply	supply	NOUN
cana-6127	53	13	in	in	ADP
cana-6127	53	14	an	an	DET
cana-6127	53	15	orthotropic	orthotropic	ADJ
cana-6127	53	16	nonhomogeneous	nonhomogeneous	ADJ
cana-6127	53	17	rectangular	rectangular	ADJ
cana-6127	53	18	plate	plate	NOUN
cana-6127	53	19	.	.	PUNCT
cana-6127	54	1	the	the	DET
cana-6127	54	2	transient	transient	ADJ
cana-6127	54	3	thermoelastic	thermoelastic	ADJ
cana-6127	54	4	deformations	deformation	NOUN
cana-6127	54	5	of	of	ADP
cana-6127	54	6	a	a	DET
cana-6127	54	7	thick	thick	ADJ
cana-6127	54	8	functionally	functionally	ADV
cana-6127	54	9	graded	grade	VERB
cana-6127	54	10	plate	plate	NOUN
cana-6127	54	11	were	be	AUX
cana-6127	54	12	investigated	investigate	VERB
cana-6127	54	13	by	by	ADP
cana-6127	54	14	qian	qian	PROPN
cana-6127	54	15	and	and	CCONJ
cana-6127	54	16	batra	batra	PROPN
cana-6127	54	17	[	[	X
cana-6127	54	18	9	9	NUM
cana-6127	54	19	]	]	PUNCT
cana-6127	54	20	.	.	PUNCT
cana-6127	55	1	the	the	DET
cana-6127	55	2	thermal	thermal	ADJ
cana-6127	55	3	behaviour	behaviour	NOUN
cana-6127	55	4	of	of	ADP
cana-6127	55	5	thermoelastic	thermoelastic	ADJ
cana-6127	55	6	thick	thick	ADJ
cana-6127	55	7	plates	plate	NOUN
cana-6127	55	8	under	under	ADP
cana-6127	55	9	lateral	lateral	ADJ
cana-6127	55	10	loads	load	NOUN
cana-6127	55	11	was	be	AUX
cana-6127	55	12	presented	present	VERB
cana-6127	55	13	by	by	ADP
cana-6127	55	14	sharma	sharma	PROPN
cana-6127	55	15	et	et	PROPN
cana-6127	55	16	.	.	PUNCT
cana-6127	56	1	al	al	PROPN
cana-6127	56	2	.	.	PUNCT
cana-6127	57	1	[	[	X
cana-6127	57	2	10	10	NUM
cana-6127	57	3	]	]	PUNCT
cana-6127	57	4	.	.	PUNCT
cana-6127	58	1	based	base	VERB
cana-6127	58	2	on	on	ADP
cana-6127	58	3	the	the	DET
cana-6127	58	4	equation	equation	NOUN
cana-6127	58	5	of	of	ADP
cana-6127	58	6	heat	heat	NOUN
cana-6127	58	7	conduction	conduction	NOUN
cana-6127	58	8	in	in	ADP
cana-6127	58	9	1d	1d	NUM
cana-6127	58	10	and	and	CCONJ
cana-6127	58	11	2d	2d	NOUN
cana-6127	58	12	with	with	ADP
cana-6127	58	13	a	a	DET
cana-6127	58	14	time	time	NOUN
cana-6127	58	15	-	-	PUNCT
cana-6127	58	16	fractional	fractional	ADJ
cana-6127	58	17	derivative	derivative	ADJ
cana-6127	58	18	and	and	CCONJ
cana-6127	58	19	related	related	ADJ
cana-6127	58	20	thermal	thermal	ADJ
cana-6127	58	21	stresses	stress	NOUN
cana-6127	58	22	,	,	PUNCT
cana-6127	58	23	povstenko	povstenko	NOUN
cana-6127	58	24	[	[	X
cana-6127	58	25	11	11	NUM
cana-6127	58	26	]	]	PUNCT
cana-6127	58	27	resolved	resolve	VERB
cana-6127	58	28	a	a	DET
cana-6127	58	29	few	few	ADJ
cana-6127	58	30	thermoelastic	thermoelastic	ADJ
cana-6127	58	31	issues	issue	NOUN
cana-6127	58	32	.	.	PUNCT
cana-6127	59	1	some	some	DET
cana-6127	59	2	contribution	contribution	NOUN
cana-6127	59	3	of	of	ADP
cana-6127	59	4	thermoelastic	thermoelastic	ADJ
cana-6127	59	5	problems	problem	NOUN
cana-6127	59	6	and	and	CCONJ
cana-6127	59	7	fractional	fractional	ADJ
cana-6127	59	8	order	order	NOUN
cana-6127	59	9	thermoelastic	thermoelastic	ADJ
cana-6127	59	10	problems	problem	NOUN
cana-6127	59	11	have	have	AUX
cana-6127	59	12	been	be	AUX
cana-6127	59	13	discussed	discuss	VERB
cana-6127	59	14	in	in	ADP
cana-6127	59	15	[	[	PUNCT
cana-6127	59	16	12	12	NUM
cana-6127	59	17	-	-	SYM
cana-6127	59	18	34	34	NUM
cana-6127	59	19	]	]	PUNCT
cana-6127	59	20	.	.	PUNCT
cana-6127	60	1	2	2	X
cana-6127	60	2	.	.	X
cana-6127	60	3	preliminaries	preliminary	NOUN
cana-6127	60	4	in	in	ADP
cana-6127	60	5	this	this	DET
cana-6127	60	6	section	section	NOUN
cana-6127	60	7	we	we	PRON
cana-6127	60	8	give	give	VERB
cana-6127	60	9	some	some	DET
cana-6127	60	10	definitions	definition	NOUN
cana-6127	60	11	,	,	PUNCT
cana-6127	60	12	notations	notation	NOUN
cana-6127	60	13	and	and	CCONJ
cana-6127	60	14	facts	fact	NOUN
cana-6127	60	15	that	that	SCONJ
cana-6127	60	16	we	we	PRON
cana-6127	60	17	need	need	VERB
cana-6127	60	18	in	in	ADP
cana-6127	60	19	this	this	DET
cana-6127	60	20	article	article	NOUN
cana-6127	60	21	.	.	PUNCT
cana-6127	61	1	•	•	NUM
cana-6127	61	2	the	the	DET
cana-6127	61	3	riemann	riemann	PROPN
cana-6127	61	4	-	-	PUNCT
cana-6127	61	5	liouville	liouville	VERB
cana-6127	61	6	fractional	fractional	ADJ
cana-6127	61	7	differential	differential	NOUN
cana-6127	61	8	operator	operator	NOUN
cana-6127	61	9	the	the	DET
cana-6127	61	10	definition	definition	NOUN
cana-6127	61	11	of	of	ADP
cana-6127	61	12	the	the	DET
cana-6127	61	13	riemann	riemann	PROPN
cana-6127	61	14	-	-	PUNCT
cana-6127	61	15	liouville	liouville	VERB
cana-6127	61	16	fractional	fractional	ADJ
cana-6127	61	17	differential	differential	NOUN
cana-6127	61	18	operator	operator	NOUN
cana-6127	61	19	given	give	VERB
cana-6127	61	20	by	by	ADP
cana-6127	61	21	[	[	PUNCT
cana-6127	61	22	37	37	NUM
cana-6127	61	23	]	]	PUNCT
cana-6127	61	24	communications	communication	NOUN
cana-6127	61	25	on	on	ADP
cana-6127	61	26	applied	apply	VERB
cana-6127	61	27	nonlinear	nonlinear	ADJ
cana-6127	61	28	analysis	analysis	NOUN
cana-6127	61	29	issn	issn	NOUN
cana-6127	61	30	:	:	PUNCT
cana-6127	61	31	1074	1074	NUM
cana-6127	61	32	-	-	PUNCT
cana-6127	61	33	133x	133x	NUM
cana-6127	61	34	vol	vol	VERB
cana-6127	61	35	32	32	NUM
cana-6127	61	36	no	no	NOUN
cana-6127	61	37	.	.	PUNCT
cana-6127	62	1	10s	10	NOUN
cana-6127	62	2	(	(	PUNCT
cana-6127	62	3	2025	2025	NUM
cana-6127	62	4	)	)	PUNCT
cana-6127	62	5	3462	3462	NUM
cana-6127	63	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	63	2	suppose	suppose	VERB
cana-6127	63	3	that	that	SCONJ
cana-6127	63	4	𝛼	𝛼	PROPN
cana-6127	63	5	>	>	X
cana-6127	63	6	0	0	PROPN
cana-6127	63	7	,	,	PUNCT
cana-6127	63	8	t	t	X
cana-6127	63	9	>	>	X
cana-6127	63	10	a	a	PROPN
cana-6127	63	11	,	,	PUNCT
cana-6127	63	12	𝛼	𝛼	PROPN
cana-6127	63	13	,	,	PUNCT
cana-6127	63	14	a	a	PRON
cana-6127	63	15	,	,	PUNCT
cana-6127	63	16	t	t	PROPN
cana-6127	63	17	∈	∈	PROPN
cana-6127	63	18	r.	r.	PROPN
cana-6127	63	19	then	then	ADV
cana-6127	63	20	𝐷𝛼𝑓(𝑡	𝐷𝛼𝑓(𝑡	NUM
cana-6127	63	21	)	)	PUNCT
cana-6127	64	1	=	=	PRON
cana-6127	64	2	{	{	PUNCT
cana-6127	64	3	1	1	NUM
cana-6127	64	4	𝛤(𝑛	𝛤(𝑛	NUM
cana-6127	64	5	−	−	PROPN
cana-6127	64	6	𝛼	𝛼	X
cana-6127	64	7	)	)	PUNCT
cana-6127	64	8	𝑑𝑛	𝑑𝑛	VERB
cana-6127	64	9	𝑑𝑡𝑛	𝑑𝑡𝑛	NOUN
cana-6127	64	10	∫	∫	PROPN
cana-6127	64	11	𝑓(𝜏	𝑓(𝜏	PROPN
cana-6127	64	12	)	)	PUNCT
cana-6127	64	13	(	(	PUNCT
cana-6127	64	14	𝑡	𝑡	NOUN
cana-6127	64	15	−	−	NOUN
cana-6127	64	16	𝜏)𝛼+1−𝑛	𝜏)𝛼+1−𝑛	NOUN
cana-6127	64	17	𝑑𝜏	𝑑𝜏	NOUN
cana-6127	64	18	𝑡	𝑡	PROPN
cana-6127	64	19	0	0	NUM
cana-6127	64	20	,	,	PUNCT
cana-6127	64	21	𝑛	𝑛	PRON
cana-6127	64	22	−	−	PROPN
cana-6127	64	23	1	1	NUM
cana-6127	64	24	<	<	X
cana-6127	64	25	𝛼	𝛼	X
cana-6127	64	26	<	<	X
cana-6127	64	27	𝑛	𝑛	PRON
cana-6127	64	28	∈	∈	NOUN
cana-6127	64	29	𝑁	𝑁	ADJ
cana-6127	64	30	𝑑𝑛𝑓(𝑡	𝑑𝑛𝑓(𝑡	PROPN
cana-6127	64	31	)	)	PUNCT
cana-6127	64	32	𝑑𝑡𝑛	𝑑𝑡𝑛	NOUN
cana-6127	64	33	,	,	PUNCT
cana-6127	64	34	𝛼	𝛼	NOUN
cana-6127	64	35	=	=	NOUN
cana-6127	64	36	𝑛	𝑛	PRON
cana-6127	64	37	∈	∈	NOUN
cana-6127	64	38	𝑁	𝑁	PROPN
cana-6127	64	39	(	(	PUNCT
cana-6127	64	40	2.1	2.1	NUM
cana-6127	64	41	)	)	PUNCT
cana-6127	64	42	is	be	AUX
cana-6127	64	43	called	call	VERB
cana-6127	64	44	the	the	DET
cana-6127	64	45	riemann	riemann	PROPN
cana-6127	64	46	-	-	PUNCT
cana-6127	64	47	liouville	liouville	VERB
cana-6127	64	48	fractional	fractional	ADJ
cana-6127	64	49	derivative	derivative	NOUN
cana-6127	64	50	or	or	CCONJ
cana-6127	64	51	the	the	DET
cana-6127	64	52	riemann	riemann	PROPN
cana-6127	64	53	-	-	PUNCT
cana-6127	64	54	liouville	liouville	VERB
cana-6127	64	55	fractional	fractional	ADJ
cana-6127	64	56	differential	differential	NOUN
cana-6127	64	57	operator	operator	NOUN
cana-6127	64	58	of	of	ADP
cana-6127	64	59	order	order	NOUN
cana-6127	64	60	𝛼.	𝛼.	NOUN
cana-6127	64	61	•	•	ADP
cana-6127	64	62	the	the	DET
cana-6127	64	63	caputo	caputo	PROPN
cana-6127	64	64	fractional	fractional	PROPN
cana-6127	64	65	differential	differential	NOUN
cana-6127	64	66	operator	operator	NOUN
cana-6127	64	67	the	the	DET
cana-6127	64	68	definition	definition	NOUN
cana-6127	64	69	of	of	ADP
cana-6127	64	70	the	the	DET
cana-6127	64	71	caputo	caputo	PROPN
cana-6127	64	72	fractional	fractional	PROPN
cana-6127	64	73	differential	differential	NOUN
cana-6127	64	74	operator	operator	NOUN
cana-6127	64	75	given	give	VERB
cana-6127	64	76	by	by	ADP
cana-6127	64	77	[	[	PUNCT
cana-6127	64	78	37	37	NUM
cana-6127	64	79	]	]	PUNCT
cana-6127	64	80	suppose	suppose	VERB
cana-6127	64	81	that	that	SCONJ
cana-6127	64	82	𝛼	𝛼	PROPN
cana-6127	64	83	>	>	X
cana-6127	64	84	0	0	PROPN
cana-6127	64	85	,	,	PUNCT
cana-6127	64	86	t	t	X
cana-6127	64	87	>	>	X
cana-6127	64	88	a	a	PROPN
cana-6127	64	89	,	,	PUNCT
cana-6127	64	90	𝛼	𝛼	PROPN
cana-6127	64	91	,	,	PUNCT
cana-6127	64	92	a	a	PRON
cana-6127	64	93	,	,	PUNCT
cana-6127	64	94	t	t	PROPN
cana-6127	64	95	∈	∈	PROPN
cana-6127	64	96	r.	r.	PROPN
cana-6127	64	97	then	then	ADV
cana-6127	64	98	𝐷𝛼𝑓(𝑡	𝐷𝛼𝑓(𝑡	NUM
cana-6127	64	99	)	)	PUNCT
cana-6127	64	100	=	=	PRON
cana-6127	64	101	{	{	PUNCT
cana-6127	64	102	1	1	NUM
cana-6127	64	103	𝛤(𝑛	𝛤(𝑛	NUM
cana-6127	64	104	−	−	PROPN
cana-6127	64	105	𝛼	𝛼	X
cana-6127	64	106	)	)	PUNCT
cana-6127	64	107	𝑑𝑛	𝑑𝑛	VERB
cana-6127	64	108	𝑑𝑡𝑛	𝑑𝑡𝑛	NOUN
cana-6127	64	109	∫	∫	PROPN
cana-6127	64	110	𝑓(𝑛)(𝜏	𝑓(𝑛)(𝜏	NUM
cana-6127	64	111	)	)	PUNCT
cana-6127	64	112	(	(	PUNCT
cana-6127	64	113	𝑡	𝑡	NOUN
cana-6127	64	114	−	−	NOUN
cana-6127	64	115	𝜏)𝛼+1−𝑛	𝜏)𝛼+1−𝑛	NOUN
cana-6127	64	116	𝑑𝜏	𝑑𝜏	NOUN
cana-6127	64	117	𝑡	𝑡	PROPN
cana-6127	64	118	0	0	NUM
cana-6127	64	119	,	,	PUNCT
cana-6127	64	120	𝑛	𝑛	PRON
cana-6127	64	121	−	−	PROPN
cana-6127	64	122	1	1	NUM
cana-6127	64	123	<	<	X
cana-6127	64	124	𝛼	𝛼	X
cana-6127	64	125	<	<	X
cana-6127	64	126	𝑛	𝑛	PRON
cana-6127	64	127	∈	∈	NOUN
cana-6127	64	128	𝑁	𝑁	ADJ
cana-6127	64	129	𝑑𝑛𝑓(𝑡	𝑑𝑛𝑓(𝑡	PROPN
cana-6127	64	130	)	)	PUNCT
cana-6127	64	131	𝑑𝑡𝑛	𝑑𝑡𝑛	NOUN
cana-6127	64	132	,	,	PUNCT
cana-6127	64	133	𝛼	𝛼	NOUN
cana-6127	64	134	=	=	NOUN
cana-6127	64	135	𝑛	𝑛	PRON
cana-6127	64	136	∈	∈	NOUN
cana-6127	64	137	𝑁	𝑁	PROPN
cana-6127	64	138	(	(	PUNCT
cana-6127	64	139	2.2	2.2	NUM
cana-6127	64	140	)	)	PUNCT
cana-6127	64	141	is	be	AUX
cana-6127	64	142	called	call	VERB
cana-6127	64	143	the	the	DET
cana-6127	64	144	caputo	caputo	PROPN
cana-6127	64	145	fractional	fractional	PROPN
cana-6127	64	146	derivative	derivative	NOUN
cana-6127	64	147	or	or	CCONJ
cana-6127	64	148	the	the	DET
cana-6127	64	149	caputo	caputo	PROPN
cana-6127	64	150	fractional	fractional	PROPN
cana-6127	64	151	differential	differential	NOUN
cana-6127	64	152	operator	operator	NOUN
cana-6127	64	153	of	of	ADP
cana-6127	64	154	order	order	NOUN
cana-6127	64	155	𝛼.	𝛼.	NOUN
cana-6127	64	156	•	•	ADP
cana-6127	65	1	the	the	DET
cana-6127	65	2	mittag	mittag	ADJ
cana-6127	65	3	-	-	PUNCT
cana-6127	65	4	leffler	leffler	NOUN
cana-6127	65	5	function	function	NOUN
cana-6127	65	6	the	the	DET
cana-6127	65	7	mittag	mittag	ADJ
cana-6127	65	8	-	-	PUNCT
cana-6127	65	9	leffler	leffler	NOUN
cana-6127	65	10	function	function	NOUN
cana-6127	65	11	is	be	AUX
cana-6127	65	12	a	a	DET
cana-6127	65	13	generalization	generalization	NOUN
cana-6127	65	14	of	of	ADP
cana-6127	65	15	the	the	DET
cana-6127	65	16	exponential	exponential	ADJ
cana-6127	65	17	function	function	NOUN
cana-6127	65	18	,	,	PUNCT
cana-6127	65	19	first	first	ADV
cana-6127	65	20	introduced	introduce	VERB
cana-6127	65	21	as	as	ADP
cana-6127	65	22	a	a	DET
cana-6127	65	23	oneparameter	oneparameter	NOUN
cana-6127	65	24	function	function	NOUN
cana-6127	65	25	by	by	ADP
cana-6127	65	26	the	the	DET
cana-6127	65	27	series	series	NOUN
cana-6127	65	28	𝐸𝛼(𝑧	𝐸𝛼(𝑧	ADJ
cana-6127	65	29	)	)	PUNCT
cana-6127	65	30	=	=	PUNCT
cana-6127	66	1	∑	∑	PUNCT
cana-6127	66	2	𝑧𝑘	𝑧𝑘	ADV
cana-6127	66	3	𝛤(𝛼𝑘	𝛤(𝛼𝑘	NOUN
cana-6127	66	4	+	+	NOUN
cana-6127	66	5	1	1	NUM
cana-6127	66	6	)	)	PUNCT
cana-6127	66	7	∞	∞	NUM
cana-6127	66	8	𝑘=0	𝑘=0	PROPN
cana-6127	66	9	,	,	PUNCT
cana-6127	66	10	 	 	SPACE
cana-6127	66	11	𝛼	𝛼	X
cana-6127	66	12	>	>	X
cana-6127	66	13	0	0	NUM
cana-6127	66	14	,	,	PUNCT
cana-6127	66	15	 	 	SPACE
cana-6127	66	16	𝛼	𝛼	VERB
cana-6127	66	17	 	 	SPACE
cana-6127	66	18	𝜖	𝜖	PROPN
cana-6127	66	19	 	 	SPACE
cana-6127	66	20	𝑅	𝑅	PROPN
cana-6127	66	21	,	,	PUNCT
cana-6127	66	22	𝑧	𝑧	NOUN
cana-6127	66	23	  	  	SPACE
cana-6127	66	24	∈	∈	PROPN
cana-6127	66	25	 	 	SPACE
cana-6127	66	26	𝐶	𝐶	PROPN
cana-6127	66	27	(	(	PUNCT
cana-6127	66	28	2.3	2.3	NUM
cana-6127	66	29	)	)	PUNCT
cana-6127	66	30	later	later	ADV
cana-6127	66	31	,	,	PUNCT
cana-6127	66	32	the	the	DET
cana-6127	66	33	two	two	NUM
cana-6127	66	34	-	-	PUNCT
cana-6127	66	35	parameter	parameter	NOUN
cana-6127	66	36	generalization	generalization	NOUN
cana-6127	66	37	mittag	mittag	ADJ
cana-6127	66	38	-	-	PUNCT
cana-6127	66	39	leffler	leffler	NOUN
cana-6127	66	40	function	function	NOUN
cana-6127	66	41	as	as	ADP
cana-6127	66	42	:	:	PUNCT
cana-6127	66	43	𝐸𝛼,𝛽(𝑧	𝐸𝛼,𝛽(𝑧	X
cana-6127	66	44	)	)	PUNCT
cana-6127	67	1	=	=	NOUN
cana-6127	67	2	∑	∑	PUNCT
cana-6127	67	3	𝑧𝑘	𝑧𝑘	PRON
cana-6127	67	4	𝛤(𝛼𝑘	𝛤(𝛼𝑘	NOUN
cana-6127	67	5	+	+	CCONJ
cana-6127	67	6	𝛽	𝛽	NOUN
cana-6127	67	7	)	)	PUNCT
cana-6127	67	8	∞	∞	PROPN
cana-6127	67	9	𝑘=0	𝑘=0	PROPN
cana-6127	67	10	,	,	PUNCT
cana-6127	67	11	 	 	SPACE
cana-6127	67	12	𝛼	𝛼	PROPN
cana-6127	67	13	,	,	PUNCT
cana-6127	67	14	𝛽	𝛽	NOUN
cana-6127	67	15	>	>	X
cana-6127	67	16	0	0	NUM
cana-6127	67	17	,	,	PUNCT
cana-6127	67	18	 	 	SPACE
cana-6127	67	19	𝛼	𝛼	VERB
cana-6127	67	20	,	,	PUNCT
cana-6127	67	21	𝛽	𝛽	NOUN
cana-6127	67	22	  	  	SPACE
cana-6127	67	23	∈	∈	PROPN
cana-6127	67	24	 	 	SPACE
cana-6127	67	25	𝑅	𝑅	PROPN
cana-6127	67	26	,	,	PUNCT
cana-6127	67	27	𝑧	𝑧	NOUN
cana-6127	67	28	  	  	SPACE
cana-6127	67	29	∈	∈	PROPN
cana-6127	67	30	 	 	SPACE
cana-6127	67	31	𝐶	𝐶	PROPN
cana-6127	67	32	(	(	PUNCT
cana-6127	67	33	2.4	2.4	NUM
cana-6127	67	34	)	)	PUNCT
cana-6127	67	35	3	3	NUM
cana-6127	67	36	.	.	X
cana-6127	67	37	problem	problem	NOUN
cana-6127	67	38	formulation	formulation	NOUN
cana-6127	67	39	consider	consider	VERB
cana-6127	67	40	a	a	DET
cana-6127	67	41	thick	thick	ADJ
cana-6127	67	42	rectangular	rectangular	ADJ
cana-6127	67	43	plate	plate	NOUN
cana-6127	67	44	with	with	ADP
cana-6127	67	45	length	length	NOUN
cana-6127	67	46	𝑎	𝑎	NOUN
cana-6127	67	47	,	,	PUNCT
cana-6127	67	48	width	width	ADJ
cana-6127	67	49	𝑏	𝑏	NOUN
cana-6127	67	50	and	and	CCONJ
cana-6127	67	51	thickness	thickness	NOUN
cana-6127	67	52	𝑐	𝑐	PROPN
cana-6127	67	53	occupying	occupy	VERB
cana-6127	67	54	the	the	DET
cana-6127	67	55	space	space	NOUN
cana-6127	67	56	𝐷	𝐷	NOUN
cana-6127	67	57	=	=	PUNCT
cana-6127	67	58	{	{	PUNCT
cana-6127	67	59	(	(	PUNCT
cana-6127	67	60	𝑥	𝑥	NOUN
cana-6127	67	61	,	,	PUNCT
cana-6127	67	62	𝑦	𝑦	NOUN
cana-6127	67	63	,	,	PUNCT
cana-6127	67	64	𝑧	𝑧	NOUN
cana-6127	67	65	)	)	PUNCT
cana-6127	67	66	∈	∈	PROPN
cana-6127	67	67	𝑅3	𝑅3	NOUN
cana-6127	67	68	:	:	PUNCT
cana-6127	67	69	0	0	NUM
cana-6127	67	70	≤	≤	NUM
cana-6127	67	71	𝑥	𝑥	DET
cana-6127	67	72	≤	≤	NUM
cana-6127	67	73	𝑎	𝑎	ADJ
cana-6127	67	74	,	,	PUNCT
cana-6127	67	75	0	0	NUM
cana-6127	67	76	≤	≤	NUM
cana-6127	67	77	𝑦	𝑦	NOUN
cana-6127	67	78	≤	≤	NOUN
cana-6127	67	79	𝑏	𝑏	NOUN
cana-6127	67	80	,	,	PUNCT
cana-6127	67	81	0	0	NUM
cana-6127	67	82	≤	≤	NOUN
cana-6127	67	83	𝑧	𝑧	PRON
cana-6127	67	84	≤	≤	NUM
cana-6127	67	85	𝑐	𝑐	NOUN
cana-6127	67	86	}	}	PUNCT
cana-6127	67	87	.	.	PUNCT
cana-6127	68	1	initially	initially	ADV
cana-6127	68	2	the	the	DET
cana-6127	68	3	rectangular	rectangular	ADJ
cana-6127	68	4	plate	plate	NOUN
cana-6127	68	5	is	be	AUX
cana-6127	68	6	at	at	ADP
cana-6127	68	7	arbitrary	arbitrary	ADJ
cana-6127	68	8	temperature	temperature	NOUN
cana-6127	68	9	𝑓(𝑥	𝑓(𝑥	NOUN
cana-6127	68	10	,	,	PUNCT
cana-6127	68	11	𝑦	𝑦	NOUN
cana-6127	68	12	,	,	PUNCT
cana-6127	68	13	𝑧	𝑧	NOUN
cana-6127	68	14	)	)	PUNCT
cana-6127	68	15	.	.	PUNCT
cana-6127	69	1	for	for	ADP
cana-6127	69	2	time	time	NOUN
cana-6127	69	3	𝑡	𝑡	X
cana-6127	69	4	>	>	X
cana-6127	69	5	0	0	NUM
cana-6127	69	6	,	,	PUNCT
cana-6127	69	7	heat	heat	NOUN
cana-6127	69	8	is	be	AUX
cana-6127	69	9	generated	generate	VERB
cana-6127	69	10	within	within	ADP
cana-6127	69	11	the	the	DET
cana-6127	69	12	plate	plate	NOUN
cana-6127	69	13	at	at	ADP
cana-6127	69	14	a	a	DET
cana-6127	69	15	rate	rate	NOUN
cana-6127	69	16	of	of	ADP
cana-6127	69	17	𝑔(𝑥	𝑔(𝑥	PROPN
cana-6127	69	18	,	,	PUNCT
cana-6127	69	19	𝑦	𝑦	NOUN
cana-6127	69	20	,	,	PUNCT
cana-6127	69	21	𝑧	𝑧	NOUN
cana-6127	69	22	,	,	PUNCT
cana-6127	69	23	𝑡	𝑡	NOUN
cana-6127	69	24	)	)	PUNCT
cana-6127	69	25	btu	btu	PROPN
cana-6127	69	26	/	/	SYM
cana-6127	69	27	hr	hr	PROPN
cana-6127	69	28	ft3	ft3	NOUN
cana-6127	69	29	,	,	PUNCT
cana-6127	69	30	while	while	SCONJ
cana-6127	69	31	the	the	DET
cana-6127	69	32	remaining	remain	VERB
cana-6127	69	33	boundaries	boundary	NOUN
cana-6127	69	34	are	be	AUX
cana-6127	69	35	kept	keep	VERB
cana-6127	69	36	at	at	ADP
cana-6127	69	37	zero	zero	NUM
cana-6127	69	38	temperature	temperature	NOUN
cana-6127	69	39	.	.	PUNCT
cana-6127	70	1	an	an	DET
cana-6127	70	2	equation	equation	NOUN
cana-6127	70	3	of	of	ADP
cana-6127	70	4	the	the	DET
cana-6127	70	5	caputo	caputo	PROPN
cana-6127	70	6	type	type	NOUN
cana-6127	70	7	time	time	NOUN
cana-6127	70	8	fractional	fractional	ADJ
cana-6127	70	9	differential	differential	ADJ
cana-6127	70	10	equation	equation	NOUN
cana-6127	70	11	of	of	ADP
cana-6127	70	12	order	order	NOUN
cana-6127	70	13	𝛼	𝛼	NOUN
cana-6127	70	14	is	be	AUX
cana-6127	70	15	used	use	VERB
cana-6127	70	16	to	to	PART
cana-6127	70	17	create	create	VERB
cana-6127	70	18	a	a	DET
cana-6127	70	19	mathematical	mathematical	ADJ
cana-6127	70	20	model	model	NOUN
cana-6127	70	21	that	that	PRON
cana-6127	70	22	consider	consider	VERB
cana-6127	70	23	a	a	DET
cana-6127	70	24	thick	thick	ADJ
cana-6127	70	25	rectangular	rectangular	ADJ
cana-6127	70	26	plate	plate	NOUN
cana-6127	70	27	with	with	ADP
cana-6127	70	28	internal	internal	ADJ
cana-6127	70	29	heat	heat	NOUN
cana-6127	70	30	generation	generation	NOUN
cana-6127	70	31	.	.	PUNCT
cana-6127	71	1	the	the	DET
cana-6127	71	2	temperature	temperature	NOUN
cana-6127	71	3	𝑇(𝑥	𝑇(𝑥	PROPN
cana-6127	71	4	,	,	PUNCT
cana-6127	71	5	𝑦	𝑦	NOUN
cana-6127	71	6	,	,	PUNCT
cana-6127	71	7	𝑧	𝑧	NOUN
cana-6127	71	8	,	,	PUNCT
cana-6127	71	9	𝑡	𝑡	NOUN
cana-6127	71	10	)	)	PUNCT
cana-6127	71	11	of	of	ADP
cana-6127	71	12	the	the	DET
cana-6127	71	13	thick	thick	ADJ
cana-6127	71	14	rectangular	rectangular	ADJ
cana-6127	71	15	plate	plate	NOUN
cana-6127	71	16	at	at	ADP
cana-6127	71	17	time	time	NOUN
cana-6127	71	18	𝑡	𝑡	PART
cana-6127	71	19	satisfying	satisfy	VERB
cana-6127	71	20	the	the	DET
cana-6127	71	21	time	time	NOUN
cana-6127	71	22	fractional	fractional	ADJ
cana-6127	71	23	heat	heat	NOUN
cana-6127	71	24	conduction	conduction	NOUN
cana-6127	71	25	equation	equation	NOUN
cana-6127	71	26	∂2𝑇	∂2𝑇	VERB
cana-6127	71	27	∂𝑥2	∂𝑥2	PROPN
cana-6127	72	1	+	+	CCONJ
cana-6127	72	2	∂𝑇	∂𝑇	ADJ
cana-6127	72	3	∂𝑦2	∂𝑦2	NOUN
cana-6127	72	4	+	+	CCONJ
cana-6127	72	5	∂2𝑇	∂2𝑇	X
cana-6127	72	6	∂𝑧2	∂𝑧2	NOUN
cana-6127	72	7	+	+	CCONJ
cana-6127	72	8	𝑔(𝑥	𝑔(𝑥	PROPN
cana-6127	72	9	,	,	PUNCT
cana-6127	72	10	𝑦	𝑦	NOUN
cana-6127	72	11	,	,	PUNCT
cana-6127	72	12	𝑧	𝑧	NOUN
cana-6127	72	13	,	,	PUNCT
cana-6127	72	14	𝑡	𝑡	NOUN
cana-6127	72	15	)	)	PUNCT
cana-6127	72	16	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	73	1	=	=	NOUN
cana-6127	73	2	1	1	NUM
cana-6127	73	3	𝑘	𝑘	DET
cana-6127	73	4	∂𝛼𝑇	∂𝛼𝑇	ADJ
cana-6127	73	5	∂𝑡𝛼	∂𝑡𝛼	PROPN
cana-6127	73	6	,	,	PUNCT
cana-6127	73	7	(	(	PUNCT
cana-6127	73	8	3.1	3.1	NUM
cana-6127	73	9	)	)	PUNCT
cana-6127	73	10	where	where	SCONJ
cana-6127	73	11	𝑘𝑡	𝑘𝑡	PROPN
cana-6127	73	12	and	and	CCONJ
cana-6127	73	13	𝑘	𝑘	PROPN
cana-6127	73	14	are	be	AUX
cana-6127	73	15	thermal	thermal	ADJ
cana-6127	73	16	conductivity	conductivity	NOUN
cana-6127	73	17	and	and	CCONJ
cana-6127	73	18	thermal	thermal	ADJ
cana-6127	73	19	diffusivity	diffusivity	NOUN
cana-6127	73	20	of	of	ADP
cana-6127	73	21	the	the	DET
cana-6127	73	22	material	material	NOUN
cana-6127	73	23	of	of	ADP
cana-6127	73	24	the	the	DET
cana-6127	73	25	plate	plate	NOUN
cana-6127	73	26	.	.	PUNCT
cana-6127	74	1	with	with	ADP
cana-6127	74	2	the	the	DET
cana-6127	74	3	boundary	boundary	ADJ
cana-6127	74	4	conditions	condition	NOUN
cana-6127	74	5	,	,	PUNCT
cana-6127	74	6	𝑇	𝑇	PROPN
cana-6127	74	7	=	=	SYM
cana-6127	74	8	0	0	NUM
cana-6127	74	9	,	,	PUNCT
cana-6127	74	10	  	  	SPACE
cana-6127	74	11	at	at	ADP
cana-6127	74	12	all	all	DET
cana-6127	74	13	boundary	boundary	ADJ
cana-6127	74	14	surfaces	surface	NOUN
cana-6127	74	15	for	for	ADP
cana-6127	74	16	𝑡	𝑡	X
cana-6127	74	17	>	>	X
cana-6127	74	18	0	0	NUM
cana-6127	74	19	,	,	PUNCT
cana-6127	74	20	(	(	PUNCT
cana-6127	74	21	3.2	3.2	NUM
cana-6127	74	22	)	)	PUNCT
cana-6127	74	23	communications	communication	NOUN
cana-6127	74	24	on	on	ADP
cana-6127	74	25	applied	apply	VERB
cana-6127	74	26	nonlinear	nonlinear	ADJ
cana-6127	74	27	analysis	analysis	NOUN
cana-6127	74	28	issn	issn	NOUN
cana-6127	74	29	:	:	PUNCT
cana-6127	74	30	1074	1074	NUM
cana-6127	74	31	-	-	PUNCT
cana-6127	74	32	133x	133x	NUM
cana-6127	74	33	vol	vol	VERB
cana-6127	74	34	32	32	NUM
cana-6127	74	35	no	no	NOUN
cana-6127	74	36	.	.	PUNCT
cana-6127	75	1	10s	10	NOUN
cana-6127	75	2	(	(	PUNCT
cana-6127	75	3	2025	2025	NUM
cana-6127	75	4	)	)	PUNCT
cana-6127	75	5	3463	3463	NUM
cana-6127	75	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	75	7	and	and	CCONJ
cana-6127	75	8	initial	initial	ADJ
cana-6127	75	9	conditions	condition	NOUN
cana-6127	75	10	,	,	PUNCT
cana-6127	75	11	𝑇	𝑇	PROPN
cana-6127	75	12	=	=	PUNCT
cana-6127	75	13	𝑓(𝑥	𝑓(𝑥	NOUN
cana-6127	75	14	,	,	PUNCT
cana-6127	75	15	𝑦	𝑦	NOUN
cana-6127	75	16	,	,	PUNCT
cana-6127	75	17	𝑧	𝑧	NOUN
cana-6127	75	18	)	)	PUNCT
cana-6127	75	19	,	,	PUNCT
cana-6127	75	20	  	  	SPACE
cana-6127	75	21	at	at	ADP
cana-6127	75	22	𝑡	𝑡	X
cana-6127	75	23	=	=	SYM
cana-6127	75	24	0	0	NUM
cana-6127	75	25	,	,	PUNCT
cana-6127	75	26	0	0	NUM
cana-6127	75	27	<	<	X
cana-6127	75	28	𝛼	𝛼	X
cana-6127	75	29	≤	≤	NUM
cana-6127	75	30	1	1	NUM
cana-6127	75	31	,	,	PUNCT
cana-6127	75	32	(	(	PUNCT
cana-6127	75	33	3.3	3.3	NUM
cana-6127	75	34	)	)	PUNCT
cana-6127	75	35	∂𝑇	∂𝑇	NOUN
cana-6127	75	36	∂𝑡	∂𝑡	PROPN
cana-6127	75	37	=	=	SYM
cana-6127	75	38	0	0	PROPN
cana-6127	75	39	,	,	PUNCT
cana-6127	75	40	  	  	SPACE
cana-6127	75	41	at	at	ADP
cana-6127	75	42	𝑡	𝑡	X
cana-6127	75	43	=	=	SYM
cana-6127	75	44	0	0	NUM
cana-6127	75	45	,	,	PUNCT
cana-6127	75	46	1	1	NUM
cana-6127	75	47	<	<	X
cana-6127	75	48	𝛼	𝛼	X
cana-6127	75	49	≤	≤	NUM
cana-6127	75	50	2	2	NUM
cana-6127	75	51	(	(	PUNCT
cana-6127	75	52	3.4	3.4	NUM
cana-6127	75	53	)	)	PUNCT
cana-6127	75	54	fig	fig	NOUN
cana-6127	75	55	.	.	PUNCT
cana-6127	76	1	1	1	X
cana-6127	76	2	.	.	X
cana-6127	76	3	geometrical	geometrical	ADJ
cana-6127	76	4	representation	representation	NOUN
cana-6127	76	5	of	of	ADP
cana-6127	76	6	the	the	DET
cana-6127	76	7	plate	plate	NOUN
cana-6127	76	8	.	.	PUNCT
cana-6127	77	1	4	4	X
cana-6127	77	2	.	.	X
cana-6127	77	3	analysis	analysis	NOUN
cana-6127	77	4	here	here	ADV
cana-6127	77	5	the	the	DET
cana-6127	77	6	plate	plate	NOUN
cana-6127	77	7	is	be	AUX
cana-6127	77	8	assumed	assume	VERB
cana-6127	77	9	sufficiently	sufficiently	ADV
cana-6127	77	10	thick	thick	ADJ
cana-6127	77	11	and	and	CCONJ
cana-6127	77	12	considered	consider	VERB
cana-6127	77	13	free	free	ADJ
cana-6127	77	14	from	from	ADP
cana-6127	77	15	traction	traction	PROPN
cana-6127	77	16	.	.	PUNCT
cana-6127	78	1	since	since	SCONJ
cana-6127	78	2	the	the	DET
cana-6127	78	3	plate	plate	NOUN
cana-6127	78	4	is	be	AUX
cana-6127	78	5	in	in	ADP
cana-6127	78	6	a	a	DET
cana-6127	78	7	plane	plane	NOUN
cana-6127	78	8	stress	stress	NOUN
cana-6127	78	9	state	state	NOUN
cana-6127	78	10	without	without	ADP
cana-6127	78	11	bending	bend	VERB
cana-6127	78	12	.	.	PUNCT
cana-6127	79	1	airy	airy	ADJ
cana-6127	79	2	stress	stress	NOUN
cana-6127	79	3	function	function	NOUN
cana-6127	79	4	method	method	NOUN
cana-6127	79	5	is	be	AUX
cana-6127	79	6	applicable	applicable	ADJ
cana-6127	79	7	to	to	ADP
cana-6127	79	8	the	the	DET
cana-6127	79	9	analytical	analytical	ADJ
cana-6127	79	10	development	development	NOUN
cana-6127	79	11	of	of	ADP
cana-6127	79	12	the	the	DET
cana-6127	79	13	thermoelastic	thermoelastic	ADJ
cana-6127	79	14	field	field	NOUN
cana-6127	79	15	.	.	PUNCT
cana-6127	80	1	airy	airy	ADJ
cana-6127	80	2	stress	stress	NOUN
cana-6127	80	3	function	function	NOUN
cana-6127	80	4	𝑈(𝑥	𝑈(𝑥	NOUN
cana-6127	80	5	,	,	PUNCT
cana-6127	80	6	𝑦	𝑦	NOUN
cana-6127	80	7	,	,	PUNCT
cana-6127	80	8	𝑧	𝑧	NOUN
cana-6127	80	9	,	,	PUNCT
cana-6127	80	10	𝑡	𝑡	NOUN
cana-6127	80	11	)	)	PUNCT
cana-6127	80	12	which	which	PRON
cana-6127	80	13	satisfy	satisfy	VERB
cana-6127	80	14	the	the	DET
cana-6127	80	15	following	follow	VERB
cana-6127	80	16	relation	relation	NOUN
cana-6127	80	17	(	(	PUNCT
cana-6127	80	18	∂2	∂2	NOUN
cana-6127	80	19	∂𝑥2	∂𝑥2	NOUN
cana-6127	80	20	+	+	CCONJ
cana-6127	80	21	∂	∂	NUM
cana-6127	80	22	∂𝑦2	∂𝑦2	NOUN
cana-6127	80	23	+	+	CCONJ
cana-6127	80	24	∂2	∂2	PROPN
cana-6127	80	25	∂𝑧2	∂𝑧2	PROPN
cana-6127	80	26	)	)	PUNCT
cana-6127	80	27	2	2	NUM
cana-6127	80	28	𝑈	𝑈	NOUN
cana-6127	80	29	=	=	PRON
cana-6127	80	30	−𝜆𝐸	−𝜆𝐸	NOUN
cana-6127	80	31	(	(	PUNCT
cana-6127	80	32	∂2	∂2	NOUN
cana-6127	80	33	∂𝑥2	∂𝑥2	NOUN
cana-6127	80	34	+	+	CCONJ
cana-6127	80	35	∂	∂	NUM
cana-6127	80	36	∂𝑦2	∂𝑦2	NOUN
cana-6127	80	37	+	+	CCONJ
cana-6127	80	38	∂2	∂2	PROPN
cana-6127	80	39	∂𝑧2	∂𝑧2	NOUN
cana-6127	80	40	)	)	PUNCT
cana-6127	80	41	𝑇	𝑇	PROPN
cana-6127	80	42	(	(	PUNCT
cana-6127	80	43	4.1	4.1	NUM
cana-6127	80	44	)	)	PUNCT
cana-6127	80	45	where	where	SCONJ
cana-6127	80	46	𝜆	𝜆	NOUN
cana-6127	80	47	and	and	CCONJ
cana-6127	80	48	𝐸	𝐸	PROPN
cana-6127	80	49	are	be	AUX
cana-6127	80	50	linear	linear	ADJ
cana-6127	80	51	coefficient	coefficient	NOUN
cana-6127	80	52	of	of	ADP
cana-6127	80	53	the	the	DET
cana-6127	80	54	thermal	thermal	ADJ
cana-6127	80	55	expansion	expansion	NOUN
cana-6127	80	56	,	,	PUNCT
cana-6127	80	57	youngs	young	NOUN
cana-6127	80	58	modulus	modulus	VERB
cana-6127	80	59	elasticity	elasticity	NOUN
cana-6127	80	60	of	of	ADP
cana-6127	80	61	the	the	DET
cana-6127	80	62	material	material	NOUN
cana-6127	80	63	of	of	ADP
cana-6127	80	64	the	the	DET
cana-6127	80	65	plate	plate	NOUN
cana-6127	80	66	.	.	PUNCT
cana-6127	81	1	the	the	DET
cana-6127	81	2	displacement	displacement	ADJ
cana-6127	81	3	components	component	NOUN
cana-6127	81	4	𝑢𝑥	𝑢𝑥	ADP
cana-6127	81	5	,	,	PUNCT
cana-6127	81	6	𝑢𝑦	𝑢𝑦	PROPN
cana-6127	81	7	and	and	CCONJ
cana-6127	81	8	𝑢𝑧	𝑢𝑧	PROPN
cana-6127	81	9	in	in	ADP
cana-6127	81	10	the	the	DET
cana-6127	81	11	𝑋	𝑋	PROPN
cana-6127	81	12	,	,	PUNCT
cana-6127	81	13	𝑌	𝑌	PROPN
cana-6127	81	14	and	and	CCONJ
cana-6127	81	15	𝑍	𝑍	PROPN
cana-6127	81	16	direction	direction	NOUN
cana-6127	81	17	are	be	AUX
cana-6127	81	18	represented	represent	VERB
cana-6127	81	19	in	in	ADP
cana-6127	81	20	the	the	DET
cana-6127	81	21	integral	integral	ADJ
cana-6127	81	22	form	form	NOUN
cana-6127	81	23	as	as	ADP
cana-6127	81	24	𝑢𝑥	𝑢𝑥	ADP
cana-6127	81	25	=	=	NOUN
cana-6127	81	26	∫	∫	PROPN
cana-6127	81	27	[	[	PUNCT
cana-6127	81	28	1	1	NUM
cana-6127	81	29	𝐸	𝐸	PROPN
cana-6127	81	30	(	(	PUNCT
cana-6127	81	31	∂2𝑈	∂2𝑈	PROPN
cana-6127	81	32	∂𝑦2	∂𝑦2	PROPN
cana-6127	81	33	+	+	PROPN
cana-6127	81	34	∂2𝑈	∂2𝑈	PROPN
cana-6127	81	35	∂𝑧2	∂𝑧2	PROPN
cana-6127	81	36	−	−	PROPN
cana-6127	81	37	𝜈	𝜈	X
cana-6127	81	38	∂2𝑈	∂2𝑈	PROPN
cana-6127	81	39	∂𝑥2	∂𝑥2	ADV
cana-6127	81	40	)	)	PUNCT
cana-6127	82	1	+	+	CCONJ
cana-6127	82	2	𝜆𝑇	𝜆𝑇	X
cana-6127	82	3	]	]	X
cana-6127	82	4	𝑑𝑥	𝑑𝑥	VERB
cana-6127	82	5	(	(	PUNCT
cana-6127	82	6	4.2	4.2	NUM
cana-6127	82	7	)	)	PUNCT
cana-6127	82	8	𝑢𝑦	𝑢𝑦	PROPN
cana-6127	82	9	=	=	SYM
cana-6127	82	10	∫	∫	PROPN
cana-6127	82	11	[	[	PUNCT
cana-6127	82	12	1	1	NUM
cana-6127	82	13	𝐸	𝐸	PROPN
cana-6127	82	14	(	(	PUNCT
cana-6127	82	15	∂2𝑈	∂2𝑈	PROPN
cana-6127	82	16	∂𝑥2	∂𝑥2	PROPN
cana-6127	82	17	+	+	CCONJ
cana-6127	82	18	∂2𝑈	∂2𝑈	PROPN
cana-6127	82	19	∂𝑧2	∂𝑧2	PROPN
cana-6127	82	20	−	−	PROPN
cana-6127	82	21	𝜈	𝜈	PROPN
cana-6127	82	22	∂2𝑈	∂2𝑈	PROPN
cana-6127	82	23	∂𝑦2	∂𝑦2	NOUN
cana-6127	82	24	)	)	PUNCT
cana-6127	83	1	+	+	CCONJ
cana-6127	83	2	𝜆𝑇	𝜆𝑇	X
cana-6127	83	3	]	]	X
cana-6127	83	4	𝑑𝑦	𝑑𝑦	X
cana-6127	83	5	(	(	PUNCT
cana-6127	83	6	4.3	4.3	NUM
cana-6127	83	7	)	)	PUNCT
cana-6127	83	8	𝑢𝑧	𝑢𝑧	PROPN
cana-6127	83	9	=	=	SYM
cana-6127	83	10	∫	∫	PROPN
cana-6127	83	11	[	[	PUNCT
cana-6127	83	12	1	1	NUM
cana-6127	83	13	𝐸	𝐸	PROPN
cana-6127	83	14	(	(	PUNCT
cana-6127	83	15	∂2𝑈	∂2𝑈	PROPN
cana-6127	83	16	∂𝑥2	∂𝑥2	PROPN
cana-6127	83	17	+	+	CCONJ
cana-6127	83	18	∂2𝑈	∂2𝑈	PROPN
cana-6127	83	19	∂𝑦2	∂𝑦2	NOUN
cana-6127	83	20	−	−	PROPN
cana-6127	83	21	𝜈	𝜈	X
cana-6127	83	22	∂2𝑈	∂2𝑈	PROPN
cana-6127	83	23	∂𝑧2	∂𝑧2	PROPN
cana-6127	83	24	)	)	PUNCT
cana-6127	84	1	+	+	CCONJ
cana-6127	84	2	𝜆𝑇	𝜆𝑇	PROPN
cana-6127	84	3	]	]	X
cana-6127	84	4	𝑑𝑧	𝑑𝑧	NOUN
cana-6127	84	5	(	(	PUNCT
cana-6127	84	6	4.4	4.4	NUM
cana-6127	84	7	)	)	PUNCT
cana-6127	84	8	where	where	SCONJ
cana-6127	84	9	𝜈	𝜈	PROPN
cana-6127	84	10	is	be	AUX
cana-6127	84	11	the	the	DET
cana-6127	84	12	poissons	poisson	NOUN
cana-6127	84	13	ratio	ratio	NOUN
cana-6127	84	14	of	of	ADP
cana-6127	84	15	the	the	DET
cana-6127	84	16	material	material	NOUN
cana-6127	84	17	of	of	ADP
cana-6127	84	18	the	the	DET
cana-6127	84	19	plate	plate	NOUN
cana-6127	84	20	.	.	PUNCT
cana-6127	85	1	the	the	DET
cana-6127	85	2	stress	stress	NOUN
cana-6127	85	3	components	component	NOUN
cana-6127	85	4	are	be	AUX
cana-6127	85	5	:	:	PUNCT
cana-6127	85	6	communications	communication	NOUN
cana-6127	85	7	on	on	ADP
cana-6127	85	8	applied	apply	VERB
cana-6127	85	9	nonlinear	nonlinear	ADJ
cana-6127	85	10	analysis	analysis	NOUN
cana-6127	85	11	issn	issn	NOUN
cana-6127	85	12	:	:	PUNCT
cana-6127	85	13	1074	1074	NUM
cana-6127	85	14	-	-	PUNCT
cana-6127	85	15	133x	133x	NUM
cana-6127	85	16	vol	vol	VERB
cana-6127	85	17	32	32	NUM
cana-6127	85	18	no	no	NOUN
cana-6127	85	19	.	.	PUNCT
cana-6127	86	1	10s	10	NOUN
cana-6127	86	2	(	(	PUNCT
cana-6127	86	3	2025	2025	NUM
cana-6127	86	4	)	)	PUNCT
cana-6127	86	5	3464	3464	NUM
cana-6127	86	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	86	7	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-6127	86	8	=	=	SYM
cana-6127	86	9	(	(	PUNCT
cana-6127	86	10	∂2𝑈	∂2𝑈	PROPN
cana-6127	86	11	∂𝑦2	∂𝑦2	PROPN
cana-6127	86	12	+	+	PROPN
cana-6127	86	13	∂2𝑈	∂2𝑈	PROPN
cana-6127	86	14	∂𝑧2	∂𝑧2	PROPN
cana-6127	86	15	)	)	PUNCT
cana-6127	86	16	(	(	PUNCT
cana-6127	86	17	4.5	4.5	X
cana-6127	86	18	)	)	PUNCT
cana-6127	86	19	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
cana-6127	86	20	=	=	SYM
cana-6127	86	21	(	(	PUNCT
cana-6127	86	22	∂2𝑈	∂2𝑈	PROPN
cana-6127	86	23	∂𝑥2	∂𝑥2	PROPN
cana-6127	86	24	+	+	NUM
cana-6127	86	25	∂2𝑈	∂2𝑈	PROPN
cana-6127	86	26	∂𝑧2	∂𝑧2	PROPN
cana-6127	86	27	)	)	PUNCT
cana-6127	86	28	(	(	PUNCT
cana-6127	86	29	4.6	4.6	NUM
cana-6127	86	30	)	)	PUNCT
cana-6127	86	31	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6127	86	32	=	=	SYM
cana-6127	86	33	(	(	PUNCT
cana-6127	86	34	∂2𝑈	∂2𝑈	PROPN
cana-6127	86	35	∂𝑥2	∂𝑥2	PROPN
cana-6127	87	1	+	+	NUM
cana-6127	87	2	∂2𝑈	∂2𝑈	PROPN
cana-6127	87	3	∂𝑦2	∂𝑦2	NOUN
cana-6127	87	4	)	)	PUNCT
cana-6127	87	5	(	(	PUNCT
cana-6127	87	6	4.7	4.7	NUM
cana-6127	87	7	)	)	PUNCT
cana-6127	87	8	equations	equation	NOUN
cana-6127	88	1	[	[	X
cana-6127	88	2	3.1	3.1	NUM
cana-6127	88	3	]	]	PUNCT
cana-6127	88	4	to	to	ADP
cana-6127	88	5	[	[	X
cana-6127	88	6	4.7	4.7	NUM
cana-6127	88	7	]	]	PUNCT
cana-6127	88	8	constitute	constitute	VERB
cana-6127	88	9	the	the	DET
cana-6127	88	10	mathematical	mathematical	ADJ
cana-6127	88	11	formulation	formulation	NOUN
cana-6127	88	12	of	of	ADP
cana-6127	88	13	the	the	DET
cana-6127	88	14	problem	problem	NOUN
cana-6127	88	15	under	under	ADP
cana-6127	88	16	consideration	consideration	NOUN
cana-6127	88	17	.	.	PUNCT
cana-6127	89	1	5	5	X
cana-6127	89	2	.	.	X
cana-6127	89	3	determination	determination	NOUN
cana-6127	89	4	of	of	ADP
cana-6127	89	5	temperature	temperature	NOUN
cana-6127	89	6	field	field	NOUN
cana-6127	89	7	to	to	PART
cana-6127	89	8	obtain	obtain	VERB
cana-6127	89	9	the	the	DET
cana-6127	89	10	expression	expression	NOUN
cana-6127	89	11	for	for	ADP
cana-6127	89	12	temperature	temperature	NOUN
cana-6127	89	13	function	function	NOUN
cana-6127	89	14	𝑇(𝑥	𝑇(𝑥	PROPN
cana-6127	89	15	,	,	PUNCT
cana-6127	89	16	𝑦	𝑦	NOUN
cana-6127	89	17	,	,	PUNCT
cana-6127	89	18	𝑧	𝑧	NOUN
cana-6127	89	19	,	,	PUNCT
cana-6127	89	20	𝑡	𝑡	PROPN
cana-6127	89	21	)	)	PUNCT
cana-6127	89	22	;	;	PUNCT
cana-6127	89	23	we	we	PRON
cana-6127	89	24	introduce	introduce	VERB
cana-6127	89	25	the	the	DET
cana-6127	89	26	‘	'	PUNCT
cana-6127	89	27	‘	'	PUNCT
cana-6127	89	28	triple	triple	ADJ
cana-6127	89	29	integral	integral	ADJ
cana-6127	89	30	transform’’and	transform’’and	NOUN
cana-6127	89	31	its	its	PRON
cana-6127	89	32	corresponding	corresponding	ADJ
cana-6127	89	33	‘	'	PUNCT
cana-6127	89	34	triple	triple	ADJ
cana-6127	89	35	-	-	PUNCT
cana-6127	89	36	inversion	inversion	NOUN
cana-6127	89	37	formula	formula	NOUN
cana-6127	89	38	’	'	PUNCT
cana-6127	89	39	as	as	SCONJ
cana-6127	89	40	defined	define	VERB
cana-6127	89	41	in	in	ADP
cana-6127	89	42	[	[	X
cana-6127	89	43	35	35	NUM
cana-6127	89	44	]	]	PUNCT
cana-6127	89	45	respectively	respectively	ADV
cana-6127	89	46	as	as	ADP
cana-6127	89	47	𝑇(𝛽𝑚	𝑇(𝛽𝑚	NOUN
cana-6127	89	48	,	,	PUNCT
cana-6127	89	49	𝜈𝑛	𝜈𝑛	ADP
cana-6127	89	50	,	,	PUNCT
cana-6127	89	51	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	89	52	,	,	PUNCT
cana-6127	89	53	𝑡	𝑡	X
cana-6127	89	54	)	)	PUNCT
cana-6127	89	55	=	=	SYM
cana-6127	90	1	∫	∫	PROPN
cana-6127	90	2	∫	∫	PROPN
cana-6127	90	3	∫	∫	PROPN
cana-6127	90	4	𝐾	𝐾	PROPN
cana-6127	90	5	𝑐	𝑐	PROPN
cana-6127	90	6	𝑧′=0	𝑧′=0	PROPN
cana-6127	90	7	𝑏	𝑏	PROPN
cana-6127	90	8	𝑦′=0	𝑦′=0	PROPN
cana-6127	90	9	𝑎	𝑎	NOUN
cana-6127	90	10	𝑥′=0	𝑥′=0	NOUN
cana-6127	90	11	(	(	PUNCT
cana-6127	90	12	𝛽𝑚	𝛽𝑚	PROPN
cana-6127	90	13	,	,	PUNCT
cana-6127	90	14	𝑥	𝑥	PROPN
cana-6127	90	15	′	′	NUM
cana-6127	90	16	)	)	PUNCT
cana-6127	90	17	.	.	PUNCT
cana-6127	91	1	𝐾(𝜈𝑛	𝐾(𝜈𝑛	PROPN
cana-6127	91	2	,	,	PUNCT
cana-6127	91	3	𝑦	𝑦	NOUN
cana-6127	91	4	′	′	NOUN
cana-6127	91	5	)	)	PUNCT
cana-6127	91	6	.	.	PUNCT
cana-6127	92	1	𝐾(𝜂𝑝	𝐾(𝜂𝑝	PROPN
cana-6127	92	2	,	,	PUNCT
cana-6127	92	3	𝑧	𝑧	PROPN
cana-6127	92	4	′	′	NOUN
cana-6127	92	5	)	)	PUNCT
cana-6127	92	6	(	(	PUNCT
cana-6127	92	7	5.1	5.1	NUM
cana-6127	92	8	)	)	PUNCT
cana-6127	92	9	×	×	NOUN
cana-6127	92	10	𝑇(𝑥′	𝑇(𝑥′	NOUN
cana-6127	92	11	,	,	PUNCT
cana-6127	92	12	𝑦′	𝑦′	PROPN
cana-6127	92	13	,	,	PUNCT
cana-6127	92	14	𝑧′	𝑧′	NUM
cana-6127	92	15	,	,	PUNCT
cana-6127	92	16	𝑡)𝑑𝑥′𝑑𝑦′𝑑𝑧′	𝑡)𝑑𝑥′𝑑𝑦′𝑑𝑧′	PROPN
cana-6127	92	17	𝑇(𝑥	𝑇(𝑥	PROPN
cana-6127	92	18	,	,	PUNCT
cana-6127	92	19	𝑦	𝑦	PROPN
cana-6127	92	20	,	,	PUNCT
cana-6127	92	21	𝑧	𝑧	NOUN
cana-6127	92	22	,	,	PUNCT
cana-6127	92	23	𝑡	𝑡	NOUN
cana-6127	92	24	)	)	PUNCT
cana-6127	92	25	=	=	SYM
cana-6127	93	1	∑∑∑𝐾	∑∑∑𝐾	PUNCT
cana-6127	93	2	∞	∞	NUM
cana-6127	93	3	𝑝=0	𝑝=0	PROPN
cana-6127	93	4	∞	∞	NUM
cana-6127	93	5	𝑛=0	𝑛=0	PROPN
cana-6127	93	6	∞	∞	NUM
cana-6127	93	7	𝑚=0	𝑚=0	PUNCT
cana-6127	93	8	(	(	PUNCT
cana-6127	93	9	𝛽𝑚	𝛽𝑚	X
cana-6127	93	10	,	,	PUNCT
cana-6127	93	11	𝑥	𝑥	NOUN
cana-6127	93	12	)	)	PUNCT
cana-6127	93	13	.	.	PUNCT
cana-6127	94	1	𝐾(𝜈𝑛	𝐾(𝜈𝑛	PROPN
cana-6127	94	2	,	,	PUNCT
cana-6127	94	3	𝑦).𝐾(𝜂𝑝	𝑦).𝐾(𝜂𝑝	X
cana-6127	94	4	,	,	PUNCT
cana-6127	94	5	𝑧)𝑇(𝛽𝑚	𝑧)𝑇(𝛽𝑚	PROPN
cana-6127	94	6	,	,	PUNCT
cana-6127	94	7	𝜈𝑛	𝜈𝑛	ADP
cana-6127	94	8	,	,	PUNCT
cana-6127	94	9	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	94	10	,	,	PUNCT
cana-6127	94	11	𝑡	𝑡	PROPN
cana-6127	94	12	)	)	PUNCT
cana-6127	94	13	(	(	PUNCT
cana-6127	94	14	5.2	5.2	NUM
cana-6127	94	15	)	)	PUNCT
cana-6127	94	16	where	where	SCONJ
cana-6127	94	17	the	the	DET
cana-6127	94	18	kernels	kernel	NOUN
cana-6127	94	19	𝐾(𝛽𝑚	𝐾(𝛽𝑚	PROPN
cana-6127	94	20	,	,	PUNCT
cana-6127	94	21	𝑥	𝑥	NOUN
cana-6127	94	22	)	)	PUNCT
cana-6127	94	23	=	=	SYM
cana-6127	95	1	√	√	ADP
cana-6127	95	2	2	2	NUM
cana-6127	95	3	𝑎	𝑎	X
cana-6127	95	4	sin(𝛽𝑚𝑥	sin(𝛽𝑚𝑥	NOUN
cana-6127	95	5	)	)	PUNCT
cana-6127	95	6	(	(	PUNCT
cana-6127	95	7	5.3	5.3	NUM
cana-6127	95	8	)	)	PUNCT
cana-6127	95	9	𝐾(𝜈𝑛	𝐾(𝜈𝑛	PROPN
cana-6127	95	10	,	,	PUNCT
cana-6127	95	11	𝑦	𝑦	NOUN
cana-6127	95	12	)	)	PUNCT
cana-6127	95	13	=	=	SYM
cana-6127	95	14	√	√	ADP
cana-6127	95	15	2	2	NUM
cana-6127	95	16	𝑏	𝑏	PRON
cana-6127	95	17	sin(𝜈𝑛𝑦	sin(𝜈𝑛𝑦	NOUN
cana-6127	95	18	)	)	PUNCT
cana-6127	95	19	(	(	PUNCT
cana-6127	95	20	5.4	5.4	NUM
cana-6127	95	21	)	)	PUNCT
cana-6127	95	22	𝐾(𝜂𝑝	𝐾(𝜂𝑝	NOUN
cana-6127	95	23	,	,	PUNCT
cana-6127	95	24	𝑧	𝑧	NOUN
cana-6127	95	25	)	)	PUNCT
cana-6127	95	26	=	=	SYM
cana-6127	95	27	√	√	ADP
cana-6127	95	28	2	2	NUM
cana-6127	95	29	𝑐	𝑐	NOUN
cana-6127	95	30	sin(𝜂𝑝𝑧	sin(𝜂𝑝𝑧	NOUN
cana-6127	95	31	)	)	PUNCT
cana-6127	95	32	(	(	PUNCT
cana-6127	95	33	5.5	5.5	NUM
cana-6127	95	34	)	)	PUNCT
cana-6127	95	35	and	and	CCONJ
cana-6127	95	36	eigenvalues	eigenvalue	NOUN
cana-6127	95	37	are	be	AUX
cana-6127	95	38	𝛽𝑚	𝛽𝑚	NOUN
cana-6127	95	39	is	be	AUX
cana-6127	95	40	𝑚𝑡ℎ	𝑚𝑡ℎ	NOUN
cana-6127	95	41	root	root	NOUN
cana-6127	95	42	of	of	ADP
cana-6127	95	43	transcendental	transcendental	ADJ
cana-6127	95	44	equation	equation	NOUN
cana-6127	95	45	sin(𝛽𝑚	sin(𝛽𝑚	NOUN
cana-6127	95	46	.	.	PUNCT
cana-6127	96	1	𝑎	𝑎	X
cana-6127	96	2	)	)	PUNCT
cana-6127	96	3	=	=	SYM
cana-6127	96	4	0	0	NUM
cana-6127	96	5	i.e.	i.e.	X
cana-6127	96	6	𝛽𝑚	𝛽𝑚	X
cana-6127	96	7	=	=	PUNCT
cana-6127	96	8	𝑚𝜋	𝑚𝜋	ADP
cana-6127	96	9	𝑎	𝑎	X
cana-6127	96	10	,	,	PUNCT
cana-6127	96	11	  	  	SPACE
cana-6127	96	12	𝑚	𝑚	NOUN
cana-6127	96	13	=	=	SYM
cana-6127	96	14	1,2,3	1,2,3	NUM
cana-6127	96	15	,	,	PUNCT
cana-6127	96	16	…	…	PUNCT
cana-6127	96	17	(	(	PUNCT
cana-6127	96	18	5.6	5.6	NUM
cana-6127	96	19	)	)	PUNCT
cana-6127	96	20	𝜈𝑛	𝜈𝑛	ADV
cana-6127	96	21	is	be	AUX
cana-6127	96	22	𝑛𝑡ℎ	𝑛𝑡ℎ	PRON
cana-6127	96	23	root	root	VERB
cana-6127	96	24	of	of	ADP
cana-6127	96	25	transcendental	transcendental	ADJ
cana-6127	96	26	equation	equation	NOUN
cana-6127	96	27	sin(𝜈𝑛.	sin(𝜈𝑛.	NOUN
cana-6127	96	28	𝑏	𝑏	NOUN
cana-6127	96	29	)	)	PUNCT
cana-6127	96	30	=	=	SYM
cana-6127	96	31	0	0	NUM
cana-6127	96	32	i.e.	i.e.	X
cana-6127	96	33	𝜈𝑛	𝜈𝑛	ADP
cana-6127	96	34	=	=	PRON
cana-6127	96	35	𝑛𝜋	𝑛𝜋	NOUN
cana-6127	96	36	𝑏	𝑏	NOUN
cana-6127	96	37	,	,	PUNCT
cana-6127	96	38	  	  	SPACE
cana-6127	96	39	𝑛	𝑛	PRON
cana-6127	96	40	=	=	SYM
cana-6127	96	41	1,2,3	1,2,3	NUM
cana-6127	96	42	,	,	PUNCT
cana-6127	96	43	…	…	PUNCT
cana-6127	96	44	(	(	PUNCT
cana-6127	96	45	5.7	5.7	NUM
cana-6127	96	46	)	)	PUNCT
cana-6127	96	47	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	96	48	is	be	AUX
cana-6127	96	49	𝑝𝑡ℎ	𝑝𝑡ℎ	NOUN
cana-6127	96	50	root	root	NOUN
cana-6127	96	51	of	of	ADP
cana-6127	96	52	transcendental	transcendental	ADJ
cana-6127	96	53	equation	equation	NOUN
cana-6127	96	54	sin(𝜂𝑝.	sin(𝜂𝑝.	PROPN
cana-6127	96	55	𝑐	𝑐	NOUN
cana-6127	96	56	)	)	PUNCT
cana-6127	96	57	=	=	SYM
cana-6127	96	58	0	0	NUM
cana-6127	96	59	communications	communication	NOUN
cana-6127	96	60	on	on	ADP
cana-6127	96	61	applied	apply	VERB
cana-6127	96	62	nonlinear	nonlinear	ADJ
cana-6127	96	63	analysis	analysis	NOUN
cana-6127	96	64	issn	issn	NOUN
cana-6127	96	65	:	:	PUNCT
cana-6127	96	66	1074	1074	NUM
cana-6127	96	67	-	-	PUNCT
cana-6127	96	68	133x	133x	NUM
cana-6127	96	69	vol	vol	VERB
cana-6127	96	70	32	32	NUM
cana-6127	96	71	no	no	NOUN
cana-6127	96	72	.	.	PUNCT
cana-6127	97	1	10s	10	NOUN
cana-6127	97	2	(	(	PUNCT
cana-6127	97	3	2025	2025	NUM
cana-6127	97	4	)	)	PUNCT
cana-6127	97	5	3465	3465	NUM
cana-6127	97	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	97	7	i.e.	i.e.	X
cana-6127	97	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	97	9	=	=	NOUN
cana-6127	97	10	𝑝𝜋	𝑝𝜋	NOUN
cana-6127	97	11	𝑐	𝑐	NOUN
cana-6127	97	12	,	,	PUNCT
cana-6127	97	13	  	  	SPACE
cana-6127	97	14	𝑝	𝑝	NOUN
cana-6127	97	15	=	=	SYM
cana-6127	97	16	1,2,3	1,2,3	NUM
cana-6127	97	17	,	,	PUNCT
cana-6127	97	18	…	…	PUNCT
cana-6127	97	19	(	(	PUNCT
cana-6127	97	20	5.7	5.7	NUM
cana-6127	97	21	)	)	PUNCT
cana-6127	97	22	on	on	ADP
cana-6127	97	23	applying	apply	VERB
cana-6127	97	24	triple	triple	ADJ
cana-6127	97	25	-	-	PUNCT
cana-6127	97	26	integral	integral	ADJ
cana-6127	97	27	transform	transform	NOUN
cana-6127	97	28	defined	define	VERB
cana-6127	97	29	in	in	ADP
cana-6127	97	30	equation	equation	NOUN
cana-6127	97	31	[	[	X
cana-6127	97	32	5.1	5.1	NUM
cana-6127	97	33	]	]	PUNCT
cana-6127	97	34	to	to	ADP
cana-6127	97	35	equations	equation	NOUN
cana-6127	97	36	[	[	X
cana-6127	97	37	3.1]–[3.4	3.1]–[3.4	NUM
cana-6127	97	38	]	]	PUNCT
cana-6127	97	39	and	and	CCONJ
cana-6127	97	40	then	then	ADV
cana-6127	97	41	using	use	VERB
cana-6127	97	42	their	their	PRON
cana-6127	97	43	inversions	inversion	NOUN
cana-6127	97	44	defined	define	VERB
cana-6127	97	45	in	in	ADP
cana-6127	97	46	equation	equation	NOUN
cana-6127	97	47	[	[	X
cana-6127	97	48	4.2	4.2	NUM
cana-6127	97	49	]	]	PUNCT
cana-6127	97	50	,	,	PUNCT
cana-6127	97	51	one	one	PRON
cana-6127	97	52	obtains	obtain	VERB
cana-6127	97	53	the	the	DET
cana-6127	97	54	expressions	expression	NOUN
cana-6127	97	55	of	of	ADP
cana-6127	97	56	the	the	DET
cana-6127	97	57	temperature	temperature	NOUN
cana-6127	97	58	as	as	ADP
cana-6127	97	59	:	:	PUNCT
cana-6127	97	60	𝑇(𝑥	𝑇(𝑥	NUM
cana-6127	97	61	,	,	PUNCT
cana-6127	97	62	𝑦	𝑦	NOUN
cana-6127	97	63	,	,	PUNCT
cana-6127	97	64	𝑧	𝑧	NOUN
cana-6127	97	65	,	,	PUNCT
cana-6127	97	66	𝑡	𝑡	NOUN
cana-6127	97	67	)	)	PUNCT
cana-6127	97	68	=	=	SYM
cana-6127	98	1	∑∑∑𝐾	∑∑∑𝐾	PUNCT
cana-6127	98	2	∞	∞	NUM
cana-6127	98	3	𝑝=0	𝑝=0	PROPN
cana-6127	98	4	∞	∞	NUM
cana-6127	98	5	𝑛=0	𝑛=0	PROPN
cana-6127	98	6	∞	∞	NUM
cana-6127	98	7	𝑚=0	𝑚=0	PUNCT
cana-6127	98	8	(	(	PUNCT
cana-6127	98	9	𝛽𝑚	𝛽𝑚	X
cana-6127	98	10	,	,	PUNCT
cana-6127	98	11	𝑥	𝑥	NOUN
cana-6127	98	12	)	)	PUNCT
cana-6127	98	13	.	.	PUNCT
cana-6127	99	1	𝐾(𝜈𝑛	𝐾(𝜈𝑛	PROPN
cana-6127	99	2	,	,	PUNCT
cana-6127	99	3	𝑦).𝐾(𝜂𝑝	𝑦).𝐾(𝜂𝑝	X
cana-6127	99	4	,	,	PUNCT
cana-6127	99	5	𝑧	𝑧	NOUN
cana-6127	99	6	)	)	PUNCT
cana-6127	99	7	1	1	NUM
cana-6127	99	8	𝑘(𝛽𝑚2	𝑘(𝛽𝑚2	NOUN
cana-6127	99	9	+	+	NOUN
cana-6127	99	10	𝜈𝑛2	𝜈𝑛2	NOUN
cana-6127	99	11	+	+	NOUN
cana-6127	99	12	𝜂𝑝2	𝜂𝑝2	NOUN
cana-6127	99	13	)	)	PUNCT
cana-6127	99	14	×	×	NOUN
cana-6127	100	1	[	[	X
cana-6127	100	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	ADP
cana-6127	100	3	2	2	NUM
cana-6127	100	4	+	+	NOUN
cana-6127	100	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	100	6	2	2	NUM
cana-6127	100	7	+	+	NUM
cana-6127	100	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	100	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	100	10	)	)	PUNCT
cana-6127	100	11	]	]	PUNCT
cana-6127	101	1	[	[	X
cana-6127	101	2	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	101	3	,	,	PUNCT
cana-6127	101	4	𝜈𝑛	𝜈𝑛	ADP
cana-6127	101	5	,	,	PUNCT
cana-6127	101	6	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	101	7	)	)	PUNCT
cana-6127	101	8	+	+	CCONJ
cana-6127	101	9	𝑘	𝑘	DET
cana-6127	101	10	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	101	11	×∫	×∫	PROPN
cana-6127	101	12	[	[	X
cana-6127	101	13	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	PRON
cana-6127	101	14	2	2	NUM
cana-6127	101	15	+	+	NOUN
cana-6127	101	16	𝜈𝑛	𝜈𝑛	ADP
cana-6127	101	17	2	2	NUM
cana-6127	101	18	+	+	NUM
cana-6127	101	19	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	101	20	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	101	21	)	)	PUNCT
cana-6127	101	22	]	]	PUNCT
cana-6127	102	1	𝑡	𝑡	PROPN
cana-6127	102	2	𝑡′=0	𝑡′=0	PROPN
cana-6127	102	3	𝑔(𝛽𝑚	𝑔(𝛽𝑚	X
cana-6127	102	4	,	,	PUNCT
cana-6127	102	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	102	6	,	,	PUNCT
cana-6127	102	7	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	102	8	,	,	PUNCT
cana-6127	102	9	𝑡	𝑡	PROPN
cana-6127	102	10	′	′	NOUN
cana-6127	102	11	)	)	PUNCT
cana-6127	102	12	]	]	PUNCT
cana-6127	102	13	(	(	PUNCT
cana-6127	102	14	5.9	5.9	NUM
cana-6127	102	15	)	)	PUNCT
cana-6127	102	16	where	where	SCONJ
cana-6127	102	17	𝐸𝛼,𝛼	𝐸𝛼,𝛼	PROPN
cana-6127	102	18	(	(	PUNCT
cana-6127	102	19	.	.	PUNCT
cana-6127	102	20	)	)	PUNCT
cana-6127	102	21	two	two	NUM
cana-6127	102	22	-	-	PUNCT
cana-6127	102	23	parameter	parameter	NOUN
cana-6127	102	24	mittag	mittag	ADJ
cana-6127	102	25	-	-	PUNCT
cana-6127	102	26	leffler	leffler	NOUN
cana-6127	102	27	function	function	NOUN
cana-6127	102	28	,	,	PUNCT
cana-6127	102	29	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	102	30	,	,	PUNCT
cana-6127	102	31	𝜈𝑛	𝜈𝑛	ADP
cana-6127	102	32	,	,	PUNCT
cana-6127	102	33	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	102	34	)	)	PUNCT
cana-6127	102	35	=	=	SYM
cana-6127	102	36	∫	∫	PROPN
cana-6127	102	37	∫	∫	PROPN
cana-6127	102	38	∫	∫	PROPN
cana-6127	102	39	sin	sin	PROPN
cana-6127	102	40	𝑐	𝑐	PROPN
cana-6127	102	41	𝑧′=0	𝑧′=0	PROPN
cana-6127	102	42	𝑏	𝑏	PROPN
cana-6127	102	43	𝑦′=0	𝑦′=0	PROPN
cana-6127	102	44	𝑎	𝑎	NOUN
cana-6127	102	45	𝑥′=0	𝑥′=0	NOUN
cana-6127	102	46	(	(	PUNCT
cana-6127	102	47	𝛽𝑚𝑥	𝛽𝑚𝑥	NOUN
cana-6127	102	48	′)sin(𝜈𝑛𝑦	′)sin(𝜈𝑛𝑦	VERB
cana-6127	102	49	′)sin(𝜂𝑝𝑧	′)sin(𝜂𝑝𝑧	PROPN
cana-6127	102	50	′)𝑓(𝑥′	′)𝑓(𝑥′	PROPN
cana-6127	102	51	,	,	PUNCT
cana-6127	102	52	𝑦′	𝑦′	NOUN
cana-6127	102	53	,	,	PUNCT
cana-6127	102	54	𝑧′)𝑑𝑥′𝑑𝑦′𝑑𝑧′	𝑧′)𝑑𝑥′𝑑𝑦′𝑑𝑧′	ADP
cana-6127	102	55	𝑔(𝛽𝑚	𝑔(𝛽𝑚	NOUN
cana-6127	102	56	,	,	PUNCT
cana-6127	102	57	𝜈𝑛	𝜈𝑛	ADP
cana-6127	102	58	,	,	PUNCT
cana-6127	102	59	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	102	60	,	,	PUNCT
cana-6127	102	61	𝑡	𝑡	PROPN
cana-6127	102	62	′	′	NOUN
cana-6127	102	63	)	)	PUNCT
cana-6127	102	64	=	=	SYM
cana-6127	103	1	∫	∫	PROPN
cana-6127	103	2	∫	∫	PROPN
cana-6127	103	3	∫	∫	PROPN
cana-6127	103	4	sin	sin	PROPN
cana-6127	103	5	𝑐	𝑐	PROPN
cana-6127	103	6	𝑧′=0	𝑧′=0	PROPN
cana-6127	103	7	𝑏	𝑏	PROPN
cana-6127	103	8	𝑦′=0	𝑦′=0	PROPN
cana-6127	103	9	𝑎	𝑎	NOUN
cana-6127	103	10	𝑥′=0	𝑥′=0	NOUN
cana-6127	103	11	(	(	PUNCT
cana-6127	103	12	𝛽𝑚𝑥	𝛽𝑚𝑥	NOUN
cana-6127	103	13	′)sin(𝜈𝑛𝑦	′)sin(𝜈𝑛𝑦	VERB
cana-6127	103	14	′)sin(𝜂𝑝𝑧	′)sin(𝜂𝑝𝑧	PROPN
cana-6127	103	15	′)𝑔(𝑥′	′)𝑔(𝑥′	PROPN
cana-6127	103	16	,	,	PUNCT
cana-6127	103	17	𝑦′	𝑦′	PROPN
cana-6127	103	18	,	,	PUNCT
cana-6127	103	19	𝑧′	𝑧′	NUM
cana-6127	103	20	,	,	PUNCT
cana-6127	103	21	𝑡′)𝑑𝑥′𝑑𝑦′𝑑𝑧′	𝑡′)𝑑𝑥′𝑑𝑦′𝑑𝑧′	NUM
cana-6127	103	22	6	6	NUM
cana-6127	103	23	.	.	PUNCT
cana-6127	104	1	distributions	distribution	NOUN
cana-6127	104	2	of	of	ADP
cana-6127	104	3	displacement	displacement	NOUN
cana-6127	104	4	and	and	CCONJ
cana-6127	104	5	stresses	stress	VERB
cana-6127	104	6	using	use	VERB
cana-6127	104	7	equation	equation	NOUN
cana-6127	104	8	[	[	X
cana-6127	104	9	5.9	5.9	NUM
cana-6127	104	10	]	]	PUNCT
cana-6127	104	11	in	in	ADP
cana-6127	104	12	[	[	X
cana-6127	104	13	4.1	4.1	NUM
cana-6127	104	14	]	]	PUNCT
cana-6127	104	15	,	,	PUNCT
cana-6127	104	16	one	one	PRON
cana-6127	104	17	obtains	obtain	VERB
cana-6127	104	18	𝑈	𝑈	PROPN
cana-6127	104	19	=	=	PUNCT
cana-6127	104	20	8𝐸	8𝐸	NOUN
cana-6127	104	21	𝑎𝑏𝑐	𝑎𝑏𝑐	ADJ
cana-6127	104	22	∑	∑	PROPN
cana-6127	104	23	∑∑sin	∑∑sin	PROPN
cana-6127	104	24	∞	∞	PROPN
cana-6127	104	25	𝑝=0	𝑝=0	PROPN
cana-6127	104	26	∞	∞	PROPN
cana-6127	104	27	𝑛=0	𝑛=0	PROPN
cana-6127	104	28	∞	∞	NUM
cana-6127	104	29	𝑚=0	𝑚=0	PUNCT
cana-6127	104	30	(	(	PUNCT
cana-6127	104	31	𝛽𝑚𝑥)sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	𝛽𝑚𝑥)sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	NOUN
cana-6127	104	32	)	)	PUNCT
cana-6127	104	33	1	1	NUM
cana-6127	104	34	𝑘(𝛽𝑚2	𝑘(𝛽𝑚2	NOUN
cana-6127	104	35	+	+	NOUN
cana-6127	104	36	𝜈𝑛2	𝜈𝑛2	NOUN
cana-6127	104	37	+	+	NOUN
cana-6127	104	38	𝜂𝑝2	𝜂𝑝2	CCONJ
cana-6127	104	39	)	)	PUNCT
cana-6127	105	1	2	2	NUM
cana-6127	105	2	×	×	NOUN
cana-6127	106	1	[	[	X
cana-6127	106	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	ADP
cana-6127	106	3	2	2	NUM
cana-6127	106	4	+	+	NOUN
cana-6127	106	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	106	6	2	2	NUM
cana-6127	106	7	+	+	NUM
cana-6127	106	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	106	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	106	10	)	)	PUNCT
cana-6127	106	11	]	]	PUNCT
cana-6127	107	1	[	[	X
cana-6127	107	2	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	107	3	,	,	PUNCT
cana-6127	107	4	𝜈𝑛	𝜈𝑛	ADP
cana-6127	107	5	,	,	PUNCT
cana-6127	107	6	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	107	7	)	)	PUNCT
cana-6127	107	8	+	+	CCONJ
cana-6127	107	9	𝑘	𝑘	DET
cana-6127	107	10	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	107	11	×∫	×∫	PROPN
cana-6127	107	12	[	[	X
cana-6127	107	13	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	PRON
cana-6127	107	14	2	2	NUM
cana-6127	107	15	+	+	NOUN
cana-6127	107	16	𝜈𝑛	𝜈𝑛	ADP
cana-6127	107	17	2	2	NUM
cana-6127	107	18	+	+	NUM
cana-6127	107	19	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	107	20	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	107	21	)	)	PUNCT
cana-6127	107	22	]	]	PUNCT
cana-6127	108	1	𝑡	𝑡	PROPN
cana-6127	108	2	𝑡′=0	𝑡′=0	PROPN
cana-6127	108	3	𝑔(𝛽𝑚	𝑔(𝛽𝑚	PROPN
cana-6127	108	4	,	,	PUNCT
cana-6127	108	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	108	6	,	,	PUNCT
cana-6127	108	7	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	108	8	,	,	PUNCT
cana-6127	108	9	𝑡	𝑡	PROPN
cana-6127	108	10	′	′	NOUN
cana-6127	108	11	)	)	PUNCT
cana-6127	108	12	]	]	PUNCT
cana-6127	108	13	(	(	PUNCT
cana-6127	108	14	6.1	6.1	NUM
cana-6127	108	15	)	)	PUNCT
cana-6127	108	16	now	now	ADV
cana-6127	108	17	using	use	VERB
cana-6127	108	18	equations	equation	NOUN
cana-6127	108	19	[	[	X
cana-6127	108	20	5.9	5.9	NUM
cana-6127	108	21	]	]	PUNCT
cana-6127	108	22	and	and	CCONJ
cana-6127	108	23	[	[	X
cana-6127	108	24	6.1	6.1	NUM
cana-6127	108	25	]	]	PUNCT
cana-6127	108	26	in	in	ADP
cana-6127	108	27	equations	equation	NOUN
cana-6127	108	28	[	[	X
cana-6127	108	29	4.2	4.2	NUM
cana-6127	108	30	]	]	PUNCT
cana-6127	108	31	to	to	ADP
cana-6127	108	32	[	[	X
cana-6127	108	33	4.4	4.4	NUM
cana-6127	108	34	]	]	PUNCT
cana-6127	108	35	,	,	PUNCT
cana-6127	108	36	one	one	PRON
cana-6127	108	37	obtains	obtain	VERB
cana-6127	108	38	the	the	DET
cana-6127	108	39	expressions	expression	NOUN
cana-6127	108	40	for	for	ADP
cana-6127	108	41	displacement	displacement	NOUN
cana-6127	108	42	as	as	ADP
cana-6127	108	43	𝑢𝑥	𝑢𝑥	ADP
cana-6127	108	44	=	=	PRON
cana-6127	108	45	−8	−8	X
cana-6127	108	46	𝑎𝑏𝑐	𝑎𝑏𝑐	INTJ
cana-6127	108	47	∑	∑	PUNCT
cana-6127	108	48	∑∑	∑∑	PROPN
cana-6127	108	49	(	(	PUNCT
cana-6127	108	50	cos(𝛽𝑚𝑥	cos(𝛽𝑚𝑥	NOUN
cana-6127	108	51	)	)	PUNCT
cana-6127	108	52	𝛽𝑚	𝛽𝑚	ADP
cana-6127	108	53	)	)	PUNCT
cana-6127	109	1	∞	∞	PROPN
cana-6127	109	2	𝑝=0	𝑝=0	PROPN
cana-6127	109	3	∞	∞	NUM
cana-6127	109	4	𝑛=0	𝑛=0	PROPN
cana-6127	109	5	∞	∞	PROPN
cana-6127	109	6	𝑚=0	𝑚=0	SYM
cana-6127	109	7	sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	NOUN
cana-6127	109	8	)	)	PUNCT
cana-6127	109	9	[	[	PUNCT
cana-6127	109	10	(	(	PUNCT
cana-6127	109	11	𝜈	𝜈	X
cana-6127	109	12	−	−	PROPN
cana-6127	109	13	1)𝛽𝑚	1)𝛽𝑚	NUM
cana-6127	109	14	2	2	NUM
cana-6127	109	15	−	−	NOUN
cana-6127	109	16	2(𝜈𝑛	2(𝜈𝑛	NUM
cana-6127	109	17	2	2	NUM
cana-6127	109	18	+	+	CCONJ
cana-6127	109	19	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	109	20	2	2	NUM
cana-6127	109	21	)	)	PUNCT
cana-6127	109	22	𝑘(𝛽𝑚2	𝑘(𝛽𝑚2	VERB
cana-6127	110	1	+	+	NOUN
cana-6127	110	2	𝜈𝑛2	𝜈𝑛2	NOUN
cana-6127	110	3	+	+	NOUN
cana-6127	110	4	𝜂𝑝2	𝜂𝑝2	CCONJ
cana-6127	110	5	)	)	PUNCT
cana-6127	110	6	2	2	NUM
cana-6127	110	7	]	]	PUNCT
cana-6127	110	8	×	×	NOUN
cana-6127	111	1	[	[	X
cana-6127	111	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	ADP
cana-6127	111	3	2	2	NUM
cana-6127	111	4	+	+	NOUN
cana-6127	111	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	111	6	2	2	NUM
cana-6127	111	7	+	+	NUM
cana-6127	111	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	111	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	111	10	)	)	PUNCT
cana-6127	111	11	]	]	PUNCT
cana-6127	112	1	[	[	X
cana-6127	112	2	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	112	3	,	,	PUNCT
cana-6127	112	4	𝜈𝑛	𝜈𝑛	ADP
cana-6127	112	5	,	,	PUNCT
cana-6127	112	6	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	112	7	)	)	PUNCT
cana-6127	112	8	+	+	CCONJ
cana-6127	112	9	𝑘	𝑘	DET
cana-6127	112	10	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	112	11	×∫	×∫	PROPN
cana-6127	112	12	[	[	X
cana-6127	112	13	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	PRON
cana-6127	112	14	2	2	NUM
cana-6127	112	15	+	+	NOUN
cana-6127	112	16	𝜈𝑛	𝜈𝑛	ADP
cana-6127	112	17	2	2	NUM
cana-6127	112	18	+	+	NUM
cana-6127	112	19	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	112	20	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	112	21	)	)	PUNCT
cana-6127	112	22	]	]	PUNCT
cana-6127	113	1	𝑡	𝑡	PROPN
cana-6127	113	2	𝑡′=0	𝑡′=0	PROPN
cana-6127	113	3	𝑔(𝛽𝑚	𝑔(𝛽𝑚	X
cana-6127	113	4	,	,	PUNCT
cana-6127	113	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	113	6	,	,	PUNCT
cana-6127	113	7	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	113	8	,	,	PUNCT
cana-6127	113	9	𝑡	𝑡	PROPN
cana-6127	113	10	′	′	NOUN
cana-6127	113	11	)	)	PUNCT
cana-6127	113	12	]	]	PUNCT
cana-6127	114	1	(	(	PUNCT
cana-6127	114	2	6.2	6.2	NUM
cana-6127	114	3	)	)	PUNCT
cana-6127	114	4	𝑢𝑦	𝑢𝑦	NOUN
cana-6127	114	5	=	=	PUNCT
cana-6127	115	1	−8	−8	X
cana-6127	115	2	𝑎𝑏𝑐	𝑎𝑏𝑐	X
cana-6127	115	3	∑	∑	PROPN
cana-6127	115	4	∑∑sin	∑∑sin	PROPN
cana-6127	115	5	∞	∞	PROPN
cana-6127	115	6	𝑝=0	𝑝=0	PROPN
cana-6127	115	7	∞	∞	PROPN
cana-6127	115	8	𝑛=0	𝑛=0	PROPN
cana-6127	115	9	∞	∞	NUM
cana-6127	115	10	𝑚=0	𝑚=0	PUNCT
cana-6127	115	11	(	(	PUNCT
cana-6127	115	12	𝛽𝑚𝑥	𝛽𝑚𝑥	X
cana-6127	115	13	)	)	PUNCT
cana-6127	115	14	(	(	PUNCT
cana-6127	115	15	cos(𝜈𝑛𝑦	cos(𝜈𝑛𝑦	NOUN
cana-6127	115	16	)	)	PUNCT
cana-6127	115	17	𝜈𝑛	𝜈𝑛	ADP
cana-6127	115	18	)	)	PUNCT
cana-6127	115	19	sin(𝜂𝑝𝑧	sin(𝜂𝑝𝑧	NOUN
cana-6127	115	20	)	)	PUNCT
cana-6127	115	21	[	[	PUNCT
cana-6127	115	22	(	(	PUNCT
cana-6127	115	23	𝜈	𝜈	X
cana-6127	115	24	−	−	PROPN
cana-6127	115	25	1)𝜈𝑛	1)𝜈𝑛	PROPN
cana-6127	115	26	2	2	NUM
cana-6127	115	27	−	−	NUM
cana-6127	115	28	2(𝛽𝑚	2(𝛽𝑚	NOUN
cana-6127	115	29	2	2	NUM
cana-6127	115	30	+	+	CCONJ
cana-6127	115	31	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	115	32	2	2	NUM
cana-6127	115	33	)	)	PUNCT
cana-6127	115	34	𝑘(𝛽𝑚2	𝑘(𝛽𝑚2	VERB
cana-6127	116	1	+	+	NOUN
cana-6127	116	2	𝜈𝑛2	𝜈𝑛2	NOUN
cana-6127	116	3	+	+	NOUN
cana-6127	116	4	𝜂𝑝2	𝜂𝑝2	CCONJ
cana-6127	116	5	)	)	PUNCT
cana-6127	116	6	2	2	NUM
cana-6127	116	7	]	]	PUNCT
cana-6127	116	8	×	×	NOUN
cana-6127	117	1	[	[	X
cana-6127	117	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	ADP
cana-6127	117	3	2	2	NUM
cana-6127	117	4	+	+	NOUN
cana-6127	117	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	117	6	2	2	NUM
cana-6127	117	7	+	+	NUM
cana-6127	117	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	117	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	117	10	)	)	PUNCT
cana-6127	117	11	]	]	PUNCT
cana-6127	118	1	[	[	X
cana-6127	118	2	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	118	3	,	,	PUNCT
cana-6127	118	4	𝜈𝑛	𝜈𝑛	ADP
cana-6127	118	5	,	,	PUNCT
cana-6127	118	6	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	118	7	)	)	PUNCT
cana-6127	118	8	+	+	CCONJ
cana-6127	118	9	𝑘	𝑘	DET
cana-6127	118	10	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	118	11	×	×	NOUN
cana-6127	118	12	∫	∫	PROPN
cana-6127	119	1	[	[	X
cana-6127	119	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	INTJ
cana-6127	119	3	2	2	NUM
cana-6127	119	4	+	+	NOUN
cana-6127	119	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	119	6	2	2	NUM
cana-6127	119	7	+	+	NUM
cana-6127	119	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	119	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	119	10	)	)	PUNCT
cana-6127	119	11	]	]	PUNCT
cana-6127	120	1	𝑡	𝑡	PROPN
cana-6127	120	2	𝑡′=0	𝑡′=0	PROPN
cana-6127	120	3	𝑔(𝛽𝑚	𝑔(𝛽𝑚	PROPN
cana-6127	120	4	,	,	PUNCT
cana-6127	120	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	120	6	,	,	PUNCT
cana-6127	120	7	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	120	8	,	,	PUNCT
cana-6127	120	9	𝑡	𝑡	PROPN
cana-6127	120	10	′	′	NOUN
cana-6127	120	11	)	)	PUNCT
cana-6127	120	12	]	]	PUNCT
cana-6127	120	13	(	(	PUNCT
cana-6127	120	14	6.3	6.3	NUM
cana-6127	120	15	)	)	PUNCT
cana-6127	120	16	communications	communication	NOUN
cana-6127	120	17	on	on	ADP
cana-6127	120	18	applied	apply	VERB
cana-6127	120	19	nonlinear	nonlinear	ADJ
cana-6127	120	20	analysis	analysis	NOUN
cana-6127	120	21	issn	issn	NOUN
cana-6127	120	22	:	:	PUNCT
cana-6127	120	23	1074	1074	NUM
cana-6127	120	24	-	-	PUNCT
cana-6127	120	25	133x	133x	NUM
cana-6127	120	26	vol	vol	VERB
cana-6127	120	27	32	32	NUM
cana-6127	120	28	no	no	NOUN
cana-6127	120	29	.	.	PUNCT
cana-6127	121	1	10s	10	NOUN
cana-6127	121	2	(	(	PUNCT
cana-6127	121	3	2025	2025	NUM
cana-6127	121	4	)	)	PUNCT
cana-6127	121	5	3466	3466	NUM
cana-6127	121	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	121	7	𝑢𝑧	𝑢𝑧	PROPN
cana-6127	121	8	=	=	SYM
cana-6127	121	9	−8	−8	X
cana-6127	121	10	𝑎𝑏𝑐	𝑎𝑏𝑐	X
cana-6127	121	11	∑	∑	PROPN
cana-6127	121	12	∑∑sin	∑∑sin	PROPN
cana-6127	121	13	∞	∞	PROPN
cana-6127	121	14	𝑝=0	𝑝=0	PROPN
cana-6127	121	15	∞	∞	PROPN
cana-6127	121	16	𝑛=0	𝑛=0	PROPN
cana-6127	121	17	∞	∞	NUM
cana-6127	121	18	𝑚=0	𝑚=0	PUNCT
cana-6127	121	19	(	(	PUNCT
cana-6127	121	20	𝛽𝑚𝑥)sin(𝜈𝑛𝑦	𝛽𝑚𝑥)sin(𝜈𝑛𝑦	NOUN
cana-6127	121	21	)	)	PUNCT
cana-6127	121	22	(	(	PUNCT
cana-6127	121	23	cos(𝜂𝑝𝑧	cos(𝜂𝑝𝑧	NOUN
cana-6127	121	24	)	)	PUNCT
cana-6127	121	25	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	121	26	)	)	PUNCT
cana-6127	122	1	[	[	PUNCT
cana-6127	122	2	(	(	PUNCT
cana-6127	122	3	𝜈	𝜈	X
cana-6127	122	4	−	−	PROPN
cana-6127	122	5	1)𝜂𝑝	1)𝜂𝑝	NUM
cana-6127	122	6	2	2	NUM
cana-6127	122	7	−	−	NOUN
cana-6127	122	8	2(𝛽𝑚	2(𝛽𝑚	NOUN
cana-6127	122	9	2	2	NUM
cana-6127	122	10	+	+	CCONJ
cana-6127	122	11	𝜈𝑛	𝜈𝑛	ADP
cana-6127	122	12	2	2	NUM
cana-6127	122	13	)	)	PUNCT
cana-6127	122	14	𝑘(𝛽𝑚2	𝑘(𝛽𝑚2	NOUN
cana-6127	123	1	+	+	NOUN
cana-6127	123	2	𝜈𝑛2	𝜈𝑛2	NOUN
cana-6127	123	3	+	+	NOUN
cana-6127	123	4	𝜂𝑝2	𝜂𝑝2	CCONJ
cana-6127	123	5	)	)	PUNCT
cana-6127	123	6	2	2	NUM
cana-6127	123	7	]	]	PUNCT
cana-6127	123	8	×	×	NOUN
cana-6127	124	1	[	[	X
cana-6127	124	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	ADP
cana-6127	124	3	2	2	NUM
cana-6127	124	4	+	+	NOUN
cana-6127	124	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	124	6	2	2	NUM
cana-6127	124	7	+	+	NUM
cana-6127	124	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	124	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	124	10	)	)	PUNCT
cana-6127	124	11	]	]	PUNCT
cana-6127	125	1	[	[	X
cana-6127	125	2	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	125	3	,	,	PUNCT
cana-6127	125	4	𝜈𝑛	𝜈𝑛	ADP
cana-6127	125	5	,	,	PUNCT
cana-6127	125	6	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	125	7	)	)	PUNCT
cana-6127	125	8	+	+	CCONJ
cana-6127	125	9	𝑘	𝑘	DET
cana-6127	125	10	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	125	11	×∫	×∫	PROPN
cana-6127	125	12	[	[	X
cana-6127	125	13	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	PRON
cana-6127	125	14	2	2	NUM
cana-6127	125	15	+	+	NOUN
cana-6127	125	16	𝜈𝑛	𝜈𝑛	ADP
cana-6127	125	17	2	2	NUM
cana-6127	125	18	+	+	NUM
cana-6127	125	19	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	125	20	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	125	21	)	)	PUNCT
cana-6127	125	22	]	]	PUNCT
cana-6127	126	1	𝑡	𝑡	PROPN
cana-6127	126	2	𝑡′=0	𝑡′=0	PROPN
cana-6127	126	3	𝑔(𝛽𝑚	𝑔(𝛽𝑚	X
cana-6127	126	4	,	,	PUNCT
cana-6127	126	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	126	6	,	,	PUNCT
cana-6127	126	7	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	126	8	,	,	PUNCT
cana-6127	126	9	𝑡	𝑡	PROPN
cana-6127	126	10	′	′	NOUN
cana-6127	126	11	)	)	PUNCT
cana-6127	126	12	]	]	PUNCT
cana-6127	126	13	(	(	PUNCT
cana-6127	126	14	6.4	6.4	NUM
cana-6127	126	15	)	)	PUNCT
cana-6127	126	16	now	now	ADV
cana-6127	126	17	using	use	VERB
cana-6127	126	18	equations	equation	NOUN
cana-6127	126	19	[	[	X
cana-6127	126	20	5.9	5.9	NUM
cana-6127	126	21	]	]	PUNCT
cana-6127	126	22	and	and	CCONJ
cana-6127	126	23	[	[	X
cana-6127	126	24	6.1	6.1	NUM
cana-6127	126	25	]	]	PUNCT
cana-6127	126	26	in	in	ADP
cana-6127	126	27	equations	equation	NOUN
cana-6127	126	28	[	[	X
cana-6127	126	29	4.5	4.5	NUM
cana-6127	126	30	]	]	PUNCT
cana-6127	126	31	to	to	ADP
cana-6127	126	32	[	[	X
cana-6127	126	33	4.7	4.7	NUM
cana-6127	126	34	]	]	PUNCT
cana-6127	126	35	,	,	PUNCT
cana-6127	126	36	one	one	NOUN
cana-6127	126	37	obtains	obtain	VERB
cana-6127	126	38	expressions	expression	NOUN
cana-6127	126	39	for	for	ADP
cana-6127	126	40	thermal	thermal	ADJ
cana-6127	126	41	stresses	stress	NOUN
cana-6127	126	42	as	as	ADP
cana-6127	126	43	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-6127	126	44	=	=	SYM
cana-6127	126	45	−8𝐸	−8𝐸	PROPN
cana-6127	126	46	𝑎𝑏𝑐	𝑎𝑏𝑐	ADJ
cana-6127	126	47	∑	∑	PROPN
cana-6127	126	48	∑∑sin	∑∑sin	PROPN
cana-6127	126	49	∞	∞	PROPN
cana-6127	126	50	𝑝=0	𝑝=0	PROPN
cana-6127	126	51	∞	∞	PROPN
cana-6127	126	52	𝑛=0	𝑛=0	PROPN
cana-6127	126	53	∞	∞	NUM
cana-6127	126	54	𝑚=0	𝑚=0	PUNCT
cana-6127	126	55	(	(	PUNCT
cana-6127	126	56	𝛽𝑚𝑥)sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	𝛽𝑚𝑥)sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	NOUN
cana-6127	126	57	)	)	PUNCT
cana-6127	126	58	(	(	PUNCT
cana-6127	126	59	𝜈𝑛	𝜈𝑛	ADP
cana-6127	126	60	2	2	NUM
cana-6127	126	61	+	+	NUM
cana-6127	126	62	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	126	63	2	2	NUM
cana-6127	126	64	)	)	PUNCT
cana-6127	127	1	𝑘(𝛽𝑚2	𝑘(𝛽𝑚2	VERB
cana-6127	128	1	+	+	NOUN
cana-6127	128	2	𝜈𝑛2	𝜈𝑛2	NOUN
cana-6127	128	3	+	+	NOUN
cana-6127	128	4	𝜂𝑝2	𝜂𝑝2	CCONJ
cana-6127	128	5	)	)	PUNCT
cana-6127	128	6	2	2	NUM
cana-6127	128	7	×	×	NOUN
cana-6127	129	1	[	[	X
cana-6127	129	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	ADP
cana-6127	129	3	2	2	NUM
cana-6127	129	4	+	+	NOUN
cana-6127	129	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	129	6	2	2	NUM
cana-6127	129	7	+	+	NUM
cana-6127	129	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	129	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	129	10	)	)	PUNCT
cana-6127	129	11	]	]	PUNCT
cana-6127	130	1	[	[	X
cana-6127	130	2	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	130	3	,	,	PUNCT
cana-6127	130	4	𝜈𝑛	𝜈𝑛	ADP
cana-6127	130	5	,	,	PUNCT
cana-6127	130	6	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	130	7	)	)	PUNCT
cana-6127	130	8	+	+	CCONJ
cana-6127	130	9	𝑘	𝑘	DET
cana-6127	130	10	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	130	11	×	×	NOUN
cana-6127	130	12	∫	∫	PROPN
cana-6127	131	1	[	[	X
cana-6127	131	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	INTJ
cana-6127	131	3	2	2	NUM
cana-6127	131	4	+	+	NOUN
cana-6127	131	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	131	6	2	2	NUM
cana-6127	131	7	+	+	NUM
cana-6127	131	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	131	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	131	10	)	)	PUNCT
cana-6127	131	11	]	]	PUNCT
cana-6127	132	1	𝑡	𝑡	PROPN
cana-6127	132	2	𝑡′=0	𝑡′=0	PROPN
cana-6127	132	3	𝑔(𝛽𝑚	𝑔(𝛽𝑚	PROPN
cana-6127	132	4	,	,	PUNCT
cana-6127	132	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	132	6	,	,	PUNCT
cana-6127	132	7	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	132	8	,	,	PUNCT
cana-6127	132	9	𝑡	𝑡	PROPN
cana-6127	132	10	′	′	NOUN
cana-6127	132	11	)	)	PUNCT
cana-6127	132	12	]	]	PUNCT
cana-6127	132	13	(	(	PUNCT
cana-6127	132	14	6.5	6.5	NUM
cana-6127	132	15	)	)	PUNCT
cana-6127	132	16	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
cana-6127	132	17	=	=	PUNCT
cana-6127	132	18	−8𝐸	−8𝐸	PROPN
cana-6127	132	19	𝑎𝑏𝑐	𝑎𝑏𝑐	ADJ
cana-6127	132	20	∑	∑	PROPN
cana-6127	132	21	∑∑sin	∑∑sin	PROPN
cana-6127	132	22	∞	∞	PROPN
cana-6127	132	23	𝑝=0	𝑝=0	PROPN
cana-6127	132	24	∞	∞	PROPN
cana-6127	132	25	𝑛=0	𝑛=0	PROPN
cana-6127	132	26	∞	∞	NUM
cana-6127	132	27	𝑚=0	𝑚=0	PUNCT
cana-6127	132	28	(	(	PUNCT
cana-6127	132	29	𝛽𝑚𝑥)sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	𝛽𝑚𝑥)sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	NOUN
cana-6127	132	30	)	)	PUNCT
cana-6127	132	31	(	(	PUNCT
cana-6127	132	32	𝛽𝑚	𝛽𝑚	ADP
cana-6127	132	33	2	2	NUM
cana-6127	132	34	+	+	CCONJ
cana-6127	132	35	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	132	36	2	2	NUM
cana-6127	132	37	)	)	PUNCT
cana-6127	132	38	𝑘(𝛽𝑚2	𝑘(𝛽𝑚2	VERB
cana-6127	133	1	+	+	NOUN
cana-6127	133	2	𝜈𝑛2	𝜈𝑛2	NOUN
cana-6127	133	3	+	+	NOUN
cana-6127	133	4	𝜂𝑝2	𝜂𝑝2	CCONJ
cana-6127	133	5	)	)	PUNCT
cana-6127	133	6	2	2	NUM
cana-6127	133	7	×	×	NOUN
cana-6127	134	1	[	[	X
cana-6127	134	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	ADP
cana-6127	134	3	2	2	NUM
cana-6127	134	4	+	+	NOUN
cana-6127	134	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	134	6	2	2	NUM
cana-6127	134	7	+	+	NUM
cana-6127	134	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	134	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	134	10	)	)	PUNCT
cana-6127	134	11	]	]	PUNCT
cana-6127	135	1	[	[	X
cana-6127	135	2	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	135	3	,	,	PUNCT
cana-6127	135	4	𝜈𝑛	𝜈𝑛	ADP
cana-6127	135	5	,	,	PUNCT
cana-6127	135	6	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	135	7	)	)	PUNCT
cana-6127	135	8	+	+	CCONJ
cana-6127	135	9	𝑘	𝑘	DET
cana-6127	135	10	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	135	11	×∫	×∫	PROPN
cana-6127	135	12	[	[	X
cana-6127	135	13	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	PRON
cana-6127	135	14	2	2	NUM
cana-6127	135	15	+	+	NOUN
cana-6127	135	16	𝜈𝑛	𝜈𝑛	ADP
cana-6127	135	17	2	2	NUM
cana-6127	135	18	+	+	NUM
cana-6127	135	19	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	135	20	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	135	21	)	)	PUNCT
cana-6127	135	22	]	]	PUNCT
cana-6127	136	1	𝑡	𝑡	PROPN
cana-6127	136	2	𝑡′=0	𝑡′=0	PROPN
cana-6127	136	3	𝑔(𝛽𝑚	𝑔(𝛽𝑚	PROPN
cana-6127	136	4	,	,	PUNCT
cana-6127	136	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	136	6	,	,	PUNCT
cana-6127	136	7	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	136	8	,	,	PUNCT
cana-6127	136	9	𝑡	𝑡	PROPN
cana-6127	136	10	′	′	NOUN
cana-6127	136	11	)	)	PUNCT
cana-6127	136	12	]	]	PUNCT
cana-6127	136	13	(	(	PUNCT
cana-6127	136	14	6.6	6.6	NUM
cana-6127	136	15	)	)	PUNCT
cana-6127	136	16	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6127	136	17	=	=	PUNCT
cana-6127	136	18	−8𝐸	−8𝐸	PROPN
cana-6127	136	19	𝑎𝑏𝑐	𝑎𝑏𝑐	ADJ
cana-6127	136	20	∑	∑	PROPN
cana-6127	136	21	∑∑sin	∑∑sin	PROPN
cana-6127	136	22	∞	∞	PROPN
cana-6127	136	23	𝑝=0	𝑝=0	PROPN
cana-6127	136	24	∞	∞	PROPN
cana-6127	136	25	𝑛=0	𝑛=0	PROPN
cana-6127	136	26	∞	∞	NUM
cana-6127	136	27	𝑚=0	𝑚=0	PUNCT
cana-6127	136	28	(	(	PUNCT
cana-6127	136	29	𝛽𝑚𝑥)sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	𝛽𝑚𝑥)sin(𝜈𝑛𝑦)sin(𝜂𝑝𝑧	NOUN
cana-6127	136	30	)	)	PUNCT
cana-6127	136	31	(	(	PUNCT
cana-6127	136	32	𝛽𝑚	𝛽𝑚	ADV
cana-6127	136	33	2	2	NUM
cana-6127	136	34	+	+	CCONJ
cana-6127	136	35	𝜈𝑛	𝜈𝑛	ADP
cana-6127	136	36	2	2	NUM
cana-6127	136	37	)	)	PUNCT
cana-6127	136	38	𝑘(𝛽𝑚2	𝑘(𝛽𝑚2	NOUN
cana-6127	137	1	+	+	NOUN
cana-6127	137	2	𝜈𝑛2	𝜈𝑛2	NOUN
cana-6127	137	3	+	+	NOUN
cana-6127	137	4	𝜂𝑝2	𝜂𝑝2	CCONJ
cana-6127	137	5	)	)	PUNCT
cana-6127	137	6	2	2	NUM
cana-6127	137	7	×	×	NOUN
cana-6127	138	1	[	[	X
cana-6127	138	2	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	ADP
cana-6127	138	3	2	2	NUM
cana-6127	138	4	+	+	NOUN
cana-6127	138	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	138	6	2	2	NUM
cana-6127	138	7	+	+	NUM
cana-6127	138	8	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	138	9	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	138	10	)	)	PUNCT
cana-6127	138	11	]	]	PUNCT
cana-6127	139	1	[	[	X
cana-6127	139	2	𝑓(𝛽𝑚	𝑓(𝛽𝑚	NOUN
cana-6127	139	3	,	,	PUNCT
cana-6127	139	4	𝜈𝑛	𝜈𝑛	ADP
cana-6127	139	5	,	,	PUNCT
cana-6127	139	6	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	139	7	)	)	PUNCT
cana-6127	139	8	+	+	CCONJ
cana-6127	139	9	𝑘	𝑘	DET
cana-6127	139	10	𝑘𝑡	𝑘𝑡	NOUN
cana-6127	139	11	×∫	×∫	PROPN
cana-6127	139	12	[	[	X
cana-6127	139	13	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	𝑡𝛼−1𝐸𝛼,𝛼(−𝑘(𝛽𝑚	PRON
cana-6127	139	14	2	2	NUM
cana-6127	139	15	+	+	NOUN
cana-6127	139	16	𝜈𝑛	𝜈𝑛	ADP
cana-6127	139	17	2	2	NUM
cana-6127	139	18	+	+	NUM
cana-6127	139	19	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	139	20	2)𝑡𝛼	2)𝑡𝛼	PROPN
cana-6127	139	21	)	)	PUNCT
cana-6127	139	22	]	]	PUNCT
cana-6127	140	1	𝑡	𝑡	PROPN
cana-6127	140	2	𝑡′=0	𝑡′=0	PROPN
cana-6127	140	3	𝑔(𝛽𝑚	𝑔(𝛽𝑚	PROPN
cana-6127	140	4	,	,	PUNCT
cana-6127	140	5	𝜈𝑛	𝜈𝑛	ADP
cana-6127	140	6	,	,	PUNCT
cana-6127	140	7	𝜂𝑝	𝜂𝑝	NOUN
cana-6127	140	8	,	,	PUNCT
cana-6127	140	9	𝑡	𝑡	PROPN
cana-6127	140	10	′	′	NOUN
cana-6127	140	11	)	)	PUNCT
cana-6127	140	12	]	]	PUNCT
cana-6127	140	13	(	(	PUNCT
cana-6127	140	14	6.7	6.7	NUM
cana-6127	140	15	)	)	PUNCT
cana-6127	140	16	7	7	NUM
cana-6127	140	17	.	.	PUNCT
cana-6127	140	18	numerical	numerical	ADJ
cana-6127	140	19	calculations	calculation	NOUN
cana-6127	140	20	and	and	CCONJ
cana-6127	140	21	discussion	discussion	NOUN
cana-6127	140	22	setting	set	VERB
cana-6127	140	23	𝑓(𝑥	𝑓(𝑥	NOUN
cana-6127	140	24	,	,	PUNCT
cana-6127	140	25	𝑦	𝑦	NOUN
cana-6127	140	26	,	,	PUNCT
cana-6127	140	27	𝑧	𝑧	NOUN
cana-6127	140	28	)	)	PUNCT
cana-6127	140	29	=	=	SYM
cana-6127	140	30	𝑒𝑡(𝑎	𝑒𝑡(𝑎	NUM
cana-6127	140	31	−	−	PROPN
cana-6127	140	32	𝑥)(1	𝑥)(1	X
cana-6127	140	33	−	−	PROPN
cana-6127	140	34	𝑒𝑥)(𝑏	𝑒𝑥)(𝑏	PROPN
cana-6127	140	35	−	−	PROPN
cana-6127	140	36	𝑦)(1	𝑦)(1	NUM
cana-6127	140	37	−	−	PROPN
cana-6127	140	38	𝑒𝑦)(𝑐	𝑒𝑦)(𝑐	PROPN
cana-6127	140	39	−	−	PROPN
cana-6127	140	40	𝑧)(1	𝑧)(1	PRON
cana-6127	140	41	−	−	PROPN
cana-6127	140	42	𝑒𝑧	𝑒𝑧	PROPN
cana-6127	140	43	)	)	PUNCT
cana-6127	140	44	,	,	PUNCT
cana-6127	140	45	𝑔(𝑥	𝑔(𝑥	PROPN
cana-6127	140	46	,	,	PUNCT
cana-6127	140	47	𝑦	𝑦	NOUN
cana-6127	140	48	,	,	PUNCT
cana-6127	140	49	𝑧	𝑧	NOUN
cana-6127	140	50	,	,	PUNCT
cana-6127	140	51	𝑡	𝑡	NOUN
cana-6127	140	52	)	)	PUNCT
cana-6127	140	53	=	=	PUNCT
cana-6127	140	54	𝑔𝑖𝛿(𝑥	𝑔𝑖𝛿(𝑥	VERB
cana-6127	140	55	−	−	ADP
cana-6127	140	56	𝑥1)𝛿(𝑦	𝑥1)𝛿(𝑦	ADJ
cana-6127	140	57	−	−	PROPN
cana-6127	140	58	𝑦1)𝛿(𝑧	𝑦1)𝛿(𝑧	PROPN
cana-6127	140	59	−	−	NOUN
cana-6127	140	60	𝑧1)𝛿(𝑡	𝑧1)𝛿(𝑡	PROPN
cana-6127	140	61	−	−	PROPN
cana-6127	140	62	𝜏	𝜏	NOUN
cana-6127	140	63	)	)	PUNCT
cana-6127	140	64	where	where	SCONJ
cana-6127	140	65	𝛿	𝛿	PROPN
cana-6127	140	66	is	be	AUX
cana-6127	140	67	the	the	DET
cana-6127	140	68	derac	derac	NOUN
cana-6127	140	69	-	-	PUNCT
cana-6127	140	70	delta	delta	NOUN
cana-6127	140	71	function	function	NOUN
cana-6127	140	72	and	and	CCONJ
cana-6127	140	73	𝑔(𝑥	𝑔(𝑥	PROPN
cana-6127	140	74	,	,	PUNCT
cana-6127	140	75	𝑦	𝑦	NOUN
cana-6127	140	76	,	,	PUNCT
cana-6127	140	77	𝑧	𝑧	NOUN
cana-6127	140	78	,	,	PUNCT
cana-6127	140	79	𝑡	𝑡	X
cana-6127	140	80	)	)	PUNCT
cana-6127	140	81	is	be	AUX
cana-6127	140	82	an	an	DET
cana-6127	140	83	instantaneous	instantaneous	ADJ
cana-6127	140	84	line	line	NOUN
cana-6127	140	85	heat	heat	NOUN
cana-6127	140	86	source	source	NOUN
cana-6127	140	87	situated	situate	VERB
cana-6127	140	88	at	at	ADP
cana-6127	140	89	the	the	DET
cana-6127	140	90	center	center	NOUN
cana-6127	140	91	of	of	ADP
cana-6127	140	92	the	the	DET
cana-6127	140	93	rectangular	rectangular	ADJ
cana-6127	140	94	plates	plate	NOUN
cana-6127	140	95	.	.	PUNCT
cana-6127	141	1	dimension	dimension	NOUN
cana-6127	141	2	length	length	NOUN
cana-6127	141	3	of	of	ADP
cana-6127	141	4	rectangular	rectangular	ADJ
cana-6127	141	5	plate	plate	NOUN
cana-6127	141	6	𝑎	𝑎	NOUN
cana-6127	141	7	=	=	SYM
cana-6127	141	8	3	3	NUM
cana-6127	141	9	ft	ft	NOUN
cana-6127	141	10	breadth	breadth	NOUN
cana-6127	141	11	of	of	ADP
cana-6127	141	12	rectangular	rectangular	ADJ
cana-6127	141	13	plate	plate	NOUN
cana-6127	141	14	𝑏	𝑏	NOUN
cana-6127	141	15	=	=	SYM
cana-6127	141	16	2	2	NUM
cana-6127	141	17	ft	ft	NOUN
cana-6127	141	18	height	height	NOUN
cana-6127	141	19	of	of	ADP
cana-6127	141	20	rectangular	rectangular	ADJ
cana-6127	141	21	plate	plate	NOUN
cana-6127	141	22	𝑐	𝑐	NOUN
cana-6127	141	23	=	=	SYM
cana-6127	141	24	1	1	NUM
cana-6127	141	25	ft	ft	ADP
cana-6127	141	26	central	central	ADJ
cana-6127	141	27	length	length	NOUN
cana-6127	141	28	of	of	ADP
cana-6127	141	29	rectangular	rectangular	ADJ
cana-6127	141	30	plate	plate	NOUN
cana-6127	141	31	𝑥1	𝑥1	NOUN
cana-6127	141	32	=	=	NOUN
cana-6127	141	33	1.5	1.5	NUM
cana-6127	141	34	ft	ft	NOUN
cana-6127	141	35	communications	communication	NOUN
cana-6127	141	36	on	on	ADP
cana-6127	141	37	applied	apply	VERB
cana-6127	141	38	nonlinear	nonlinear	ADJ
cana-6127	141	39	analysis	analysis	NOUN
cana-6127	141	40	issn	issn	NOUN
cana-6127	141	41	:	:	PUNCT
cana-6127	141	42	1074	1074	NUM
cana-6127	141	43	-	-	PUNCT
cana-6127	141	44	133x	133x	NUM
cana-6127	141	45	vol	vol	VERB
cana-6127	141	46	32	32	NUM
cana-6127	141	47	no	no	NOUN
cana-6127	141	48	.	.	PUNCT
cana-6127	142	1	10s	10	NOUN
cana-6127	142	2	(	(	PUNCT
cana-6127	142	3	2025	2025	NUM
cana-6127	142	4	)	)	PUNCT
cana-6127	142	5	3467	3467	NUM
cana-6127	142	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	142	7	central	central	ADJ
cana-6127	142	8	breadth	breadth	NOUN
cana-6127	142	9	of	of	ADP
cana-6127	142	10	rectangular	rectangular	ADJ
cana-6127	142	11	plate	plate	NOUN
cana-6127	142	12	𝑦1	𝑦1	NOUN
cana-6127	142	13	=	=	SYM
cana-6127	142	14	1	1	NUM
cana-6127	142	15	ft	ft	NOUN
cana-6127	142	16	central	central	ADJ
cana-6127	142	17	1eight	1eight	NUM
cana-6127	142	18	of	of	ADP
cana-6127	142	19	rectangular	rectangular	ADJ
cana-6127	142	20	plate	plate	NOUN
cana-6127	142	21	𝑧1	𝑧1	NOUN
cana-6127	142	22	=	=	SYM
cana-6127	142	23	0.5	0.5	NUM
cana-6127	142	24	ft	ft	NOUN
cana-6127	142	25	for	for	ADP
cana-6127	142	26	the	the	DET
cana-6127	142	27	purpose	purpose	NOUN
cana-6127	142	28	of	of	ADP
cana-6127	142	29	doing	do	VERB
cana-6127	142	30	a	a	DET
cana-6127	142	31	numerical	numerical	ADJ
cana-6127	142	32	calculation	calculation	NOUN
cana-6127	142	33	for	for	ADP
cana-6127	142	34	a	a	DET
cana-6127	142	35	thick	thick	ADJ
cana-6127	142	36	rectangular	rectangular	ADJ
cana-6127	142	37	plate	plate	NOUN
cana-6127	142	38	,	,	PUNCT
cana-6127	142	39	the	the	DET
cana-6127	142	40	material	material	NOUN
cana-6127	142	41	aluminium	aluminium	NOUN
cana-6127	142	42	(	(	PUNCT
cana-6127	142	43	pure	pure	ADJ
cana-6127	142	44	)	)	PUNCT
cana-6127	142	45	was	be	AUX
cana-6127	142	46	selected	select	VERB
cana-6127	142	47	.	.	PUNCT
cana-6127	143	1	ptc	ptc	PROPN
cana-6127	143	2	mathcad	mathcad	PROPN
cana-6127	143	3	prime	prime	PROPN
cana-6127	143	4	,	,	PUNCT
cana-6127	143	5	a	a	DET
cana-6127	143	6	computational	computational	ADJ
cana-6127	143	7	mathematical	mathematical	ADJ
cana-6127	143	8	software	software	NOUN
cana-6127	143	9	,	,	PUNCT
cana-6127	143	10	was	be	AUX
cana-6127	143	11	used	use	VERB
cana-6127	143	12	to	to	PART
cana-6127	143	13	create	create	VERB
cana-6127	143	14	the	the	DET
cana-6127	143	15	numerical	numerical	ADJ
cana-6127	143	16	calculations	calculation	NOUN
cana-6127	143	17	and	and	CCONJ
cana-6127	143	18	graphics	graphic	NOUN
cana-6127	143	19	.	.	PUNCT
cana-6127	144	1	the	the	DET
cana-6127	144	2	aluminium	aluminium	NOUN
cana-6127	144	3	(	(	PUNCT
cana-6127	144	4	pure	pure	ADJ
cana-6127	144	5	)	)	PUNCT
cana-6127	144	6	material	material	NOUN
cana-6127	144	7	was	be	AUX
cana-6127	144	8	chosen	choose	VERB
cana-6127	144	9	for	for	ADP
cana-6127	144	10	purposes	purpose	NOUN
cana-6127	144	11	of	of	ADP
cana-6127	144	12	numerical	numerical	ADJ
cana-6127	144	13	evaluations	evaluation	NOUN
cana-6127	144	14	.	.	PUNCT
cana-6127	145	1	the	the	DET
cana-6127	145	2	parameters	parameter	NOUN
cana-6127	145	3	of	of	ADP
cana-6127	145	4	the	the	DET
cana-6127	145	5	problem	problem	NOUN
cana-6127	145	6	are	be	AUX
cana-6127	145	7	given	give	VERB
cana-6127	145	8	in	in	ADP
cana-6127	145	9	fps	fps	PROPN
cana-6127	145	10	units	unit	NOUN
cana-6127	145	11	,	,	PUNCT
cana-6127	145	12	as	as	SCONJ
cana-6127	145	13	illustrated	illustrate	VERB
cana-6127	145	14	in	in	ADP
cana-6127	145	15	table	table	NOUN
cana-6127	145	16	1	1	NUM
cana-6127	145	17	.	.	PUNCT
cana-6127	145	18	table	table	NOUN
cana-6127	145	19	-1	-1	NOUN
cana-6127	145	20	:	:	PUNCT
cana-6127	145	21	material	material	ADJ
cana-6127	145	22	constant	constant	ADJ
cana-6127	145	23	physical	physical	ADJ
cana-6127	145	24	constant	constant	ADJ
cana-6127	145	25	value	value	NOUN
cana-6127	145	26	thermal	thermal	ADJ
cana-6127	145	27	diffusivity	diffusivity	NOUN
cana-6127	145	28	(	(	PUNCT
cana-6127	145	29	k	k	NOUN
cana-6127	145	30	)	)	PUNCT
cana-6127	145	31	3.33	3.33	NUM
cana-6127	145	32	ft2	ft2	NOUN
cana-6127	145	33	/	/	SYM
cana-6127	145	34	hr	hr	NOUN
cana-6127	145	35	thermal	thermal	ADJ
cana-6127	145	36	conductivity	conductivity	NOUN
cana-6127	145	37	(	(	PUNCT
cana-6127	145	38	𝑘𝑡	𝑘𝑡	PROPN
cana-6127	145	39	)	)	PUNCT
cana-6127	145	40	117	117	NUM
cana-6127	145	41	btu/(hr.ft.0f	btu/(hr.ft.0f	NOUN
cana-6127	145	42	)	)	PUNCT
cana-6127	145	43	density	density	NOUN
cana-6127	145	44	(	(	PUNCT
cana-6127	145	45	𝜌	𝜌	NOUN
cana-6127	145	46	)	)	PUNCT
cana-6127	145	47	169	169	NUM
cana-6127	145	48	lb	lb	NUM
cana-6127	145	49	/	/	SYM
cana-6127	145	50	ft3	ft3	NOUN
cana-6127	145	51	specific	specific	ADJ
cana-6127	145	52	heat	heat	NOUN
cana-6127	145	53	(	(	PUNCT
cana-6127	145	54	𝑐𝑝	𝑐𝑝	NOUN
cana-6127	145	55	)	)	PUNCT
cana-6127	145	56	0.208	0.208	NUM
cana-6127	145	57	btu/(lb.0f	btu/(lb.0f	NOUN
cana-6127	145	58	)	)	PUNCT
cana-6127	145	59	coefficient	coefficient	NOUN
cana-6127	145	60	of	of	ADP
cana-6127	145	61	linear	linear	ADJ
cana-6127	145	62	thermal	thermal	ADJ
cana-6127	145	63	expansion	expansion	NOUN
cana-6127	145	64	(	(	PUNCT
cana-6127	145	65	𝑎𝑡	𝑎𝑡	PROPN
cana-6127	145	66	)	)	PUNCT
cana-6127	145	67	12.84×10−6	12.84×10−6	PROPN
cana-6127	145	68	1	1	NUM
cana-6127	145	69	/	/	SYM
cana-6127	145	70	f	f	PROPN
cana-6127	145	71	poisson	poisson	PROPN
cana-6127	145	72	ratio	ratio	PROPN
cana-6127	145	73	(	(	PUNCT
cana-6127	145	74	𝜈	𝜈	X
cana-6127	145	75	)	)	PUNCT
cana-6127	145	76	0.35	0.35	NUM
cana-6127	145	77	lame	lame	NOUN
cana-6127	145	78	’s	’s	PART
cana-6127	145	79	constants	constant	NOUN
cana-6127	145	80	(	(	PUNCT
cana-6127	145	81	𝜇	𝜇	ADP
cana-6127	145	82	)	)	PUNCT
cana-6127	145	83	26.67	26.67	NUM
cana-6127	145	84	young	young	PROPN
cana-6127	145	85	’s	’s	PART
cana-6127	145	86	modulus	modulus	NOUN
cana-6127	145	87	(	(	PUNCT
cana-6127	145	88	𝐸	𝐸	PROPN
cana-6127	145	89	)	)	PUNCT
cana-6127	145	90	70	70	NUM
cana-6127	145	91	gpa	gpa	NOUN
cana-6127	145	92	in	in	ADP
cana-6127	145	93	this	this	DET
cana-6127	145	94	section	section	NOUN
cana-6127	145	95	,	,	PUNCT
cana-6127	145	96	we	we	PRON
cana-6127	145	97	analysed	analyse	VERB
cana-6127	145	98	a	a	DET
cana-6127	145	99	fractional	fractional	ADJ
cana-6127	145	100	heat	heat	NOUN
cana-6127	145	101	conduction	conduction	NOUN
cana-6127	145	102	problem	problem	NOUN
cana-6127	145	103	for	for	ADP
cana-6127	145	104	a	a	DET
cana-6127	145	105	thick	thick	ADJ
cana-6127	145	106	rectangular	rectangular	ADJ
cana-6127	145	107	plate	plate	NOUN
cana-6127	145	108	.	.	PUNCT
cana-6127	146	1	we	we	PRON
cana-6127	146	2	have	have	AUX
cana-6127	146	3	discussed	discuss	VERB
cana-6127	146	4	the	the	DET
cana-6127	146	5	variation	variation	NOUN
cana-6127	146	6	of	of	ADP
cana-6127	146	7	temperature	temperature	NOUN
cana-6127	146	8	,	,	PUNCT
cana-6127	146	9	displacement	displacement	NOUN
cana-6127	146	10	and	and	CCONJ
cana-6127	146	11	thermal	thermal	ADJ
cana-6127	146	12	stresses	stress	NOUN
cana-6127	146	13	for	for	ADP
cana-6127	146	14	different	different	ADJ
cana-6127	146	15	values	value	NOUN
cana-6127	146	16	of	of	ADP
cana-6127	146	17	fractional	fractional	ADJ
cana-6127	146	18	-	-	PUNCT
cana-6127	146	19	order	order	NOUN
cana-6127	146	20	parameter	parameter	NOUN
cana-6127	146	21	𝛼	𝛼	NOUN
cana-6127	146	22	=	=	NOUN
cana-6127	146	23	0.5,1,1.5,2	0.5,1,1.5,2	PROPN
cana-6127	146	24	.	.	PUNCT
cana-6127	147	1	the	the	DET
cana-6127	147	2	graphs	graph	NOUN
cana-6127	147	3	are	be	AUX
cana-6127	147	4	plotted	plot	VERB
cana-6127	147	5	for	for	ADP
cana-6127	147	6	different	different	ADJ
cana-6127	147	7	fractional	fractional	ADJ
cana-6127	147	8	-	-	PUNCT
cana-6127	147	9	order	order	NOUN
cana-6127	147	10	parameter	parameter	NOUN
cana-6127	147	11	𝛼	𝛼	NOUN
cana-6127	147	12	=	=	NOUN
cana-6127	147	13	0.5,1,1.5,2	0.5,1,1.5,2	NOUN
cana-6127	147	14	at	at	ADP
cana-6127	147	15	time	time	NOUN
cana-6127	147	16	𝑡	𝑡	PROPN
cana-6127	147	17	=	=	SYM
cana-6127	147	18	1	1	NUM
cana-6127	147	19	hr	hr	NOUN
cana-6127	147	20	.	.	PUNCT
cana-6127	147	21	figure	figure	NOUN
cana-6127	147	22	2	2	NUM
cana-6127	147	23	shows	show	VERB
cana-6127	147	24	the	the	DET
cana-6127	147	25	temperature	temperature	NOUN
cana-6127	147	26	distribution	distribution	NOUN
cana-6127	147	27	for	for	ADP
cana-6127	147	28	different	different	ADJ
cana-6127	147	29	values	value	NOUN
cana-6127	147	30	of	of	ADP
cana-6127	147	31	fractional	fractional	ADJ
cana-6127	147	32	-	-	PUNCT
cana-6127	147	33	order	order	NOUN
cana-6127	147	34	parameter	parameter	NOUN
cana-6127	147	35	𝛼	𝛼	NOUN
cana-6127	147	36	=	=	NOUN
cana-6127	147	37	0.5,1,1.5,2	0.5,1,1.5,2	NOUN
cana-6127	147	38	in	in	ADP
cana-6127	147	39	𝑋-direction	𝑋-direction	PROPN
cana-6127	147	40	.	.	PUNCT
cana-6127	148	1	it	it	PRON
cana-6127	148	2	is	be	AUX
cana-6127	148	3	observed	observe	VERB
cana-6127	148	4	that	that	SCONJ
cana-6127	148	5	,	,	PUNCT
cana-6127	148	6	the	the	DET
cana-6127	148	7	magnitude	magnitude	NOUN
cana-6127	148	8	of	of	ADP
cana-6127	148	9	the	the	DET
cana-6127	148	10	temperature	temperature	NOUN
cana-6127	148	11	increases	increase	VERB
cana-6127	148	12	with	with	ADP
cana-6127	148	13	decrease	decrease	NOUN
cana-6127	148	14	the	the	DET
cana-6127	148	15	value	value	NOUN
cana-6127	148	16	of	of	ADP
cana-6127	148	17	fractional	fractional	ADJ
cana-6127	148	18	-	-	PUNCT
cana-6127	148	19	order	order	NOUN
cana-6127	148	20	parameter	parameter	NOUN
cana-6127	148	21	𝛼	𝛼	NOUN
cana-6127	148	22	and	and	CCONJ
cana-6127	148	23	it	it	PRON
cana-6127	148	24	attains	attain	VERB
cana-6127	148	25	its	its	PRON
cana-6127	148	26	peak	peak	NOUN
cana-6127	148	27	at	at	ADP
cana-6127	148	28	𝑥	𝑥	NOUN
cana-6127	148	29	=	=	SYM
cana-6127	148	30	1.5	1.5	NUM
cana-6127	148	31	.	.	PUNCT
cana-6127	149	1	also	also	ADV
cana-6127	149	2	,	,	PUNCT
cana-6127	149	3	it	it	PRON
cana-6127	149	4	is	be	AUX
cana-6127	149	5	zero	zero	NUM
cana-6127	149	6	at	at	ADP
cana-6127	149	7	both	both	DET
cana-6127	149	8	edges	edge	NOUN
cana-6127	149	9	(	(	PUNCT
cana-6127	149	10	𝑥	𝑥	NOUN
cana-6127	149	11	=	=	SYM
cana-6127	149	12	0	0	NUM
cana-6127	149	13	and	and	CCONJ
cana-6127	149	14	𝑥	𝑥	NOUN
cana-6127	149	15	=	=	SYM
cana-6127	149	16	3	3	NUM
cana-6127	149	17	)	)	PUNCT
cana-6127	149	18	of	of	ADP
cana-6127	149	19	the	the	DET
cana-6127	149	20	rectangular	rectangular	ADJ
cana-6127	149	21	plate	plate	NOUN
cana-6127	149	22	along	along	ADP
cana-6127	149	23	the	the	DET
cana-6127	149	24	𝑋-direction	𝑋-direction	PROPN
cana-6127	149	25	and	and	CCONJ
cana-6127	149	26	it	it	PRON
cana-6127	149	27	shows	show	VERB
cana-6127	149	28	the	the	DET
cana-6127	149	29	normal	normal	ADJ
cana-6127	149	30	curve	curve	NOUN
cana-6127	149	31	.	.	PUNCT
cana-6127	150	1	figures	figure	NOUN
cana-6127	151	1	3–5	3–5	NUM
cana-6127	151	2	show	show	VERB
cana-6127	151	3	the	the	DET
cana-6127	151	4	displacement	displacement	ADJ
cana-6127	151	5	distribution	distribution	NOUN
cana-6127	151	6	functions	function	NOUN
cana-6127	151	7	𝑢𝑥	𝑢𝑥	ADP
cana-6127	151	8	,	,	PUNCT
cana-6127	151	9	𝑢𝑦	𝑢𝑦	PROPN
cana-6127	151	10	and	and	CCONJ
cana-6127	151	11	𝑢𝑧	𝑢𝑧	PROPN
cana-6127	151	12	in	in	ADP
cana-6127	151	13	𝑋	𝑋	PROPN
cana-6127	151	14	,	,	PUNCT
cana-6127	151	15	𝑌	𝑌	PROPN
cana-6127	151	16	and	and	CCONJ
cana-6127	151	17	𝑍-directions	𝑍-directions	PROPN
cana-6127	151	18	for	for	ADP
cana-6127	151	19	different	different	ADJ
cana-6127	151	20	values	value	NOUN
cana-6127	151	21	of	of	ADP
cana-6127	151	22	𝛼.	𝛼.	NOUN
cana-6127	151	23	it	it	PRON
cana-6127	151	24	is	be	AUX
cana-6127	151	25	clear	clear	ADJ
cana-6127	151	26	that	that	SCONJ
cana-6127	151	27	,	,	PUNCT
cana-6127	151	28	the	the	DET
cana-6127	151	29	displacement	displacement	NOUN
cana-6127	151	30	functions	function	NOUN
cana-6127	151	31	increase	increase	VERB
cana-6127	151	32	from	from	ADP
cana-6127	151	33	initial	initial	ADJ
cana-6127	151	34	edge	edge	NOUN
cana-6127	151	35	towards	towards	ADP
cana-6127	151	36	the	the	DET
cana-6127	151	37	extreme	extreme	ADJ
cana-6127	151	38	edge	edge	NOUN
cana-6127	151	39	and	and	CCONJ
cana-6127	151	40	it	it	PRON
cana-6127	151	41	becomes	become	VERB
cana-6127	151	42	zero	zero	NUM
cana-6127	151	43	at	at	ADP
cana-6127	151	44	the	the	DET
cana-6127	151	45	middle	middle	ADJ
cana-6127	151	46	part	part	NOUN
cana-6127	151	47	for	for	ADP
cana-6127	151	48	different	different	ADJ
cana-6127	151	49	values	value	NOUN
cana-6127	151	50	of	of	ADP
cana-6127	151	51	𝛼.	𝛼.	ADJ
cana-6127	151	52	figure	figure	NOUN
cana-6127	151	53	6	6	NUM
cana-6127	151	54	-	-	SYM
cana-6127	151	55	8	8	NUM
cana-6127	151	56	shows	show	VERB
cana-6127	151	57	the	the	DET
cana-6127	151	58	stress	stress	NOUN
cana-6127	151	59	distribution	distribution	NOUN
cana-6127	151	60	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-6127	151	61	,	,	PUNCT
cana-6127	151	62	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
cana-6127	151	63	and	and	CCONJ
cana-6127	151	64	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6127	151	65	for	for	ADP
cana-6127	151	66	different	different	ADJ
cana-6127	151	67	values	value	NOUN
cana-6127	151	68	of	of	ADP
cana-6127	151	69	𝛼	𝛼	PRON
cana-6127	151	70	in	in	ADP
cana-6127	151	71	𝑋	𝑋	PROPN
cana-6127	151	72	,	,	PUNCT
cana-6127	151	73	𝑌	𝑌	PROPN
cana-6127	151	74	and	and	CCONJ
cana-6127	151	75	𝑍direction	𝑍direction	PROPN
cana-6127	151	76	respectively	respectively	ADV
cana-6127	151	77	.	.	PUNCT
cana-6127	152	1	we	we	PRON
cana-6127	152	2	observe	observe	VERB
cana-6127	152	3	that	that	SCONJ
cana-6127	152	4	,	,	PUNCT
cana-6127	152	5	the	the	DET
cana-6127	152	6	magnitude	magnitude	NOUN
cana-6127	152	7	of	of	ADP
cana-6127	152	8	both	both	CCONJ
cana-6127	152	9	the	the	DET
cana-6127	152	10	stresses	stress	NOUN
cana-6127	152	11	is	be	AUX
cana-6127	152	12	maximum	maximum	ADJ
cana-6127	152	13	at	at	ADP
cana-6127	152	14	the	the	DET
cana-6127	152	15	middle	middle	ADJ
cana-6127	152	16	part	part	NOUN
cana-6127	152	17	with	with	ADP
cana-6127	152	18	increasing	increase	VERB
cana-6127	152	19	the	the	DET
cana-6127	152	20	value	value	NOUN
cana-6127	152	21	of	of	ADP
cana-6127	152	22	fractional	fractional	ADJ
cana-6127	152	23	-	-	PUNCT
cana-6127	152	24	order	order	NOUN
cana-6127	152	25	parameter	parameter	NOUN
cana-6127	152	26	𝛼	𝛼	NOUN
cana-6127	152	27	and	and	CCONJ
cana-6127	152	28	becomes	become	VERB
cana-6127	152	29	zero	zero	NUM
cana-6127	152	30	at	at	ADP
cana-6127	152	31	the	the	DET
cana-6127	152	32	initial	initial	ADJ
cana-6127	152	33	and	and	CCONJ
cana-6127	152	34	extreme	extreme	ADJ
cana-6127	152	35	edges	edge	NOUN
cana-6127	152	36	in	in	ADP
cana-6127	152	37	the	the	DET
cana-6127	152	38	𝑋	𝑋	PROPN
cana-6127	152	39	,	,	PUNCT
cana-6127	152	40	𝑌	𝑌	PROPN
cana-6127	152	41	and	and	CCONJ
cana-6127	152	42	𝑍-direction	𝑍-direction	PROPN
cana-6127	152	43	respectively	respectively	ADV
cana-6127	152	44	.	.	PUNCT
cana-6127	153	1	also	also	ADV
cana-6127	153	2	,	,	PUNCT
cana-6127	153	3	the	the	DET
cana-6127	153	4	stress	stress	NOUN
cana-6127	153	5	components	component	NOUN
cana-6127	153	6	𝜎𝑥𝑥	𝜎𝑥𝑥	VERB
cana-6127	153	7	,	,	PUNCT
cana-6127	153	8	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
cana-6127	153	9	and	and	CCONJ
cana-6127	153	10	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6127	153	11	are	be	AUX
cana-6127	153	12	compressive	compressive	ADJ
cana-6127	153	13	throughout	throughout	ADP
cana-6127	153	14	the	the	DET
cana-6127	153	15	plate	plate	NOUN
cana-6127	153	16	and	and	CCONJ
cana-6127	153	17	shows	show	VERB
cana-6127	153	18	the	the	DET
cana-6127	153	19	normal	normal	ADJ
cana-6127	153	20	curve	curve	NOUN
cana-6127	153	21	.	.	PUNCT
cana-6127	154	1	communications	communication	NOUN
cana-6127	154	2	on	on	ADP
cana-6127	154	3	applied	apply	VERB
cana-6127	154	4	nonlinear	nonlinear	ADJ
cana-6127	154	5	analysis	analysis	NOUN
cana-6127	154	6	issn	issn	NOUN
cana-6127	154	7	:	:	PUNCT
cana-6127	154	8	1074	1074	NUM
cana-6127	154	9	-	-	PUNCT
cana-6127	154	10	133x	133x	NUM
cana-6127	154	11	vol	vol	VERB
cana-6127	154	12	32	32	NUM
cana-6127	154	13	no	no	NOUN
cana-6127	154	14	.	.	PUNCT
cana-6127	155	1	10s	10	NOUN
cana-6127	155	2	(	(	PUNCT
cana-6127	155	3	2025	2025	NUM
cana-6127	155	4	)	)	PUNCT
cana-6127	155	5	3468	3468	NUM
cana-6127	155	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	155	7	fig	fig	NOUN
cana-6127	155	8	.	.	PUNCT
cana-6127	156	1	2	2	X
cana-6127	156	2	.	.	X
cana-6127	156	3	temperature	temperature	NOUN
cana-6127	156	4	distribution	distribution	NOUN
cana-6127	156	5	for	for	ADP
cana-6127	156	6	different	different	ADJ
cana-6127	156	7	values	value	NOUN
cana-6127	156	8	of	of	ADP
cana-6127	156	9	𝛼	𝛼	PRON
cana-6127	156	10	in	in	ADP
cana-6127	156	11	𝑋-direction	𝑋-direction	PROPN
cana-6127	156	12	.	.	PUNCT
cana-6127	156	13	fig	fig	NOUN
cana-6127	156	14	.	.	PUNCT
cana-6127	157	1	3	3	X
cana-6127	157	2	.	.	X
cana-6127	157	3	displacement	displacement	ADJ
cana-6127	157	4	distribution	distribution	NOUN
cana-6127	157	5	𝑢𝑥	𝑢𝑥	ADP
cana-6127	157	6	for	for	ADP
cana-6127	157	7	different	different	ADJ
cana-6127	157	8	values	value	NOUN
cana-6127	157	9	of	of	ADP
cana-6127	157	10	𝛼	𝛼	PRON
cana-6127	157	11	in	in	ADP
cana-6127	157	12	𝑋-direction	𝑋-direction	PROPN
cana-6127	157	13	.	.	PUNCT
cana-6127	158	1	fig	fig	NOUN
cana-6127	158	2	.	.	PUNCT
cana-6127	159	1	4	4	X
cana-6127	159	2	.	.	X
cana-6127	159	3	displacement	displacement	ADJ
cana-6127	159	4	distribution	distribution	NOUN
cana-6127	159	5	𝑢𝑦	𝑢𝑦	NOUN
cana-6127	159	6	for	for	ADP
cana-6127	159	7	different	different	ADJ
cana-6127	159	8	values	value	NOUN
cana-6127	159	9	of	of	ADP
cana-6127	159	10	𝛼	𝛼	PRON
cana-6127	159	11	in	in	ADP
cana-6127	159	12	𝑌-direction	𝑌-direction	PROPN
cana-6127	159	13	.	.	PUNCT
cana-6127	160	1	communications	communication	NOUN
cana-6127	160	2	on	on	ADP
cana-6127	160	3	applied	apply	VERB
cana-6127	160	4	nonlinear	nonlinear	ADJ
cana-6127	160	5	analysis	analysis	NOUN
cana-6127	160	6	issn	issn	NOUN
cana-6127	160	7	:	:	PUNCT
cana-6127	160	8	1074	1074	NUM
cana-6127	160	9	-	-	PUNCT
cana-6127	160	10	133x	133x	NUM
cana-6127	160	11	vol	vol	VERB
cana-6127	160	12	32	32	NUM
cana-6127	160	13	no	no	NOUN
cana-6127	160	14	.	.	PUNCT
cana-6127	161	1	10s	10	NOUN
cana-6127	161	2	(	(	PUNCT
cana-6127	161	3	2025	2025	NUM
cana-6127	161	4	)	)	PUNCT
cana-6127	161	5	3469	3469	NUM
cana-6127	161	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	161	7	fig	fig	NOUN
cana-6127	161	8	.	.	PUNCT
cana-6127	162	1	5	5	X
cana-6127	162	2	.	.	X
cana-6127	162	3	displacement	displacement	ADJ
cana-6127	162	4	distribution	distribution	NOUN
cana-6127	162	5	𝑢𝑧	𝑢𝑧	PROPN
cana-6127	162	6	for	for	ADP
cana-6127	162	7	different	different	ADJ
cana-6127	162	8	values	value	NOUN
cana-6127	162	9	of	of	ADP
cana-6127	162	10	𝛼	𝛼	PRON
cana-6127	162	11	in	in	ADP
cana-6127	162	12	𝑍-direction	𝑍-direction	PROPN
cana-6127	162	13	.	.	PUNCT
cana-6127	163	1	fig	fig	NOUN
cana-6127	163	2	.	.	PUNCT
cana-6127	164	1	6	6	NUM
cana-6127	164	2	.	.	X
cana-6127	164	3	stress	stress	NOUN
cana-6127	164	4	distribution	distribution	NOUN
cana-6127	164	5	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-6127	164	6	for	for	ADP
cana-6127	164	7	different	different	ADJ
cana-6127	164	8	values	value	NOUN
cana-6127	164	9	of	of	ADP
cana-6127	164	10	𝛼	𝛼	PRON
cana-6127	164	11	in	in	ADP
cana-6127	164	12	𝑋-direction	𝑋-direction	PROPN
cana-6127	164	13	.	.	PUNCT
cana-6127	165	1	fig	fig	NOUN
cana-6127	165	2	.	.	PUNCT
cana-6127	166	1	7	7	X
cana-6127	166	2	.	.	X
cana-6127	166	3	stress	stress	ADJ
cana-6127	166	4	distribution	distribution	NOUN
cana-6127	166	5	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
cana-6127	166	6	for	for	ADP
cana-6127	166	7	different	different	ADJ
cana-6127	166	8	values	value	NOUN
cana-6127	166	9	of	of	ADP
cana-6127	166	10	𝛼	𝛼	PRON
cana-6127	166	11	in	in	ADP
cana-6127	166	12	𝑌-direction	𝑌-direction	PROPN
cana-6127	166	13	.	.	PUNCT
cana-6127	167	1	communications	communication	NOUN
cana-6127	167	2	on	on	ADP
cana-6127	167	3	applied	apply	VERB
cana-6127	167	4	nonlinear	nonlinear	ADJ
cana-6127	167	5	analysis	analysis	NOUN
cana-6127	167	6	issn	issn	NOUN
cana-6127	167	7	:	:	PUNCT
cana-6127	167	8	1074	1074	NUM
cana-6127	167	9	-	-	PUNCT
cana-6127	167	10	133x	133x	NUM
cana-6127	167	11	vol	vol	VERB
cana-6127	167	12	32	32	NUM
cana-6127	167	13	no	no	NOUN
cana-6127	167	14	.	.	PUNCT
cana-6127	168	1	10s	10	NOUN
cana-6127	168	2	(	(	PUNCT
cana-6127	168	3	2025	2025	NUM
cana-6127	168	4	)	)	PUNCT
cana-6127	168	5	3470	3470	NUM
cana-6127	168	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	168	7	fig	fig	NOUN
cana-6127	168	8	.	.	PUNCT
cana-6127	169	1	8	8	NUM
cana-6127	169	2	.	.	X
cana-6127	169	3	stress	stress	NOUN
cana-6127	169	4	distribution	distribution	NOUN
cana-6127	169	5	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6127	169	6	for	for	ADP
cana-6127	169	7	different	different	ADJ
cana-6127	169	8	values	value	NOUN
cana-6127	169	9	of	of	ADP
cana-6127	169	10	𝛼	𝛼	PRON
cana-6127	169	11	in	in	ADP
cana-6127	169	12	𝑍-direction	𝑍-direction	PROPN
cana-6127	169	13	.	.	PUNCT
cana-6127	170	1	8	8	NUM
cana-6127	170	2	.	.	PUNCT
cana-6127	170	3	conclusion	conclusion	NOUN
cana-6127	170	4	in	in	ADP
cana-6127	170	5	this	this	DET
cana-6127	170	6	article	article	NOUN
cana-6127	170	7	,	,	PUNCT
cana-6127	170	8	we	we	PRON
cana-6127	170	9	proposed	propose	VERB
cana-6127	170	10	the	the	DET
cana-6127	170	11	time	time	NOUN
cana-6127	170	12	-	-	PUNCT
cana-6127	170	13	fractional	fractional	ADJ
cana-6127	170	14	heat	heat	NOUN
cana-6127	170	15	conduction	conduction	NOUN
cana-6127	170	16	equation	equation	NOUN
cana-6127	170	17	with	with	ADP
cana-6127	170	18	zero	zero	NUM
cana-6127	170	19	initial	initial	ADJ
cana-6127	170	20	conditions	condition	NOUN
cana-6127	170	21	.	.	PUNCT
cana-6127	171	1	integral	integral	ADJ
cana-6127	171	2	transform	transform	NOUN
cana-6127	171	3	technique	technique	NOUN
cana-6127	171	4	is	be	AUX
cana-6127	171	5	adopted	adopt	VERB
cana-6127	171	6	for	for	ADP
cana-6127	171	7	computing	compute	VERB
cana-6127	171	8	the	the	DET
cana-6127	171	9	temperature	temperature	NOUN
cana-6127	171	10	of	of	ADP
cana-6127	171	11	heat	heat	NOUN
cana-6127	171	12	conduction	conduction	NOUN
cana-6127	171	13	equation	equation	NOUN
cana-6127	171	14	.	.	PUNCT
cana-6127	172	1	the	the	DET
cana-6127	172	2	results	result	NOUN
cana-6127	172	3	are	be	AUX
cana-6127	172	4	obtained	obtain	VERB
cana-6127	172	5	in	in	ADP
cana-6127	172	6	the	the	DET
cana-6127	172	7	form	form	NOUN
cana-6127	172	8	of	of	ADP
cana-6127	172	9	two	two	NUM
cana-6127	172	10	-	-	PUNCT
cana-6127	172	11	parameter	parameter	NOUN
cana-6127	172	12	mittag	mittag	ADJ
cana-6127	172	13	-	-	PUNCT
cana-6127	172	14	leffler	leffler	NOUN
cana-6127	172	15	function	function	NOUN
cana-6127	172	16	.	.	PUNCT
cana-6127	173	1	figures	figure	NOUN
cana-6127	173	2	2	2	NUM
cana-6127	173	3	-	-	SYM
cana-6127	173	4	8	8	NUM
cana-6127	173	5	shows	show	VERB
cana-6127	173	6	the	the	DET
cana-6127	173	7	behavior	behavior	NOUN
cana-6127	173	8	of	of	ADP
cana-6127	173	9	temperature	temperature	NOUN
cana-6127	173	10	,	,	PUNCT
cana-6127	173	11	displacement	displacement	NOUN
cana-6127	173	12	and	and	CCONJ
cana-6127	173	13	thermal	thermal	ADJ
cana-6127	173	14	stresses	stress	NOUN
cana-6127	173	15	along	along	ADP
cana-6127	173	16	𝑋	𝑋	PROPN
cana-6127	173	17	,	,	PUNCT
cana-6127	173	18	𝑌	𝑌	PROPN
cana-6127	173	19	and	and	CCONJ
cana-6127	173	20	𝑍	𝑍	PROPN
cana-6127	173	21	directions	direction	NOUN
cana-6127	173	22	for	for	ADP
cana-6127	173	23	the	the	DET
cana-6127	173	24	different	different	ADJ
cana-6127	173	25	values	value	NOUN
cana-6127	173	26	of	of	ADP
cana-6127	173	27	the	the	DET
cana-6127	173	28	fractional	fractional	ADJ
cana-6127	173	29	-	-	PUNCT
cana-6127	173	30	order	order	NOUN
cana-6127	173	31	parameter	parameter	NOUN
cana-6127	173	32	𝛼	𝛼	NOUN
cana-6127	173	33	=	=	NOUN
cana-6127	173	34	0.5,1,1.5,2	0.5,1,1.5,2	NOUN
cana-6127	173	35	and	and	CCONJ
cana-6127	173	36	shows	show	VERB
cana-6127	173	37	the	the	DET
cana-6127	173	38	variation	variation	NOUN
cana-6127	173	39	between	between	ADP
cana-6127	173	40	classical	classical	ADJ
cana-6127	173	41	and	and	CCONJ
cana-6127	173	42	fractional	fractional	ADJ
cana-6127	173	43	-	-	PUNCT
cana-6127	173	44	order	order	NOUN
cana-6127	173	45	thermoelasticity	thermoelasticity	NOUN
cana-6127	173	46	.	.	PUNCT
cana-6127	174	1	the	the	DET
cana-6127	174	2	following	follow	VERB
cana-6127	174	3	concluding	conclude	VERB
cana-6127	174	4	remakes	remake	NOUN
cana-6127	174	5	can	can	AUX
cana-6127	174	6	be	be	AUX
cana-6127	174	7	considered	consider	VERB
cana-6127	174	8	according	accord	VERB
cana-6127	174	9	to	to	ADP
cana-6127	174	10	the	the	DET
cana-6127	174	11	results	result	NOUN
cana-6127	174	12	of	of	ADP
cana-6127	174	13	the	the	DET
cana-6127	174	14	present	present	ADJ
cana-6127	174	15	study	study	NOUN
cana-6127	174	16	.	.	PUNCT
cana-6127	175	1	1	1	X
cana-6127	175	2	.	.	X
cana-6127	175	3	when	when	SCONJ
cana-6127	175	4	𝛼	𝛼	X
cana-6127	175	5	=	=	SYM
cana-6127	175	6	1	1	NUM
cana-6127	175	7	,	,	PUNCT
cana-6127	175	8	all	all	DET
cana-6127	175	9	the	the	DET
cana-6127	175	10	graphical	graphical	ADJ
cana-6127	175	11	representation	representation	NOUN
cana-6127	175	12	satisfied	satisfy	VERB
cana-6127	175	13	the	the	DET
cana-6127	175	14	heat	heat	NOUN
cana-6127	175	15	diffusion	diffusion	NOUN
cana-6127	175	16	equation	equation	NOUN
cana-6127	175	17	,	,	PUNCT
cana-6127	175	18	whereas	whereas	SCONJ
cana-6127	175	19	𝛼	𝛼	X
cana-6127	175	20	=	=	SYM
cana-6127	175	21	2	2	NUM
cana-6127	175	22	,	,	PUNCT
cana-6127	175	23	gives	give	VERB
cana-6127	175	24	the	the	DET
cana-6127	175	25	representation	representation	NOUN
cana-6127	175	26	of	of	ADP
cana-6127	175	27	wave	wave	NOUN
cana-6127	175	28	equations	equation	NOUN
cana-6127	175	29	.	.	PUNCT
cana-6127	176	1	2	2	X
cana-6127	176	2	.	.	X
cana-6127	176	3	it	it	PRON
cana-6127	176	4	is	be	AUX
cana-6127	176	5	observed	observe	VERB
cana-6127	176	6	that	that	SCONJ
cana-6127	176	7	,	,	PUNCT
cana-6127	176	8	for	for	ADP
cana-6127	176	9	the	the	DET
cana-6127	176	10	different	different	ADJ
cana-6127	176	11	values	value	NOUN
cana-6127	176	12	of	of	ADP
cana-6127	176	13	the	the	DET
cana-6127	176	14	fractional	fractional	ADJ
cana-6127	176	15	-	-	PUNCT
cana-6127	176	16	order	order	NOUN
cana-6127	176	17	parameter	parameter	NOUN
cana-6127	176	18	𝛼	𝛼	NOUN
cana-6127	176	19	in	in	ADP
cana-6127	176	20	the	the	DET
cana-6127	176	21	𝑋	𝑋	PROPN
cana-6127	176	22	,	,	PUNCT
cana-6127	176	23	𝑌	𝑌	PROPN
cana-6127	176	24	and	and	CCONJ
cana-6127	176	25	𝑍	𝑍	PROPN
cana-6127	176	26	directions	direction	NOUN
cana-6127	176	27	the	the	DET
cana-6127	176	28	effect	effect	NOUN
cana-6127	176	29	temperature	temperature	NOUN
cana-6127	176	30	,	,	PUNCT
cana-6127	176	31	displacement	displacement	NOUN
cana-6127	176	32	and	and	CCONJ
cana-6127	176	33	thermal	thermal	ADJ
cana-6127	176	34	stresses	stress	NOUN
cana-6127	176	35	represents	represent	VERB
cana-6127	176	36	the	the	DET
cana-6127	176	37	weak	weak	ADJ
cana-6127	176	38	,	,	PUNCT
cana-6127	176	39	normal	normal	ADJ
cana-6127	176	40	and	and	CCONJ
cana-6127	176	41	strong	strong	ADJ
cana-6127	176	42	conductivity	conductivity	NOUN
cana-6127	176	43	,	,	PUNCT
cana-6127	176	44	within	within	ADP
cana-6127	176	45	the	the	DET
cana-6127	176	46	range	range	NOUN
cana-6127	176	47	of	of	ADP
cana-6127	176	48	0	0	NUM
cana-6127	176	49	<	<	X
cana-6127	176	50	𝛼	𝛼	X
cana-6127	176	51	<	<	X
cana-6127	176	52	1	1	NUM
cana-6127	176	53	,	,	PUNCT
cana-6127	176	54	𝛼	𝛼	NOUN
cana-6127	176	55	=	=	SYM
cana-6127	176	56	1	1	NUM
cana-6127	176	57	and	and	CCONJ
cana-6127	176	58	1	1	NUM
cana-6127	176	59	<	<	X
cana-6127	176	60	𝛼	𝛼	X
cana-6127	176	61	<	<	X
cana-6127	176	62	2	2	NUM
cana-6127	176	63	respectively	respectively	ADV
cana-6127	176	64	.	.	PUNCT
cana-6127	177	1	3	3	X
cana-6127	177	2	.	.	X
cana-6127	177	3	the	the	DET
cana-6127	177	4	stress	stress	NOUN
cana-6127	177	5	distribution	distribution	NOUN
cana-6127	177	6	functions	function	NOUN
cana-6127	177	7	𝜎𝑥𝑥	𝜎𝑥𝑥	VERB
cana-6127	177	8	,	,	PUNCT
cana-6127	177	9	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
cana-6127	177	10	and	and	CCONJ
cana-6127	177	11	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6127	177	12	are	be	AUX
cana-6127	177	13	tensile	tensile	ADJ
cana-6127	177	14	and	and	CCONJ
cana-6127	177	15	they	they	PRON
cana-6127	177	16	form	form	VERB
cana-6127	177	17	normal	normal	ADJ
cana-6127	177	18	curve	curve	NOUN
cana-6127	177	19	along	along	ADP
cana-6127	177	20	the	the	DET
cana-6127	177	21	𝑋	𝑋	PROPN
cana-6127	177	22	,	,	PUNCT
cana-6127	177	23	𝑌	𝑌	PROPN
cana-6127	177	24	and	and	CCONJ
cana-6127	177	25	𝑍	𝑍	PROPN
cana-6127	177	26	direction	direction	NOUN
cana-6127	177	27	respectively	respectively	ADV
cana-6127	177	28	.	.	PUNCT
cana-6127	178	1	also	also	ADV
cana-6127	178	2	,	,	PUNCT
cana-6127	178	3	they	they	PRON
cana-6127	178	4	are	be	AUX
cana-6127	178	5	directly	directly	ADV
cana-6127	178	6	proportional	proportional	ADJ
cana-6127	178	7	to	to	ADP
cana-6127	178	8	the	the	DET
cana-6127	178	9	different	different	ADJ
cana-6127	178	10	values	value	NOUN
cana-6127	178	11	of	of	ADP
cana-6127	178	12	𝛼	𝛼	PRON
cana-6127	178	13	in	in	ADP
cana-6127	178	14	the	the	DET
cana-6127	178	15	𝑋	𝑋	PROPN
cana-6127	178	16	,	,	PUNCT
cana-6127	178	17	𝑌	𝑌	PROPN
cana-6127	178	18	and	and	CCONJ
cana-6127	178	19	𝑍	𝑍	PROPN
cana-6127	178	20	direction	direction	NOUN
cana-6127	178	21	respectively	respectively	ADV
cana-6127	178	22	.	.	PUNCT
cana-6127	179	1	4	4	X
cana-6127	179	2	.	.	X
cana-6127	179	3	fractional	fractional	ADJ
cana-6127	179	4	order	order	NOUN
cana-6127	179	5	𝛼	𝛼	NOUN
cana-6127	179	6	governs	govern	VERB
cana-6127	179	7	the	the	DET
cana-6127	179	8	non	non	ADJ
cana-6127	179	9	-	-	ADJ
cana-6127	179	10	local	local	ADJ
cana-6127	179	11	behavior	behavior	NOUN
cana-6127	179	12	of	of	ADP
cana-6127	179	13	heat	heat	NOUN
cana-6127	179	14	transfer	transfer	NOUN
cana-6127	179	15	process	process	NOUN
cana-6127	179	16	,	,	PUNCT
cana-6127	179	17	and	and	CCONJ
cana-6127	179	18	then	then	ADV
cana-6127	179	19	alters	alter	VERB
cana-6127	179	20	the	the	DET
cana-6127	179	21	response	response	NOUN
cana-6127	179	22	time	time	NOUN
cana-6127	179	23	and	and	CCONJ
cana-6127	179	24	overshooting	overshoot	VERB
cana-6127	179	25	occurrence	occurrence	NOUN
cana-6127	179	26	of	of	ADP
cana-6127	179	27	the	the	DET
cana-6127	179	28	temperature	temperature	NOUN
cana-6127	179	29	.	.	PUNCT
cana-6127	180	1	larger	large	ADJ
cana-6127	180	2	the	the	DET
cana-6127	180	3	parameter	parameter	NOUN
cana-6127	180	4	𝛼	𝛼	PROPN
cana-6127	180	5	,	,	PUNCT
cana-6127	180	6	the	the	PRON
cana-6127	180	7	slower	slow	ADJ
cana-6127	180	8	the	the	DET
cana-6127	180	9	velocity	velocity	NOUN
cana-6127	180	10	of	of	ADP
cana-6127	180	11	heat	heat	NOUN
cana-6127	180	12	waves	wave	NOUN
cana-6127	180	13	-	-	PUNCT
cana-6127	180	14	like	like	ADJ
cana-6127	180	15	.	.	PUNCT
cana-6127	181	1	its	its	PRON
cana-6127	181	2	effect	effect	NOUN
cana-6127	181	3	is	be	AUX
cana-6127	181	4	limited	limit	VERB
cana-6127	181	5	to	to	ADP
cana-6127	181	6	short	short	ADJ
cana-6127	181	7	times	time	NOUN
cana-6127	181	8	and	and	CCONJ
cana-6127	181	9	disappears	disappear	VERB
cana-6127	181	10	for	for	ADP
cana-6127	181	11	long	long	ADJ
cana-6127	181	12	time	time	NOUN
cana-6127	181	13	.	.	PUNCT
cana-6127	182	1	refrences	refrence	VERB
cana-6127	182	2	[	[	X
cana-6127	182	3	1	1	X
cana-6127	182	4	]	]	PUNCT
cana-6127	182	5	m.	m.	NOUN
cana-6127	182	6	a.	a.	PROPN
cana-6127	182	7	biot	biot	PROPN
cana-6127	182	8	.	.	PROPN
cana-6127	182	9	,	,	PUNCT
cana-6127	182	10	“	"	PUNCT
cana-6127	182	11	thermoelasticity	thermoelasticity	NOUN
cana-6127	182	12	and	and	CCONJ
cana-6127	182	13	irreversible	irreversible	ADJ
cana-6127	182	14	thermodynamics	thermodynamic	NOUN
cana-6127	182	15	”	"	PUNCT
cana-6127	182	16	,	,	PUNCT
cana-6127	182	17	j.	j.	PROPN
cana-6127	182	18	appl	appl	PROPN
cana-6127	182	19	.	.	PUNCT
cana-6127	183	1	phys	phy	NOUN
cana-6127	183	2	,	,	PUNCT
cana-6127	183	3	vol	vol	NOUN
cana-6127	183	4	.	.	PROPN
cana-6127	183	5	27	27	NUM
cana-6127	183	6	,	,	PUNCT
cana-6127	183	7	pp	pp	ADJ
cana-6127	183	8	.	.	PUNCT
cana-6127	183	9	240	240	NUM
cana-6127	183	10	–	–	PUNCT
cana-6127	183	11	253	253	NUM
cana-6127	183	12	,	,	PUNCT
cana-6127	183	13	1956	1956	NUM
cana-6127	183	14	.	.	PUNCT
cana-6127	184	1	[	[	X
cana-6127	184	2	2	2	X
cana-6127	184	3	]	]	PUNCT
cana-6127	184	4	h.	h.	PROPN
cana-6127	184	5	h.	h.	PROPN
cana-6127	184	6	sherief	sherief	PROPN
cana-6127	184	7	,	,	PUNCT
cana-6127	184	8	f.	f.	PROPN
cana-6127	184	9	a.	a.	PROPN
cana-6127	184	10	hamza	hamza	PROPN
cana-6127	184	11	,	,	PUNCT
cana-6127	184	12	‘	'	PUNCT
cana-6127	184	13	‘	'	PUNCT
cana-6127	184	14	generalized	generalized	ADJ
cana-6127	184	15	thermoelastic	thermoelastic	ADJ
cana-6127	184	16	problem	problem	NOUN
cana-6127	184	17	of	of	ADP
cana-6127	184	18	a	a	DET
cana-6127	184	19	thick	thick	ADJ
cana-6127	184	20	plate	plate	NOUN
cana-6127	184	21	under	under	ADP
cana-6127	184	22	axisymmetric	axisymmetric	ADJ
cana-6127	184	23	temperature	temperature	NOUN
cana-6127	184	24	distribution	distribution	NOUN
cana-6127	184	25	’’	’'	PUNCT
cana-6127	184	26	,	,	PUNCT
cana-6127	184	27	journal	journal	NOUN
cana-6127	184	28	of	of	ADP
cana-6127	184	29	thermal	thermal	ADJ
cana-6127	184	30	stresses	stress	NOUN
cana-6127	184	31	,	,	PUNCT
cana-6127	184	32	vol	vol	NOUN
cana-6127	184	33	.	.	PUNCT
cana-6127	184	34	17(3	17(3	NUM
cana-6127	184	35	)	)	PUNCT
cana-6127	184	36	,	,	PUNCT
cana-6127	184	37	pp	pp	ADP
cana-6127	184	38	.	.	PUNCT
cana-6127	185	1	435–452	435–452	NUM
cana-6127	185	2	,	,	PUNCT
cana-6127	185	3	1994	1994	NUM
cana-6127	185	4	.	.	PUNCT
cana-6127	186	1	communications	communication	NOUN
cana-6127	186	2	on	on	ADP
cana-6127	186	3	applied	apply	VERB
cana-6127	186	4	nonlinear	nonlinear	ADJ
cana-6127	186	5	analysis	analysis	NOUN
cana-6127	186	6	issn	issn	NOUN
cana-6127	186	7	:	:	PUNCT
cana-6127	186	8	1074	1074	NUM
cana-6127	186	9	-	-	PUNCT
cana-6127	186	10	133x	133x	NUM
cana-6127	186	11	vol	vol	VERB
cana-6127	186	12	32	32	NUM
cana-6127	186	13	no	no	NOUN
cana-6127	186	14	.	.	PUNCT
cana-6127	187	1	10s	10	NOUN
cana-6127	187	2	(	(	PUNCT
cana-6127	187	3	2025	2025	NUM
cana-6127	187	4	)	)	PUNCT
cana-6127	187	5	3471	3471	NUM
cana-6127	187	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	188	1	[	[	X
cana-6127	188	2	3	3	X
cana-6127	188	3	]	]	X
cana-6127	188	4	h.	h.	PROPN
cana-6127	188	5	w.	w.	PROPN
cana-6127	188	6	lord	lord	PROPN
cana-6127	188	7	,	,	PUNCT
cana-6127	188	8	y.	y.	PROPN
cana-6127	188	9	shulman	shulman	PROPN
cana-6127	188	10	,	,	PUNCT
cana-6127	188	11	‘	'	PUNCT
cana-6127	188	12	‘	'	PUNCT
cana-6127	188	13	a	a	DET
cana-6127	188	14	generalized	generalized	ADJ
cana-6127	188	15	dynamical	dynamical	ADJ
cana-6127	188	16	theory	theory	NOUN
cana-6127	188	17	of	of	ADP
cana-6127	188	18	thermoelasticity	thermoelasticity	NOUN
cana-6127	188	19	’’	’'	PUNCT
cana-6127	188	20	,	,	PUNCT
cana-6127	188	21	j.	j.	PROPN
cana-6127	188	22	mech	mech	PROPN
cana-6127	188	23	.	.	PUNCT
cana-6127	189	1	phys	phy	NOUN
cana-6127	189	2	.	.	PUNCT
cana-6127	190	1	solids	solid	NOUN
cana-6127	190	2	,	,	PUNCT
cana-6127	190	3	vol	vol	NOUN
cana-6127	190	4	.	.	PROPN
cana-6127	190	5	15	15	NUM
cana-6127	190	6	,	,	PUNCT
cana-6127	190	7	pp	pp	ADJ
cana-6127	190	8	.	.	PUNCT
cana-6127	191	1	299–307	299–307	NUM
cana-6127	191	2	,	,	PUNCT
cana-6127	191	3	1967	1967	NUM
cana-6127	191	4	.	.	PUNCT
cana-6127	192	1	[	[	X
cana-6127	192	2	4	4	X
cana-6127	192	3	]	]	X
cana-6127	192	4	y.	y.	PROPN
cana-6127	192	5	tanigawa	tanigawa	PROPN
cana-6127	192	6	,	,	PUNCT
cana-6127	192	7	y.	y.	PROPN
cana-6127	192	8	komatsubara	komatsubara	PROPN
cana-6127	192	9	,	,	PUNCT
cana-6127	192	10	‘	'	PUNCT
cana-6127	192	11	‘	'	PUNCT
cana-6127	192	12	theoretical	theoretical	ADJ
cana-6127	192	13	analysis	analysis	NOUN
cana-6127	192	14	of	of	ADP
cana-6127	192	15	a	a	DET
cana-6127	192	16	rectangular	rectangular	ADJ
cana-6127	192	17	plate	plate	NOUN
cana-6127	192	18	and	and	CCONJ
cana-6127	192	19	its	its	PRON
cana-6127	192	20	thermal	thermal	ADJ
cana-6127	192	21	stress	stress	NOUN
cana-6127	192	22	intensity	intensity	NOUN
cana-6127	192	23	factor	factor	NOUN
cana-6127	192	24	compressive	compressive	ADJ
cana-6127	192	25	stress	stress	NOUN
cana-6127	192	26	field	field	NOUN
cana-6127	192	27	’’	’'	PUNCT
cana-6127	192	28	,	,	PUNCT
cana-6127	192	29	journal	journal	NOUN
cana-6127	192	30	of	of	ADP
cana-6127	192	31	thermal	thermal	ADJ
cana-6127	192	32	stresses	stress	NOUN
cana-6127	192	33	,	,	PUNCT
cana-6127	192	34	vol	vol	NOUN
cana-6127	192	35	.	.	PROPN
cana-6127	192	36	20	20	NUM
cana-6127	192	37	,	,	PUNCT
cana-6127	192	38	pp	pp	ADJ
cana-6127	192	39	.	.	PUNCT
cana-6127	193	1	517–542	517–542	NUM
cana-6127	193	2	,	,	PUNCT
cana-6127	193	3	1997	1997	NUM
cana-6127	193	4	.	.	PUNCT
cana-6127	194	1	[	[	X
cana-6127	194	2	5	5	X
cana-6127	194	3	]	]	PUNCT
cana-6127	194	4	v.	v.	ADP
cana-6127	194	5	m.	m.	NOUN
cana-6127	194	6	vihak	vihak	PROPN
cana-6127	194	7	,	,	PUNCT
cana-6127	194	8	m.	m.	NOUN
cana-6127	194	9	y.	y.	PROPN
cana-6127	194	10	yuzvyak	yuzvyak	PROPN
cana-6127	194	11	,	,	PUNCT
cana-6127	194	12	a.	a.	PROPN
cana-6127	194	13	v.	v.	ADP
cana-6127	194	14	yasinskij	yasinskij	PROPN
cana-6127	194	15	,	,	PUNCT
cana-6127	194	16	‘	'	PUNCT
cana-6127	194	17	‘	'	PUNCT
cana-6127	194	18	the	the	DET
cana-6127	194	19	solution	solution	NOUN
cana-6127	194	20	of	of	ADP
cana-6127	194	21	the	the	DET
cana-6127	194	22	plane	plane	NOUN
cana-6127	194	23	thermoelasticity	thermoelasticity	NOUN
cana-6127	194	24	problem	problem	NOUN
cana-6127	194	25	for	for	ADP
cana-6127	194	26	a	a	DET
cana-6127	194	27	rectangular	rectangular	ADJ
cana-6127	194	28	domain	domain	NOUN
cana-6127	194	29	’’	’'	PUNCT
cana-6127	194	30	,	,	PUNCT
cana-6127	194	31	journal	journal	NOUN
cana-6127	194	32	of	of	ADP
cana-6127	194	33	thermal	thermal	ADJ
cana-6127	194	34	stresses	stress	NOUN
cana-6127	194	35	,	,	PUNCT
cana-6127	194	36	vol	vol	NOUN
cana-6127	194	37	.	.	PROPN
cana-6127	194	38	21	21	NUM
cana-6127	194	39	,	,	PUNCT
cana-6127	194	40	pp	pp	ADJ
cana-6127	194	41	.	.	PUNCT
cana-6127	195	1	545–561	545–561	NUM
cana-6127	195	2	,	,	PUNCT
cana-6127	195	3	1998	1998	NUM
cana-6127	195	4	.	.	PUNCT
cana-6127	196	1	[	[	X
cana-6127	196	2	6	6	NUM
cana-6127	196	3	]	]	X
cana-6127	196	4	r.	r.	PROPN
cana-6127	196	5	j.adam	j.adam	PROPN
cana-6127	196	6	,	,	PUNCT
cana-6127	196	7	c.	c.	PROPN
cana-6127	196	8	w.	w.	PROPN
cana-6127	196	9	best	well	ADV
cana-6127	196	10	,	,	PUNCT
cana-6127	196	11	‘	'	PUNCT
cana-6127	196	12	‘	'	PUNCT
cana-6127	196	13	thermoelastic	thermoelastic	ADJ
cana-6127	196	14	vibrations	vibration	NOUN
cana-6127	196	15	of	of	ADP
cana-6127	196	16	a	a	DET
cana-6127	196	17	laminated	laminate	VERB
cana-6127	196	18	rectangular	rectangular	ADJ
cana-6127	196	19	plate	plate	NOUN
cana-6127	196	20	subjected	subject	VERB
cana-6127	196	21	to	to	ADP
cana-6127	196	22	a	a	DET
cana-6127	196	23	thermal	thermal	ADJ
cana-6127	196	24	shock	shock	NOUN
cana-6127	196	25	’’	’'	PUNCT
cana-6127	196	26	,	,	PUNCT
cana-6127	196	27	journal	journal	NOUN
cana-6127	196	28	of	of	ADP
cana-6127	196	29	thermal	thermal	ADJ
cana-6127	196	30	stresses	stress	NOUN
cana-6127	196	31	,	,	PUNCT
cana-6127	196	32	vol	vol	NOUN
cana-6127	196	33	.	.	PROPN
cana-6127	197	1	22	22	NUM
cana-6127	197	2	,	,	PUNCT
cana-6127	197	3	pp	pp	ADJ
cana-6127	197	4	.	.	PUNCT
cana-6127	198	1	875–895	875–895	NUM
cana-6127	198	2	,	,	PUNCT
cana-6127	198	3	1999	1999	NUM
cana-6127	198	4	.	.	PUNCT
cana-6127	199	1	[	[	X
cana-6127	199	2	7	7	X
cana-6127	199	3	]	]	X
cana-6127	199	4	t.	t.	NOUN
cana-6127	199	5	morimoto	morimoto	NOUN
cana-6127	199	6	,	,	PUNCT
cana-6127	199	7	y.	y.	PROPN
cana-6127	199	8	tanigawa	tanigawa	PROPN
cana-6127	199	9	,	,	PUNCT
cana-6127	199	10	r.	r.	PROPN
cana-6127	199	11	kawamura	kawamura	PROPN
cana-6127	199	12	,	,	PUNCT
cana-6127	199	13	‘	'	PUNCT
cana-6127	199	14	‘	'	PUNCT
cana-6127	199	15	thermal	thermal	ADJ
cana-6127	199	16	buckling	buckling	NOUN
cana-6127	199	17	analysis	analysis	NOUN
cana-6127	199	18	of	of	ADP
cana-6127	199	19	an	an	DET
cana-6127	199	20	orthotropic	orthotropic	ADJ
cana-6127	199	21	nonhomogeneous	nonhomogeneous	ADJ
cana-6127	199	22	rectangular	rectangular	ADJ
cana-6127	199	23	plate	plate	NOUN
cana-6127	199	24	due	due	ADP
cana-6127	199	25	to	to	ADP
cana-6127	199	26	uniform	uniform	ADJ
cana-6127	199	27	heat	heat	NOUN
cana-6127	199	28	supply	supply	NOUN
cana-6127	199	29	’’	’'	PUNCT
cana-6127	199	30	,	,	PUNCT
cana-6127	199	31	nippon	nippon	PROPN
cana-6127	199	32	kikai	kikai	PROPN
cana-6127	199	33	gakkai	gakkai	PROPN
cana-6127	199	34	zairyo	zairyo	PROPN
cana-6127	199	35	rikigaku	rikigaku	PROPN
cana-6127	199	36	bumon	bumon	PROPN
cana-6127	199	37	koenkai	koenkai	PROPN
cana-6127	199	38	koen	koen	PROPN
cana-6127	199	39	ronbunshu	ronbunshu	PROPN
cana-6127	199	40	,	,	PUNCT
cana-6127	199	41	vol	vol	NOUN
cana-6127	199	42	.	.	PROPN
cana-6127	200	1	202	202	NUM
cana-6127	200	2	,	,	PUNCT
cana-6127	200	3	pp	pp	ADJ
cana-6127	200	4	.	.	PUNCT
cana-6127	201	1	283–284	283–284	NUM
cana-6127	201	2	,	,	PUNCT
cana-6127	201	3	2002	2002	NUM
cana-6127	201	4	.	.	PUNCT
cana-6127	202	1	[	[	X
cana-6127	202	2	8	8	NUM
cana-6127	202	3	]	]	X
cana-6127	202	4	y.	y.	NOUN
cana-6127	202	5	ootao	ootao	PROPN
cana-6127	202	6	,	,	PUNCT
cana-6127	202	7	y.	y.	PROPN
cana-6127	202	8	tanigawa	tanigawa	PROPN
cana-6127	202	9	,	,	PUNCT
cana-6127	202	10	‘	'	PUNCT
cana-6127	202	11	‘	'	PUNCT
cana-6127	202	12	transient	transient	ADJ
cana-6127	202	13	thermoelastic	thermoelastic	ADJ
cana-6127	202	14	problem	problem	NOUN
cana-6127	202	15	of	of	ADP
cana-6127	202	16	functionally	functionally	ADV
cana-6127	202	17	graded	grade	VERB
cana-6127	202	18	thick	thick	ADJ
cana-6127	202	19	strip	strip	NOUN
cana-6127	202	20	due	due	ADP
cana-6127	202	21	to	to	ADP
cana-6127	202	22	nonuniform	nonuniform	ADJ
cana-6127	202	23	heat	heat	NOUN
cana-6127	202	24	supply	supply	NOUN
cana-6127	202	25	’’	’'	PUNCT
cana-6127	202	26	,	,	PUNCT
cana-6127	202	27	composite	composite	ADJ
cana-6127	202	28	structures	structure	NOUN
cana-6127	202	29	,	,	PUNCT
cana-6127	202	30	vol	vol	NOUN
cana-6127	202	31	.	.	PROPN
cana-6127	202	32	63	63	NUM
cana-6127	202	33	,	,	PUNCT
cana-6127	202	34	pp	pp	ADJ
cana-6127	202	35	.	.	PUNCT
cana-6127	203	1	139–146	139–146	NUM
cana-6127	203	2	,	,	PUNCT
cana-6127	203	3	2004	2004	NUM
cana-6127	203	4	.	.	PUNCT
cana-6127	204	1	[	[	X
cana-6127	204	2	9	9	NUM
cana-6127	204	3	]	]	PUNCT
cana-6127	204	4	l.	l.	PROPN
cana-6127	204	5	f.	f.	PROPN
cana-6127	204	6	qian	qian	PROPN
cana-6127	204	7	,	,	PUNCT
cana-6127	204	8	r.	r.	PROPN
cana-6127	204	9	c.	c.	PROPN
cana-6127	204	10	batra	batra	PROPN
cana-6127	204	11	,	,	PUNCT
cana-6127	204	12	‘	'	PUNCT
cana-6127	204	13	‘	'	PUNCT
cana-6127	204	14	transient	transient	ADJ
cana-6127	204	15	thermoelastic	thermoelastic	ADJ
cana-6127	204	16	deformations	deformation	NOUN
cana-6127	204	17	of	of	ADP
cana-6127	204	18	a	a	DET
cana-6127	204	19	thick	thick	ADJ
cana-6127	204	20	functionally	functionally	ADV
cana-6127	204	21	graded	grade	VERB
cana-6127	204	22	plate	plate	NOUN
cana-6127	204	23	’’	’'	PUNCT
cana-6127	204	24	,	,	PUNCT
cana-6127	204	25	journal	journal	NOUN
cana-6127	204	26	of	of	ADP
cana-6127	204	27	thermal	thermal	ADJ
cana-6127	204	28	stresses	stress	NOUN
cana-6127	204	29	,	,	PUNCT
cana-6127	204	30	vol	vol	NOUN
cana-6127	204	31	.	.	PROPN
cana-6127	204	32	27	27	NUM
cana-6127	204	33	,	,	PUNCT
cana-6127	204	34	pp	pp	ADJ
cana-6127	204	35	.	.	PUNCT
cana-6127	205	1	705–740	705–740	NUM
cana-6127	205	2	,	,	PUNCT
cana-6127	205	3	2004	2004	NUM
cana-6127	205	4	.	.	PUNCT
cana-6127	206	1	[	[	X
cana-6127	206	2	10	10	NUM
cana-6127	206	3	]	]	PUNCT
cana-6127	206	4	j.	j.	PROPN
cana-6127	206	5	n.	n.	PROPN
cana-6127	206	6	sharma	sharma	PROPN
cana-6127	206	7	,	,	PUNCT
cana-6127	206	8	p.	p.	PROPN
cana-6127	206	9	k.	k.	PROPN
cana-6127	206	10	sharma	sharma	PROPN
cana-6127	206	11	,	,	PUNCT
cana-6127	206	12	r.	r.	PROPN
cana-6127	206	13	l.	l.	PROPN
cana-6127	206	14	sharma	sharma	PROPN
cana-6127	206	15	,	,	PUNCT
cana-6127	206	16	‘	'	PUNCT
cana-6127	206	17	‘	'	PUNCT
cana-6127	206	18	behavior	behavior	NOUN
cana-6127	206	19	of	of	ADP
cana-6127	206	20	thermoelastic	thermoelastic	ADJ
cana-6127	206	21	thick	thick	ADJ
cana-6127	206	22	plate	plate	NOUN
cana-6127	206	23	under	under	ADP
cana-6127	206	24	lateral	lateral	ADJ
cana-6127	206	25	loads	load	NOUN
cana-6127	206	26	’’	’'	PUNCT
cana-6127	206	27	,	,	PUNCT
cana-6127	206	28	journal	journal	NOUN
cana-6127	206	29	of	of	ADP
cana-6127	206	30	thermal	thermal	ADJ
cana-6127	206	31	stresses	stress	NOUN
cana-6127	206	32	,	,	PUNCT
cana-6127	206	33	vol	vol	NOUN
cana-6127	206	34	.	.	PROPN
cana-6127	206	35	27	27	NUM
cana-6127	206	36	,	,	PUNCT
cana-6127	206	37	pp	pp	ADJ
cana-6127	206	38	.	.	PUNCT
cana-6127	207	1	171–191	171–191	NUM
cana-6127	207	2	,	,	PUNCT
cana-6127	207	3	2004	2004	NUM
cana-6127	207	4	.	.	PUNCT
cana-6127	208	1	[	[	X
cana-6127	208	2	11	11	NUM
cana-6127	208	3	]	]	X
cana-6127	208	4	y.	y.	PROPN
cana-6127	208	5	z.	z.	PROPN
cana-6127	208	6	povstenko	povstenko	PROPN
cana-6127	208	7	,	,	PUNCT
cana-6127	208	8	‘	'	PUNCT
cana-6127	208	9	‘	'	PUNCT
cana-6127	208	10	fractional	fractional	ADJ
cana-6127	208	11	heat	heat	NOUN
cana-6127	208	12	conduction	conduction	NOUN
cana-6127	208	13	equation	equation	NOUN
cana-6127	208	14	and	and	CCONJ
cana-6127	208	15	associated	associate	VERB
cana-6127	208	16	thermal	thermal	ADJ
cana-6127	208	17	stresses	stress	NOUN
cana-6127	208	18	’’	’'	PUNCT
cana-6127	208	19	,	,	PUNCT
cana-6127	208	20	journal	journal	NOUN
cana-6127	208	21	of	of	ADP
cana-6127	208	22	thermal	thermal	ADJ
cana-6127	208	23	stresses	stress	NOUN
cana-6127	208	24	,	,	PUNCT
cana-6127	208	25	28	28	NUM
cana-6127	208	26	,	,	PUNCT
cana-6127	208	27	83–102	83–102	NUM
cana-6127	208	28	,	,	PUNCT
cana-6127	208	29	2005	2005	NUM
cana-6127	208	30	.	.	PUNCT
cana-6127	209	1	[	[	X
cana-6127	209	2	12	12	NUM
cana-6127	209	3	]	]	PUNCT
cana-6127	209	4	k.	k.	PROPN
cana-6127	209	5	r.	r.	PROPN
cana-6127	209	6	gaikwad	gaikwad	PROPN
cana-6127	209	7	,	,	PUNCT
cana-6127	209	8	k.	k.	PROPN
cana-6127	210	1	p.	p.	PROPN
cana-6127	210	2	ghadle	ghadle	PROPN
cana-6127	210	3	,	,	PUNCT
cana-6127	210	4	‘	'	PUNCT
cana-6127	210	5	‘	'	PUNCT
cana-6127	210	6	quasi	quasi	ADJ
cana-6127	210	7	-	-	ADJ
cana-6127	210	8	static	static	ADJ
cana-6127	210	9	thermal	thermal	ADJ
cana-6127	210	10	stresses	stress	NOUN
cana-6127	210	11	in	in	ADP
cana-6127	210	12	a	a	DET
cana-6127	210	13	thick	thick	ADJ
cana-6127	210	14	rectangular	rectangular	ADJ
cana-6127	210	15	plate	plate	NOUN
cana-6127	210	16	’’	’'	PUNCT
cana-6127	210	17	,	,	PUNCT
cana-6127	210	18	global	global	ADJ
cana-6127	210	19	journal	journal	NOUN
cana-6127	210	20	of	of	ADP
cana-6127	210	21	pure	pure	ADJ
cana-6127	210	22	and	and	CCONJ
cana-6127	210	23	applied	apply	VERB
cana-6127	210	24	mathematics	mathematic	NOUN
cana-6127	210	25	vol	vol	NOUN
cana-6127	210	26	.	.	PUNCT
cana-6127	211	1	5(2	5(2	NUM
cana-6127	211	2	)	)	PUNCT
cana-6127	211	3	,	,	PUNCT
cana-6127	211	4	109	109	NUM
cana-6127	211	5	-	-	SYM
cana-6127	211	6	117	117	NUM
cana-6127	211	7	,	,	PUNCT
cana-6127	211	8	2009	2009	NUM
cana-6127	211	9	.	.	PUNCT
cana-6127	212	1	[	[	X
cana-6127	212	2	13	13	NUM
cana-6127	212	3	]	]	X
cana-6127	212	4	h.	h.	PROPN
cana-6127	212	5	h.	h.	PROPN
cana-6127	212	6	sherief	sherief	PROPN
cana-6127	212	7	,	,	PUNCT
cana-6127	212	8	a.	a.	PROPN
cana-6127	212	9	el	el	PROPN
cana-6127	212	10	-	-	PUNCT
cana-6127	212	11	said	say	VERB
cana-6127	212	12	,	,	PUNCT
cana-6127	212	13	a.	a.	PROPN
cana-6127	212	14	abd	abd	PROPN
cana-6127	212	15	el	el	PROPN
cana-6127	212	16	-	-	PUNCT
cana-6127	212	17	latief	latief	NOUN
cana-6127	212	18	,	,	PUNCT
cana-6127	212	19	‘	'	PUNCT
cana-6127	212	20	‘	'	PUNCT
cana-6127	212	21	fractional	fractional	ADJ
cana-6127	212	22	order	order	NOUN
cana-6127	212	23	theory	theory	NOUN
cana-6127	212	24	of	of	ADP
cana-6127	212	25	thermoelasticity	thermoelasticity	NOUN
cana-6127	212	26	’’	’'	PUNCT
cana-6127	212	27	,	,	PUNCT
cana-6127	212	28	international	international	ADJ
cana-6127	212	29	journal	journal	NOUN
cana-6127	212	30	of	of	ADP
cana-6127	212	31	solids	solid	NOUN
cana-6127	212	32	and	and	CCONJ
cana-6127	212	33	structures	structure	NOUN
cana-6127	212	34	,	,	PUNCT
cana-6127	212	35	vol	vol	NOUN
cana-6127	212	36	.	.	PROPN
cana-6127	213	1	47	47	NUM
cana-6127	213	2	,	,	PUNCT
cana-6127	213	3	pp	pp	ADJ
cana-6127	213	4	.	.	PUNCT
cana-6127	214	1	269–275	269–275	NUM
cana-6127	214	2	,	,	PUNCT
cana-6127	214	3	2010	2010	NUM
cana-6127	214	4	.	.	PUNCT
cana-6127	215	1	[	[	X
cana-6127	215	2	14	14	NUM
cana-6127	215	3	]	]	PUNCT
cana-6127	215	4	k.	k.	PROPN
cana-6127	215	5	r.	r.	PROPN
cana-6127	215	6	gaikwad	gaikwad	PROPN
cana-6127	215	7	,	,	PUNCT
cana-6127	215	8	k.	k.	PROPN
cana-6127	216	1	p.	p.	PROPN
cana-6127	216	2	ghadle	ghadle	PROPN
cana-6127	216	3	,	,	PUNCT
cana-6127	216	4	‘	'	PUNCT
cana-6127	216	5	‘	'	PUNCT
cana-6127	216	6	three	three	NUM
cana-6127	216	7	dimensional	dimensional	ADJ
cana-6127	216	8	non	non	ADJ
cana-6127	216	9	-	-	ADJ
cana-6127	216	10	homogeneous	homogeneous	ADJ
cana-6127	216	11	thermoelastic	thermoelastic	ADJ
cana-6127	216	12	problem	problem	NOUN
cana-6127	216	13	in	in	ADP
cana-6127	216	14	a	a	DET
cana-6127	216	15	thick	thick	ADJ
cana-6127	216	16	rectangular	rectangular	ADJ
cana-6127	216	17	plate	plate	NOUN
cana-6127	216	18	due	due	ADP
cana-6127	216	19	to	to	ADP
cana-6127	216	20	internal	internal	ADJ
cana-6127	216	21	heat	heat	NOUN
cana-6127	216	22	generation	generation	NOUN
cana-6127	216	23	’’	’'	PUNCT
cana-6127	216	24	,	,	PUNCT
cana-6127	216	25	southern	southern	PROPN
cana-6127	216	26	africa	africa	PROPN
cana-6127	216	27	journal	journal	PROPN
cana-6127	216	28	of	of	ADP
cana-6127	216	29	pure	pure	ADJ
cana-6127	216	30	and	and	CCONJ
cana-6127	216	31	applied	applied	ADJ
cana-6127	216	32	mathematics	mathematic	NOUN
cana-6127	216	33	,	,	PUNCT
cana-6127	216	34	vol	vol	NOUN
cana-6127	216	35	.	.	PROPN
cana-6127	216	36	5	5	NUM
cana-6127	216	37	,	,	PUNCT
cana-6127	216	38	pp	pp	ADJ
cana-6127	216	39	.	.	PUNCT
cana-6127	217	1	26–38	26–38	NUM
cana-6127	217	2	,	,	PUNCT
cana-6127	217	3	2011	2011	NUM
cana-6127	217	4	.	.	PUNCT
cana-6127	218	1	[	[	X
cana-6127	218	2	15	15	NUM
cana-6127	218	3	]	]	X
cana-6127	218	4	k.	k.	PROPN
cana-6127	218	5	r.	r.	PROPN
cana-6127	218	6	gaikwad	gaikwad	PROPN
cana-6127	218	7	,	,	PUNCT
cana-6127	218	8	k.	k.	PROPN
cana-6127	219	1	p.	p.	PROPN
cana-6127	219	2	ghadle	ghadle	PROPN
cana-6127	219	3	,	,	PUNCT
cana-6127	219	4	‘	'	PUNCT
cana-6127	219	5	‘	'	PUNCT
cana-6127	219	6	non	non	ADJ
cana-6127	219	7	-	-	ADJ
cana-6127	219	8	homogeneous	homogeneous	ADJ
cana-6127	219	9	heat	heat	NOUN
cana-6127	219	10	conduction	conduction	NOUN
cana-6127	219	11	problem	problem	NOUN
cana-6127	219	12	and	and	CCONJ
cana-6127	219	13	its	its	PRON
cana-6127	219	14	thermal	thermal	ADJ
cana-6127	219	15	deflection	deflection	NOUN
cana-6127	219	16	due	due	ADP
cana-6127	219	17	to	to	ADP
cana-6127	219	18	internal	internal	ADJ
cana-6127	219	19	heat	heat	NOUN
cana-6127	219	20	generation	generation	NOUN
cana-6127	219	21	in	in	ADP
cana-6127	219	22	a	a	DET
cana-6127	219	23	thin	thin	ADJ
cana-6127	219	24	hollow	hollow	ADJ
cana-6127	219	25	circular	circular	ADJ
cana-6127	219	26	disk	disk	NOUN
cana-6127	219	27	’’	’'	PUNCT
cana-6127	219	28	,	,	PUNCT
cana-6127	219	29	journal	journal	NOUN
cana-6127	219	30	of	of	ADP
cana-6127	219	31	thermal	thermal	ADJ
cana-6127	219	32	stresses	stress	NOUN
cana-6127	219	33	,	,	PUNCT
cana-6127	219	34	vol	vol	NOUN
cana-6127	219	35	.	.	PROPN
cana-6127	219	36	35	35	NUM
cana-6127	219	37	,	,	PUNCT
cana-6127	219	38	pp	pp	ADJ
cana-6127	219	39	.	.	PUNCT
cana-6127	220	1	485–498	485–498	NUM
cana-6127	220	2	,	,	PUNCT
cana-6127	220	3	2012	2012	NUM
cana-6127	220	4	.	.	PUNCT
cana-6127	221	1	[	[	X
cana-6127	221	2	16	16	NUM
cana-6127	221	3	]	]	PUNCT
cana-6127	221	4	k.	k.	PROPN
cana-6127	221	5	r.	r.	PROPN
cana-6127	221	6	gaikwad	gaikwad	PROPN
cana-6127	221	7	,	,	PUNCT
cana-6127	221	8	‘	'	PUNCT
cana-6127	221	9	‘	'	PUNCT
cana-6127	221	10	analysis	analysis	NOUN
cana-6127	221	11	of	of	ADP
cana-6127	221	12	thermoelastic	thermoelastic	ADJ
cana-6127	221	13	deformation	deformation	NOUN
cana-6127	221	14	of	of	ADP
cana-6127	221	15	a	a	DET
cana-6127	221	16	thin	thin	ADJ
cana-6127	221	17	hollow	hollow	ADJ
cana-6127	221	18	circular	circular	ADJ
cana-6127	221	19	disk	disk	NOUN
cana-6127	221	20	due	due	ADP
cana-6127	221	21	to	to	PART
cana-6127	221	22	partially	partially	ADV
cana-6127	221	23	distributed	distribute	VERB
cana-6127	221	24	heat	heat	NOUN
cana-6127	221	25	supply	supply	NOUN
cana-6127	221	26	’’	’'	PUNCT
cana-6127	221	27	,	,	PUNCT
cana-6127	221	28	journal	journal	NOUN
cana-6127	221	29	of	of	ADP
cana-6127	221	30	thermal	thermal	ADJ
cana-6127	221	31	stresses	stress	NOUN
cana-6127	221	32	,	,	PUNCT
cana-6127	221	33	vol	vol	NOUN
cana-6127	221	34	.	.	PROPN
cana-6127	221	35	36	36	NUM
cana-6127	221	36	,	,	PUNCT
cana-6127	221	37	pp	pp	ADJ
cana-6127	221	38	.	.	PUNCT
cana-6127	222	1	207–224	207–224	NUM
cana-6127	222	2	,	,	PUNCT
cana-6127	222	3	2013	2013	NUM
cana-6127	222	4	.	.	PUNCT
cana-6127	223	1	[	[	X
cana-6127	223	2	17	17	NUM
cana-6127	223	3	]	]	PUNCT
cana-6127	223	4	k.	k.	PROPN
cana-6127	223	5	r.	r.	PROPN
cana-6127	223	6	gaikwad	gaikwad	PROPN
cana-6127	223	7	,	,	PUNCT
cana-6127	223	8	‘	'	PUNCT
cana-6127	223	9	‘	'	PUNCT
cana-6127	223	10	mathematical	mathematical	ADJ
cana-6127	223	11	modelling	modelling	NOUN
cana-6127	223	12	and	and	CCONJ
cana-6127	223	13	its	its	PRON
cana-6127	223	14	simulation	simulation	NOUN
cana-6127	223	15	of	of	ADP
cana-6127	223	16	a	a	DET
cana-6127	223	17	quasi	quasi	ADJ
cana-6127	223	18	-	-	ADJ
cana-6127	223	19	static	static	ADJ
cana-6127	223	20	thermoelastic	thermoelastic	ADJ
cana-6127	223	21	problem	problem	NOUN
cana-6127	223	22	in	in	ADP
cana-6127	223	23	a	a	DET
cana-6127	223	24	semi	semi	ADJ
cana-6127	223	25	-	-	ADJ
cana-6127	223	26	infinite	infinite	ADJ
cana-6127	223	27	hollow	hollow	ADJ
cana-6127	223	28	circular	circular	ADJ
cana-6127	223	29	disk	disk	NOUN
cana-6127	223	30	due	due	ADP
cana-6127	223	31	to	to	ADP
cana-6127	223	32	internal	internal	ADJ
cana-6127	223	33	heat	heat	NOUN
cana-6127	223	34	generation	generation	NOUN
cana-6127	223	35	’’	’'	PUNCT
cana-6127	223	36	,	,	PUNCT
cana-6127	223	37	journal	journal	NOUN
cana-6127	223	38	of	of	ADP
cana-6127	223	39	the	the	DET
cana-6127	223	40	korean	korean	ADJ
cana-6127	223	41	society	society	NOUN
cana-6127	223	42	for	for	ADP
cana-6127	223	43	industrial	industrial	ADJ
cana-6127	223	44	and	and	CCONJ
cana-6127	223	45	applied	applied	ADJ
cana-6127	223	46	mathematics	mathematic	NOUN
cana-6127	223	47	,	,	PUNCT
cana-6127	223	48	vol	vol	NOUN
cana-6127	223	49	.	.	PROPN
cana-6127	223	50	19	19	NUM
cana-6127	223	51	,	,	PUNCT
cana-6127	223	52	pp	pp	ADJ
cana-6127	223	53	.	.	PUNCT
cana-6127	224	1	69–81	69–81	NUM
cana-6127	224	2	,	,	PUNCT
cana-6127	224	3	2015	2015	NUM
cana-6127	224	4	.	.	PUNCT
cana-6127	225	1	[	[	X
cana-6127	225	2	18	18	NUM
cana-6127	225	3	]	]	X
cana-6127	225	4	v.	v.	PROPN
cana-6127	225	5	r.	r.	PROPN
cana-6127	225	6	manthena	manthena	PROPN
cana-6127	225	7	,	,	PUNCT
cana-6127	225	8	n.	n.	PROPN
cana-6127	225	9	k.	k.	PROPN
cana-6127	225	10	lamba	lamba	PROPN
cana-6127	225	11	,	,	PUNCT
cana-6127	225	12	g.	g.	PROPN
cana-6127	225	13	d.	d.	PROPN
cana-6127	225	14	kedar	kedar	PROPN
cana-6127	225	15	,	,	PUNCT
cana-6127	225	16	k.	k.	PROPN
cana-6127	225	17	c.	c.	PROPN
cana-6127	225	18	deshmukh	deshmukh	PROPN
cana-6127	225	19	,	,	PUNCT
cana-6127	225	20	‘	'	PUNCT
cana-6127	225	21	‘	'	PUNCT
cana-6127	225	22	effects	effect	NOUN
cana-6127	225	23	of	of	ADP
cana-6127	225	24	stress	stress	NOUN
cana-6127	225	25	resultants	resultant	NOUN
cana-6127	225	26	on	on	ADP
cana-6127	225	27	thermal	thermal	ADJ
cana-6127	225	28	stresses	stress	NOUN
cana-6127	225	29	in	in	ADP
cana-6127	225	30	a	a	DET
cana-6127	225	31	functionally	functionally	ADV
cana-6127	225	32	graded	grade	VERB
cana-6127	225	33	rectangular	rectangular	ADJ
cana-6127	225	34	plate	plate	NOUN
cana-6127	225	35	due	due	ADP
cana-6127	225	36	to	to	ADP
cana-6127	225	37	temperature	temperature	NOUN
cana-6127	225	38	dependent	dependent	ADJ
cana-6127	225	39	material	material	NOUN
cana-6127	225	40	properties	property	NOUN
cana-6127	225	41	’’	’'	PUNCT
cana-6127	225	42	,	,	PUNCT
cana-6127	225	43	int	int	NOUN
cana-6127	225	44	.	.	PUNCT
cana-6127	226	1	j.	j.	PROPN
cana-6127	226	2	thermodyn	thermodyn	PROPN
cana-6127	226	3	.	.	PUNCT
cana-6127	226	4	,	,	PUNCT
cana-6127	226	5	vol	vol	NOUN
cana-6127	226	6	.	.	PUNCT
cana-6127	226	7	19(4	19(4	PROPN
cana-6127	226	8	)	)	PUNCT
cana-6127	226	9	,	,	PUNCT
cana-6127	226	10	pp	pp	PROPN
cana-6127	226	11	.	.	PUNCT
cana-6127	227	1	235	235	NUM
cana-6127	227	2	-	-	SYM
cana-6127	227	3	242	242	NUM
cana-6127	227	4	,	,	PUNCT
cana-6127	227	5	2016	2016	NUM
cana-6127	227	6	.	.	PUNCT
cana-6127	228	1	[	[	X
cana-6127	228	2	19	19	NUM
cana-6127	228	3	]	]	X
cana-6127	228	4	v.	v.	PROPN
cana-6127	228	5	r.	r.	PROPN
cana-6127	228	6	manthena	manthena	PROPN
cana-6127	228	7	,	,	PUNCT
cana-6127	228	8	n.	n.	PROPN
cana-6127	228	9	k.	k.	PROPN
cana-6127	228	10	lamba	lamba	PROPN
cana-6127	228	11	,	,	PUNCT
cana-6127	228	12	g.	g.	PROPN
cana-6127	228	13	d.	d.	PROPN
cana-6127	228	14	kedar	kedar	PROPN
cana-6127	228	15	,	,	PUNCT
cana-6127	228	16	‘	'	PUNCT
cana-6127	228	17	‘	'	PUNCT
cana-6127	228	18	transient	transient	ADJ
cana-6127	228	19	thermoelastic	thermoelastic	ADJ
cana-6127	228	20	problem	problem	NOUN
cana-6127	228	21	of	of	ADP
cana-6127	228	22	a	a	DET
cana-6127	228	23	nonhomogeneous	nonhomogeneous	ADJ
cana-6127	228	24	rectangular	rectangular	ADJ
cana-6127	228	25	plate	plate	NOUN
cana-6127	228	26	’’	’'	PUNCT
cana-6127	228	27	,	,	PUNCT
cana-6127	228	28	journal	journal	NOUN
cana-6127	228	29	thermal	thermal	ADJ
cana-6127	228	30	stresses	stress	NOUN
cana-6127	228	31	,	,	PUNCT
cana-6127	228	32	vol	vol	NOUN
cana-6127	228	33	.	.	PUNCT
cana-6127	228	34	40(5	40(5	NOUN
cana-6127	228	35	)	)	PUNCT
cana-6127	228	36	,	,	PUNCT
cana-6127	228	37	pp	pp	PROPN
cana-6127	228	38	.	.	PUNCT
cana-6127	229	1	627	627	NUM
cana-6127	229	2	-	-	SYM
cana-6127	229	3	640	640	NUM
cana-6127	229	4	,	,	PUNCT
cana-6127	229	5	2017	2017	NUM
cana-6127	229	6	.	.	PUNCT
cana-6127	230	1	[	[	X
cana-6127	230	2	20	20	NUM
cana-6127	230	3	]	]	PUNCT
cana-6127	230	4	k.	k.	PROPN
cana-6127	230	5	r.	r.	PROPN
cana-6127	230	6	gaikwad	gaikwad	PROPN
cana-6127	230	7	,	,	PUNCT
cana-6127	230	8	‘	'	PUNCT
cana-6127	230	9	‘	'	PUNCT
cana-6127	230	10	axi	axi	ADJ
cana-6127	230	11	-	-	PUNCT
cana-6127	230	12	symmetric	symmetric	ADJ
cana-6127	230	13	thermoelastic	thermoelastic	ADJ
cana-6127	230	14	stress	stress	NOUN
cana-6127	230	15	analysis	analysis	NOUN
cana-6127	230	16	of	of	ADP
cana-6127	230	17	a	a	DET
cana-6127	230	18	thin	thin	ADJ
cana-6127	230	19	circular	circular	ADJ
cana-6127	230	20	plate	plate	NOUN
cana-6127	230	21	due	due	ADP
cana-6127	230	22	to	to	ADP
cana-6127	230	23	heat	heat	NOUN
cana-6127	230	24	generation	generation	NOUN
cana-6127	230	25	’’	’'	PUNCT
cana-6127	230	26	,	,	PUNCT
cana-6127	230	27	international	international	ADJ
cana-6127	230	28	journal	journal	NOUN
cana-6127	230	29	of	of	ADP
cana-6127	230	30	dynamical	dynamical	ADJ
cana-6127	230	31	systems	system	NOUN
cana-6127	230	32	and	and	CCONJ
cana-6127	230	33	differential	differential	ADJ
cana-6127	230	34	equations	equation	NOUN
cana-6127	230	35	,	,	PUNCT
cana-6127	230	36	vol	vol	NOUN
cana-6127	230	37	.	.	PROPN
cana-6127	230	38	9	9	NUM
cana-6127	230	39	,	,	PUNCT
cana-6127	230	40	pp	pp	ADJ
cana-6127	230	41	.	.	PUNCT
cana-6127	231	1	187–202	187–202	NUM
cana-6127	231	2	,	,	PUNCT
cana-6127	231	3	2019	2019	NUM
cana-6127	231	4	.	.	PUNCT
cana-6127	232	1	[	[	X
cana-6127	232	2	21	21	NUM
cana-6127	232	3	]	]	PUNCT
cana-6127	232	4	k.	k.	PROPN
cana-6127	232	5	r.	r.	PROPN
cana-6127	232	6	gaikwad	gaikwad	PROPN
cana-6127	232	7	,	,	PUNCT
cana-6127	232	8	s.	s.	PROPN
cana-6127	232	9	g.	g.	PROPN
cana-6127	232	10	khavale	khavale	PROPN
cana-6127	232	11	,	,	PUNCT
cana-6127	232	12	‘	'	PUNCT
cana-6127	232	13	‘	'	PUNCT
cana-6127	232	14	time	time	ADJ
cana-6127	232	15	fractional	fractional	ADJ
cana-6127	232	16	heat	heat	NOUN
cana-6127	232	17	conduction	conduction	NOUN
cana-6127	232	18	problem	problem	NOUN
cana-6127	232	19	in	in	ADP
cana-6127	232	20	a	a	DET
cana-6127	232	21	thin	thin	ADJ
cana-6127	232	22	hollow	hollow	ADJ
cana-6127	232	23	circular	circular	ADJ
cana-6127	232	24	disk	disk	NOUN
cana-6127	232	25	and	and	CCONJ
cana-6127	232	26	it	it	PRON
cana-6127	232	27	’s	’	VERB
cana-6127	232	28	thermal	thermal	ADJ
cana-6127	232	29	deflection	deflection	NOUN
cana-6127	232	30	’’	’'	PUNCT
cana-6127	232	31	,	,	PUNCT
cana-6127	232	32	easy	easy	ADJ
cana-6127	232	33	chair	chair	NOUN
cana-6127	232	34	,	,	PUNCT
cana-6127	232	35	1672	1672	NUM
cana-6127	232	36	,	,	PUNCT
cana-6127	232	37	1–11	1–11	PROPN
cana-6127	232	38	,	,	PUNCT
cana-6127	232	39	2019	2019	NUM
cana-6127	232	40	.	.	PUNCT
cana-6127	233	1	[	[	X
cana-6127	233	2	22	22	NUM
cana-6127	233	3	]	]	X
cana-6127	233	4	f.	f.	PROPN
cana-6127	233	5	yekkalam	yekkalam	PROPN
cana-6127	233	6	tash	tash	PROPN
cana-6127	233	7	,	,	PUNCT
cana-6127	233	8	b.	b.	PROPN
cana-6127	233	9	navayi	navayi	PROPN
cana-6127	233	10	neya	neya	PROPN
cana-6127	233	11	,	,	PUNCT
cana-6127	233	12	‘	'	PUNCT
cana-6127	233	13	‘	'	PUNCT
cana-6127	233	14	an	an	DET
cana-6127	233	15	analytical	analytical	ADJ
cana-6127	233	16	solution	solution	NOUN
cana-6127	233	17	for	for	ADP
cana-6127	233	18	bending	bend	VERB
cana-6127	233	19	of	of	ADP
cana-6127	233	20	transversely	transversely	ADJ
cana-6127	233	21	isotropic	isotropic	ADJ
cana-6127	233	22	thick	thick	ADJ
cana-6127	233	23	rectangular	rectangular	ADJ
cana-6127	233	24	plates	plate	NOUN
cana-6127	233	25	with	with	ADP
cana-6127	233	26	variable	variable	ADJ
cana-6127	233	27	thickness	thickness	NOUN
cana-6127	233	28	’’	’'	PUNCT
cana-6127	233	29	,	,	PUNCT
cana-6127	233	30	appl	appl	PROPN
cana-6127	233	31	.	.	PROPN
cana-6127	233	32	math	math	PROPN
cana-6127	233	33	.	.	PUNCT
cana-6127	234	1	model	model	PROPN
cana-6127	234	2	.	.	PUNCT
cana-6127	235	1	vol	vol	NOUN
cana-6127	235	2	.	.	PUNCT
cana-6127	236	1	77(2	77(2	X
cana-6127	236	2	)	)	PUNCT
cana-6127	236	3	,	,	PUNCT
cana-6127	236	4	pp	pp	ADJ
cana-6127	236	5	.	.	PUNCT
cana-6127	237	1	1582	1582	NUM
cana-6127	237	2	-	-	SYM
cana-6127	237	3	1602	1602	NUM
cana-6127	237	4	,	,	PUNCT
cana-6127	237	5	2020	2020	NUM
cana-6127	237	6	.	.	PUNCT
cana-6127	238	1	communications	communication	NOUN
cana-6127	238	2	on	on	ADP
cana-6127	238	3	applied	apply	VERB
cana-6127	238	4	nonlinear	nonlinear	ADJ
cana-6127	238	5	analysis	analysis	NOUN
cana-6127	238	6	issn	issn	NOUN
cana-6127	238	7	:	:	PUNCT
cana-6127	238	8	1074	1074	NUM
cana-6127	238	9	-	-	PUNCT
cana-6127	238	10	133x	133x	NUM
cana-6127	238	11	vol	vol	VERB
cana-6127	238	12	32	32	NUM
cana-6127	238	13	no	no	NOUN
cana-6127	238	14	.	.	PUNCT
cana-6127	239	1	10s	10	NOUN
cana-6127	239	2	(	(	PUNCT
cana-6127	239	3	2025	2025	NUM
cana-6127	239	4	)	)	PUNCT
cana-6127	239	5	3472	3472	NUM
cana-6127	239	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6127	240	1	[	[	X
cana-6127	240	2	23	23	NUM
cana-6127	240	3	]	]	PUNCT
cana-6127	240	4	s.	s.	PROPN
cana-6127	240	5	g.	g.	PROPN
cana-6127	240	6	khavale	khavale	PROPN
cana-6127	240	7	,	,	PUNCT
cana-6127	240	8	k.	k.	PROPN
cana-6127	240	9	r.	r.	PROPN
cana-6127	240	10	gaikwad	gaikwad	PROPN
cana-6127	240	11	,	,	PUNCT
cana-6127	240	12	‘	'	PUNCT
cana-6127	240	13	‘	'	PUNCT
cana-6127	240	14	generalized	generalized	ADJ
cana-6127	240	15	theory	theory	NOUN
cana-6127	240	16	of	of	ADP
cana-6127	240	17	magneto	magneto	NOUN
cana-6127	240	18	-	-	PUNCT
cana-6127	240	19	thermo	thermo	NOUN
cana-6127	240	20	-	-	PUNCT
cana-6127	240	21	viscoelastic	viscoelastic	ADJ
cana-6127	240	22	spherical	spherical	ADJ
cana-6127	240	23	cavity	cavity	NOUN
cana-6127	240	24	problem	problem	NOUN
cana-6127	240	25	under	under	ADP
cana-6127	240	26	fractional	fractional	ADJ
cana-6127	240	27	order	order	NOUN
cana-6127	240	28	derivative	derivative	NOUN
cana-6127	240	29	:	:	PUNCT
cana-6127	240	30	state	state	NOUN
cana-6127	240	31	space	space	NOUN
cana-6127	240	32	approach	approach	NOUN
cana-6127	240	33	’’	’'	PUNCT
cana-6127	240	34	,	,	PUNCT
cana-6127	240	35	advances	advance	NOUN
cana-6127	240	36	in	in	ADP
cana-6127	240	37	mathematics	mathematic	NOUN
cana-6127	240	38	:	:	PUNCT
cana-6127	240	39	scientific	scientific	ADJ
cana-6127	240	40	journal	journal	NOUN
cana-6127	240	41	,	,	PUNCT
cana-6127	240	42	vol	vol	NOUN
cana-6127	240	43	.	.	PROPN
cana-6127	241	1	9	9	NUM
cana-6127	241	2	,	,	PUNCT
cana-6127	241	3	pp	pp	ADJ
cana-6127	241	4	.	.	PUNCT
cana-6127	242	1	9769–9780	9769–9780	NUM
cana-6127	242	2	,	,	PUNCT
cana-6127	242	3	2020	2020	NUM
cana-6127	242	4	.	.	PUNCT
cana-6127	243	1	[	[	X
cana-6127	243	2	24	24	NUM
cana-6127	243	3	]	]	PUNCT
cana-6127	243	4	k.	k.	PROPN
cana-6127	243	5	r.	r.	PROPN
cana-6127	243	6	gaikwad	gaikwad	PROPN
cana-6127	243	7	,	,	PUNCT
cana-6127	243	8	s.	s.	PROPN
cana-6127	243	9	g.	g.	PROPN
cana-6127	243	10	khavale	khavale	PROPN
cana-6127	243	11	,	,	PUNCT
cana-6127	243	12	‘	'	PUNCT
cana-6127	243	13	‘	'	PUNCT
cana-6127	243	14	time	time	NOUN
cana-6127	243	15	fractional	fractional	ADJ
cana-6127	243	16	2d	2d	NUM
cana-6127	243	17	thermoelastic	thermoelastic	ADJ
cana-6127	243	18	problem	problem	NOUN
cana-6127	243	19	of	of	ADP
cana-6127	243	20	thin	thin	ADJ
cana-6127	243	21	hollow	hollow	ADJ
cana-6127	243	22	circular	circular	ADJ
cana-6127	243	23	disk	disk	NOUN
cana-6127	243	24	and	and	CCONJ
cana-6127	243	25	it	it	PRON
cana-6127	243	26	’s	’	VERB
cana-6127	243	27	associated	associate	VERB
cana-6127	243	28	thermal	thermal	ADJ
cana-6127	243	29	stresses	stress	NOUN
cana-6127	243	30	’’	’'	PUNCT
cana-6127	243	31	,	,	PUNCT
cana-6127	243	32	bulletin	bulletin	NOUN
cana-6127	243	33	of	of	ADP
cana-6127	243	34	the	the	DET
cana-6127	243	35	marathwada	marathwada	PROPN
cana-6127	243	36	mathematical	mathematical	PROPN
cana-6127	243	37	society	society	NOUN
cana-6127	243	38	,	,	PUNCT
cana-6127	243	39	vol	vol	NOUN
cana-6127	243	40	.	.	PROPN
cana-6127	243	41	21(1	21(1	NUM
cana-6127	243	42	&	&	CCONJ
cana-6127	243	43	2	2	NUM
cana-6127	243	44	)	)	PUNCT
cana-6127	243	45	,	,	PUNCT
cana-6127	243	46	pp	pp	ADJ
cana-6127	243	47	.	.	PUNCT
cana-6127	244	1	37	37	NUM
cana-6127	244	2	-	-	SYM
cana-6127	244	3	47	47	NUM
cana-6127	244	4	,	,	PUNCT
cana-6127	244	5	2020	2020	NUM
cana-6127	244	6	.	.	PUNCT
cana-6127	245	1	[	[	X
cana-6127	245	2	25	25	NUM
cana-6127	245	3	]	]	PUNCT
cana-6127	245	4	f.	f.	PROPN
cana-6127	245	5	y.	y.	PROPN
cana-6127	245	6	tash	tash	PROPN
cana-6127	245	7	,	,	PUNCT
cana-6127	245	8	b.	b.	PROPN
cana-6127	245	9	n.	n.	PROPN
cana-6127	245	10	neya	neya	PROPN
cana-6127	245	11	,	,	PUNCT
cana-6127	245	12	‘	'	PUNCT
cana-6127	245	13	‘	'	PUNCT
cana-6127	245	14	an	an	DET
cana-6127	245	15	analytical	analytical	ADJ
cana-6127	245	16	solution	solution	NOUN
cana-6127	245	17	for	for	ADP
cana-6127	245	18	bending	bend	VERB
cana-6127	245	19	of	of	ADP
cana-6127	245	20	transversely	transversely	ADJ
cana-6127	245	21	isotropic	isotropic	ADJ
cana-6127	245	22	thick	thick	ADJ
cana-6127	245	23	rectangular	rectangular	ADJ
cana-6127	245	24	plates	plate	NOUN
cana-6127	245	25	with	with	ADP
cana-6127	245	26	variable	variable	ADJ
cana-6127	245	27	thickness	thickness	NOUN
cana-6127	245	28	’’	’'	PUNCT
cana-6127	245	29	,	,	PUNCT
cana-6127	245	30	appl	appl	PROPN
cana-6127	245	31	.	.	PROPN
cana-6127	245	32	math	math	PROPN
cana-6127	245	33	.	.	PUNCT
cana-6127	246	1	model	model	PROPN
cana-6127	246	2	.	.	PUNCT
cana-6127	247	1	,	,	PUNCT
cana-6127	247	2	vol	vol	NOUN
cana-6127	247	3	.	.	PUNCT
cana-6127	248	1	77(2	77(2	X
cana-6127	248	2	)	)	PUNCT
cana-6127	248	3	,	,	PUNCT
cana-6127	249	1	pp	pp	PROPN
cana-6127	249	2	.	.	PUNCT
cana-6127	250	1	1582-	1582-	NUM
cana-6127	250	2	–	–	PUNCT
cana-6127	250	3	1602	1602	NUM
cana-6127	250	4	,	,	PUNCT
cana-6127	250	5	2020	2020	NUM
cana-6127	250	6	.	.	PUNCT
cana-6127	251	1	[	[	X
cana-6127	251	2	26	26	NUM
cana-6127	251	3	]	]	PUNCT
cana-6127	251	4	k.	k.	PROPN
cana-6127	251	5	r.	r.	PROPN
cana-6127	251	6	gaikwad	gaikwad	PROPN
cana-6127	251	7	,	,	PUNCT
cana-6127	251	8	y.	y.	PROPN
cana-6127	251	9	u.	u.	PROPN
cana-6127	251	10	naner	naner	NOUN
cana-6127	251	11	,	,	PUNCT
cana-6127	251	12	‘	'	PUNCT
cana-6127	251	13	‘	'	PUNCT
cana-6127	251	14	analysis	analysis	NOUN
cana-6127	251	15	of	of	ADP
cana-6127	251	16	transient	transient	ADJ
cana-6127	251	17	thermoelastic	thermoelastic	ADJ
cana-6127	251	18	temperature	temperature	NOUN
cana-6127	251	19	distribution	distribution	NOUN
cana-6127	251	20	of	of	ADP
cana-6127	251	21	a	a	DET
cana-6127	251	22	thin	thin	ADJ
cana-6127	251	23	circular	circular	ADJ
cana-6127	251	24	plate	plate	NOUN
cana-6127	251	25	and	and	CCONJ
cana-6127	251	26	its	its	PRON
cana-6127	251	27	thermal	thermal	ADJ
cana-6127	251	28	deflection	deflection	NOUN
cana-6127	251	29	under	under	ADP
cana-6127	251	30	uniform	uniform	ADJ
cana-6127	251	31	heat	heat	NOUN
cana-6127	251	32	generation	generation	NOUN
cana-6127	251	33	’’	’'	PUNCT
cana-6127	251	34	,	,	PUNCT
cana-6127	251	35	journal	journal	NOUN
cana-6127	251	36	of	of	ADP
cana-6127	251	37	thermal	thermal	ADJ
cana-6127	251	38	stress	stress	NOUN
cana-6127	251	39	,	,	PUNCT
cana-6127	251	40	vol	vol	NOUN
cana-6127	251	41	.	.	PUNCT
cana-6127	252	1	44(1	44(1	NOUN
cana-6127	252	2	)	)	PUNCT
cana-6127	252	3	,	,	PUNCT
cana-6127	252	4	pp	pp	ADP
cana-6127	252	5	.	.	PUNCT
cana-6127	253	1	75–85	75–85	NUM
cana-6127	253	2	,	,	PUNCT
cana-6127	253	3	2021	2021	NUM
cana-6127	253	4	.	.	PUNCT
cana-6127	254	1	[	[	X
cana-6127	254	2	27	27	NUM
cana-6127	254	3	]	]	PUNCT
cana-6127	254	4	k.	k.	PROPN
cana-6127	254	5	r.	r.	PROPN
cana-6127	254	6	gaikwad	gaikwad	PROPN
cana-6127	254	7	,	,	PUNCT
cana-6127	254	8	y.	y.	PROPN
cana-6127	254	9	u.	u.	PROPN
cana-6127	254	10	naner	naner	NOUN
cana-6127	254	11	,	,	PUNCT
cana-6127	254	12	s.	s.	PROPN
cana-6127	254	13	g.	g.	PROPN
cana-6127	254	14	khavale	khavale	PROPN
cana-6127	254	15	,	,	PUNCT
cana-6127	254	16	‘	'	PUNCT
cana-6127	254	17	‘	'	PUNCT
cana-6127	254	18	time	time	NOUN
cana-6127	254	19	fractional	fractional	ADJ
cana-6127	254	20	thermoelastic	thermoelastic	ADJ
cana-6127	254	21	stress	stress	NOUN
cana-6127	254	22	analysis	analysis	NOUN
cana-6127	254	23	of	of	ADP
cana-6127	254	24	a	a	DET
cana-6127	254	25	thin	thin	ADJ
cana-6127	254	26	rectangular	rectangular	ADJ
cana-6127	254	27	plate	plate	NOUN
cana-6127	254	28	’’	’'	PUNCT
cana-6127	254	29	,	,	PUNCT
cana-6127	254	30	novyi	novyi	PROPN
cana-6127	254	31	mir	mir	PROPN
cana-6127	254	32	research	research	PROPN
cana-6127	254	33	journal	journal	PROPN
cana-6127	254	34	,	,	PUNCT
cana-6127	254	35	vol	vol	NOUN
cana-6127	254	36	.	.	PUNCT
cana-6127	254	37	6(1	6(1	NUM
cana-6127	254	38	)	)	PUNCT
cana-6127	254	39	,	,	PUNCT
cana-6127	254	40	pp	pp	ADP
cana-6127	254	41	.	.	PUNCT
cana-6127	255	1	42–56	42–56	NUM
cana-6127	255	2	,	,	PUNCT
cana-6127	255	3	2021	2021	NUM
cana-6127	255	4	.	.	PUNCT
cana-6127	256	1	[	[	X
cana-6127	256	2	28	28	NUM
cana-6127	256	3	]	]	X
cana-6127	256	4	s.	s.	PROPN
cana-6127	256	5	g.	g.	PROPN
cana-6127	256	6	khavale	khavale	PROPN
cana-6127	256	7	,	,	PUNCT
cana-6127	256	8	k.	k.	PROPN
cana-6127	256	9	r.	r.	PROPN
cana-6127	256	10	gaikwad	gaikwad	PROPN
cana-6127	256	11	,	,	PUNCT
cana-6127	256	12	‘	'	PUNCT
cana-6127	256	13	‘	'	PUNCT
cana-6127	256	14	fractional	fractional	ADJ
cana-6127	256	15	order	order	NOUN
cana-6127	256	16	thermoelastic	thermoelastic	ADJ
cana-6127	256	17	problem	problem	NOUN
cana-6127	256	18	of	of	ADP
cana-6127	256	19	thin	thin	ADJ
cana-6127	256	20	hollow	hollow	ADJ
cana-6127	256	21	circular	circular	ADJ
cana-6127	256	22	disk	disk	NOUN
cana-6127	256	23	and	and	CCONJ
cana-6127	256	24	its	its	PRON
cana-6127	256	25	thermal	thermal	ADJ
cana-6127	256	26	stresses	stress	NOUN
cana-6127	256	27	under	under	ADP
cana-6127	256	28	axi	axi	NOUN
cana-6127	256	29	-	-	PUNCT
cana-6127	256	30	symmetric	symmetric	ADJ
cana-6127	256	31	heat	heat	NOUN
cana-6127	256	32	supply	supply	NOUN
cana-6127	256	33	’’	’'	PUNCT
cana-6127	256	34	,	,	PUNCT
cana-6127	256	35	design	design	NOUN
cana-6127	256	36	engineering	engineering	NOUN
cana-6127	256	37	,	,	PUNCT
cana-6127	256	38	vol	vol	NOUN
cana-6127	256	39	.	.	PUNCT
cana-6127	257	1	2021(9	2021(9	NOUN
cana-6127	257	2	)	)	PUNCT
cana-6127	257	3	,	,	PUNCT
cana-6127	257	4	pp	pp	ADP
cana-6127	257	5	.	.	PUNCT
cana-6127	257	6	13851–13862	13851–13862	NUM
cana-6127	257	7	,	,	PUNCT
cana-6127	257	8	2021	2021	NUM
cana-6127	257	9	.	.	PUNCT
cana-6127	258	1	[	[	X
cana-6127	258	2	29	29	NUM
cana-6127	258	3	]	]	PUNCT
cana-6127	258	4	k.	k.	PROPN
cana-6127	258	5	r.	r.	PROPN
cana-6127	258	6	gaikwad	gaikwad	PROPN
cana-6127	258	7	,	,	PUNCT
cana-6127	258	8	v.	v.	PROPN
cana-6127	258	9	g.	g.	PROPN
cana-6127	258	10	bhandwalkar	bhandwalkar	PROPN
cana-6127	258	11	,	,	PUNCT
cana-6127	258	12	‘	'	PUNCT
cana-6127	258	13	‘	'	PUNCT
cana-6127	258	14	fractional	fractional	ADJ
cana-6127	258	15	order	order	NOUN
cana-6127	258	16	thermoelastic	thermoelastic	ADJ
cana-6127	258	17	problem	problem	NOUN
cana-6127	258	18	for	for	ADP
cana-6127	258	19	finite	finite	ADJ
cana-6127	258	20	piezoelectric	piezoelectric	NOUN
cana-6127	258	21	rod	rod	NOUN
cana-6127	258	22	subjected	subject	VERB
cana-6127	258	23	to	to	ADP
cana-6127	258	24	different	different	ADJ
cana-6127	258	25	types	type	NOUN
cana-6127	258	26	of	of	ADP
cana-6127	258	27	thermal	thermal	ADJ
cana-6127	258	28	loading	loading	NOUN
cana-6127	258	29	direct	direct	ADJ
cana-6127	258	30	approach	approach	NOUN
cana-6127	258	31	’’	’'	PUNCT
cana-6127	258	32	,	,	PUNCT
cana-6127	258	33	journal	journal	NOUN
cana-6127	258	34	of	of	ADP
cana-6127	258	35	the	the	DET
cana-6127	258	36	korean	korean	ADJ
cana-6127	258	37	society	society	NOUN
cana-6127	258	38	for	for	ADP
cana-6127	258	39	industrial	industrial	ADJ
cana-6127	258	40	and	and	CCONJ
cana-6127	258	41	apllied	apllie	VERB
cana-6127	258	42	mathematics	mathematic	NOUN
cana-6127	258	43	,	,	PUNCT
cana-6127	258	44	vol	vol	NOUN
cana-6127	258	45	.	.	PUNCT
cana-6127	259	1	25(3	25(3	NUM
cana-6127	259	2	)	)	PUNCT
cana-6127	259	3	,	,	PUNCT
cana-6127	260	1	pp	pp	PROPN
cana-6127	260	2	.	.	PUNCT
cana-6127	261	1	117	117	NUM
cana-6127	261	2	-	-	SYM
cana-6127	261	3	131	131	NUM
cana-6127	261	4	,	,	PUNCT
cana-6127	261	5	2021	2021	NUM
cana-6127	261	6	.	.	PUNCT
cana-6127	262	1	[	[	X
cana-6127	262	2	30	30	NUM
cana-6127	262	3	]	]	X
cana-6127	262	4	s.	s.	PROPN
cana-6127	262	5	g.	g.	PROPN
cana-6127	262	6	khavale	khavale	PROPN
cana-6127	262	7	,	,	PUNCT
cana-6127	262	8	k.	k.	PROPN
cana-6127	262	9	r.	r.	PROPN
cana-6127	262	10	gaikwad	gaikwad	PROPN
cana-6127	262	11	,	,	PUNCT
cana-6127	262	12	‘	'	PUNCT
cana-6127	262	13	‘	'	PUNCT
cana-6127	262	14	analysis	analysis	NOUN
cana-6127	262	15	of	of	ADP
cana-6127	262	16	non	non	ADJ
cana-6127	262	17	-	-	ADJ
cana-6127	262	18	integer	integer	ADJ
cana-6127	262	19	order	order	NOUN
cana-6127	262	20	thermoelastic	thermoelastic	ADJ
cana-6127	262	21	temperature	temperature	NOUN
cana-6127	262	22	distribution	distribution	NOUN
cana-6127	262	23	and	and	CCONJ
cana-6127	262	24	thermal	thermal	ADJ
cana-6127	262	25	deflection	deflection	NOUN
cana-6127	262	26	of	of	ADP
cana-6127	262	27	thin	thin	ADJ
cana-6127	262	28	hollow	hollow	ADJ
cana-6127	262	29	circular	circular	ADJ
cana-6127	262	30	disk	disk	NOUN
cana-6127	262	31	under	under	ADP
cana-6127	262	32	the	the	DET
cana-6127	262	33	axi	axi	NOUN
cana-6127	262	34	-	-	PUNCT
cana-6127	262	35	symmetric	symmetric	ADJ
cana-6127	262	36	heat	heat	NOUN
cana-6127	262	37	supply	supply	NOUN
cana-6127	262	38	’’	’'	PUNCT
cana-6127	262	39	,	,	PUNCT
cana-6127	262	40	journal	journal	NOUN
cana-6127	262	41	of	of	ADP
cana-6127	262	42	the	the	DET
cana-6127	262	43	korean	korean	ADJ
cana-6127	262	44	society	society	NOUN
cana-6127	262	45	for	for	ADP
cana-6127	262	46	industrial	industrial	ADJ
cana-6127	262	47	and	and	CCONJ
cana-6127	262	48	applied	applied	ADJ
cana-6127	262	49	mathematics	mathematic	NOUN
cana-6127	262	50	,	,	PUNCT
cana-6127	262	51	vol	vol	NOUN
cana-6127	262	52	.	.	PUNCT
cana-6127	263	1	26(1	26(1	NUM
cana-6127	263	2	)	)	PUNCT
cana-6127	263	3	,	,	PUNCT
cana-6127	264	1	pp	pp	PROPN
cana-6127	264	2	.	.	PUNCT
cana-6127	265	1	67	67	NUM
cana-6127	265	2	-	-	SYM
cana-6127	265	3	75	75	NUM
cana-6127	265	4	,	,	PUNCT
cana-6127	265	5	2022	2022	NUM
cana-6127	265	6	.	.	PUNCT
cana-6127	266	1	[	[	X
cana-6127	266	2	31	31	NUM
cana-6127	266	3	]	]	PUNCT
cana-6127	266	4	k.	k.	PROPN
cana-6127	266	5	r.	r.	PROPN
cana-6127	266	6	gaikwad	gaikwad	PROPN
cana-6127	266	7	,	,	PUNCT
cana-6127	266	8	s.	s.	PROPN
cana-6127	266	9	g.	g.	PROPN
cana-6127	266	10	khavale	khavale	PROPN
cana-6127	266	11	,	,	PUNCT
cana-6127	266	12	‘	'	PUNCT
cana-6127	266	13	‘	'	PUNCT
cana-6127	266	14	fractional	fractional	ADJ
cana-6127	266	15	order	order	NOUN
cana-6127	266	16	transient	transient	ADJ
cana-6127	266	17	thermoelastic	thermoelastic	ADJ
cana-6127	266	18	stress	stress	NOUN
cana-6127	266	19	analysis	analysis	NOUN
cana-6127	266	20	of	of	ADP
cana-6127	266	21	a	a	DET
cana-6127	266	22	thin	thin	ADJ
cana-6127	266	23	circular	circular	ADJ
cana-6127	266	24	sector	sector	NOUN
cana-6127	266	25	disk	disk	NOUN
cana-6127	266	26	’’	’'	PUNCT
cana-6127	266	27	,	,	PUNCT
cana-6127	266	28	international	international	ADJ
cana-6127	266	29	journal	journal	NOUN
cana-6127	266	30	of	of	ADP
cana-6127	266	31	thermodynamics	thermodynamic	NOUN
cana-6127	266	32	,	,	PUNCT
cana-6127	266	33	vol	vol	NOUN
cana-6127	266	34	.	.	PUNCT
cana-6127	267	1	25(1	25(1	NUM
cana-6127	267	2	)	)	PUNCT
cana-6127	267	3	,	,	PUNCT
cana-6127	268	1	pp	pp	PROPN
cana-6127	268	2	.	.	PUNCT
cana-6127	269	1	1	1	NUM
cana-6127	269	2	-	-	SYM
cana-6127	269	3	8	8	NUM
cana-6127	269	4	,	,	PUNCT
cana-6127	269	5	2022	2022	NUM
cana-6127	269	6	.	.	PUNCT
cana-6127	270	1	[	[	X
cana-6127	270	2	32	32	NUM
cana-6127	270	3	]	]	PUNCT
cana-6127	270	4	s.	s.	PROPN
cana-6127	270	5	g.	g.	PROPN
cana-6127	270	6	khavale	khavale	PROPN
cana-6127	270	7	,	,	PUNCT
cana-6127	270	8	k.	k.	PROPN
cana-6127	270	9	r.	r.	PROPN
cana-6127	270	10	gaikwad	gaikwad	PROPN
cana-6127	270	11	,	,	PUNCT
cana-6127	270	12	‘	'	PUNCT
cana-6127	270	13	‘	'	PUNCT
cana-6127	270	14	2d	2d	NUM
cana-6127	270	15	problem	problem	NOUN
cana-6127	270	16	for	for	ADP
cana-6127	270	17	a	a	DET
cana-6127	270	18	sphere	sphere	NOUN
cana-6127	270	19	in	in	ADP
cana-6127	270	20	the	the	DET
cana-6127	270	21	fractional	fractional	ADJ
cana-6127	270	22	order	order	NOUN
cana-6127	270	23	theory	theory	NOUN
cana-6127	270	24	thermoelasticity	thermoelasticity	NOUN
cana-6127	270	25	to	to	PART
cana-6127	270	26	axisymmetric	axisymmetric	VERB
cana-6127	270	27	temperature	temperature	NOUN
cana-6127	270	28	distribution	distribution	NOUN
cana-6127	270	29	’’	’'	PUNCT
cana-6127	270	30	,	,	PUNCT
cana-6127	270	31	advances	advance	NOUN
cana-6127	270	32	in	in	ADP
cana-6127	270	33	mathematics	mathematic	NOUN
cana-6127	270	34	:	:	PUNCT
cana-6127	270	35	scientific	scientific	ADJ
cana-6127	270	36	journal	journal	NOUN
cana-6127	270	37	,	,	PUNCT
cana-6127	270	38	vol	vol	NOUN
cana-6127	270	39	.	.	PUNCT
cana-6127	270	40	11(1	11(1	NUM
cana-6127	270	41	)	)	PUNCT
cana-6127	270	42	,	,	PUNCT
cana-6127	270	43	pp	pp	PROPN
cana-6127	270	44	.	.	PUNCT
cana-6127	271	1	1–15	1–15	NUM
cana-6127	271	2	,	,	PUNCT
cana-6127	271	3	2022	2022	NUM
cana-6127	271	4	.	.	PUNCT
cana-6127	272	1	[	[	X
cana-6127	272	2	33	33	NUM
cana-6127	272	3	]	]	PUNCT
cana-6127	272	4	s.	s.	PROPN
cana-6127	272	5	g.	g.	PROPN
cana-6127	272	6	khavale	khavale	PROPN
cana-6127	272	7	,	,	PUNCT
cana-6127	272	8	k.	k.	PROPN
cana-6127	272	9	r.	r.	PROPN
cana-6127	272	10	gaikwad	gaikwad	PROPN
cana-6127	272	11	,	,	PUNCT
cana-6127	272	12	‘	'	PUNCT
cana-6127	272	13	‘	'	PUNCT
cana-6127	272	14	two	two	NUM
cana-6127	272	15	-	-	PUNCT
cana-6127	272	16	dimensional	dimensional	ADJ
cana-6127	272	17	generalized	generalized	ADJ
cana-6127	272	18	magneto	magneto	NOUN
cana-6127	272	19	-	-	PUNCT
cana-6127	272	20	thermo	thermo	NOUN
cana-6127	272	21	-	-	PUNCT
cana-6127	272	22	viscoelasticity	viscoelasticity	NOUN
cana-6127	272	23	problem	problem	NOUN
cana-6127	272	24	for	for	ADP
cana-6127	272	25	a	a	DET
cana-6127	272	26	spherical	spherical	ADJ
cana-6127	272	27	cavity	cavity	NOUN
cana-6127	272	28	with	with	ADP
cana-6127	272	29	one	one	NUM
cana-6127	272	30	relaxation	relaxation	NOUN
cana-6127	272	31	time	time	NOUN
cana-6127	272	32	using	use	VERB
cana-6127	272	33	fractional	fractional	ADJ
cana-6127	272	34	derivative	derivative	ADJ
cana-6127	272	35	’’	’'	PUNCT
cana-6127	272	36	,	,	PUNCT
cana-6127	272	37	international	international	ADJ
cana-6127	272	38	journal	journal	NOUN
cana-6127	272	39	of	of	ADP
cana-6127	272	40	thermodynamics	thermodynamic	NOUN
cana-6127	272	41	,	,	PUNCT
cana-6127	272	42	vol	vol	NOUN
cana-6127	272	43	.	.	PUNCT
cana-6127	272	44	25(2	25(2	NUM
cana-6127	272	45	)	)	PUNCT
cana-6127	272	46	,	,	PUNCT
cana-6127	272	47	pp	pp	PROPN
cana-6127	272	48	.	.	PUNCT
cana-6127	272	49	89	89	NUM
cana-6127	272	50	-	-	SYM
cana-6127	272	51	97	97	NUM
cana-6127	272	52	,	,	PUNCT
cana-6127	272	53	2022	2022	NUM
cana-6127	272	54	.	.	PUNCT
cana-6127	273	1	[	[	X
cana-6127	273	2	34	34	NUM
cana-6127	273	3	]	]	PUNCT
cana-6127	273	4	k.	k.	PROPN
cana-6127	273	5	r.	r.	PROPN
cana-6127	273	6	gaikwad	gaikwad	PROPN
cana-6127	273	7	,	,	PUNCT
cana-6127	273	8	y.	y.	PROPN
cana-6127	273	9	u.	u.	PROPN
cana-6127	273	10	naner	naner	NOUN
cana-6127	273	11	,	,	PUNCT
cana-6127	273	12	s.	s.	PROPN
cana-6127	273	13	g.	g.	PROPN
cana-6127	273	14	khavale	khavale	PROPN
cana-6127	273	15	,	,	PUNCT
cana-6127	273	16	‘	'	PUNCT
cana-6127	273	17	‘	'	PUNCT
cana-6127	273	18	transient	transient	ADJ
cana-6127	273	19	thermoelastic	thermoelastic	ADJ
cana-6127	273	20	bending	bending	NOUN
cana-6127	273	21	analysis	analysis	NOUN
cana-6127	273	22	of	of	ADP
cana-6127	273	23	a	a	DET
cana-6127	273	24	rectangular	rectangular	ADJ
cana-6127	273	25	plate	plate	NOUN
cana-6127	273	26	with	with	ADP
cana-6127	273	27	a	a	DET
cana-6127	273	28	simply	simply	ADV
cana-6127	273	29	supported	support	VERB
cana-6127	273	30	edge	edge	NOUN
cana-6127	273	31	under	under	ADP
cana-6127	273	32	heat	heat	NOUN
cana-6127	273	33	source	source	NOUN
cana-6127	273	34	:	:	PUNCT
cana-6127	273	35	green	green	PROPN
cana-6127	273	36	’s	’s	PART
cana-6127	273	37	function	function	NOUN
cana-6127	273	38	approach	approach	NOUN
cana-6127	273	39	’’	’'	PUNCT
cana-6127	273	40	,	,	PUNCT
cana-6127	273	41	int	int	NOUN
cana-6127	273	42	.	.	PUNCT
cana-6127	274	1	j.	j.	PROPN
cana-6127	274	2	nonlinear	nonlinear	PROPN
cana-6127	274	3	anal	anal	PROPN
cana-6127	274	4	.	.	PUNCT
cana-6127	275	1	appl	appl	PROPN
cana-6127	275	2	.	.	PROPN
cana-6127	275	3	,	,	PUNCT
cana-6127	275	4	in	in	ADP
cana-6127	275	5	press	press	NOUN
cana-6127	275	6	,	,	PUNCT
cana-6127	275	7	pp	pp	ADJ
cana-6127	275	8	.	.	PUNCT
cana-6127	276	1	1	1	NUM
cana-6127	276	2	-	-	SYM
cana-6127	276	3	15	15	NUM
cana-6127	276	4	,	,	PUNCT
cana-6127	276	5	2022	2022	NUM
cana-6127	276	6	.	.	PUNCT
cana-6127	277	1	[	[	X
cana-6127	277	2	35	35	NUM
cana-6127	277	3	]	]	X
cana-6127	277	4	n.	n.	NOUN
cana-6127	277	5	m.	m.	NOUN
cana-6127	277	6	ozisik	ozisik	PROPN
cana-6127	277	7	,	,	PUNCT
cana-6127	277	8	boundary	boundary	ADJ
cana-6127	277	9	value	value	NOUN
cana-6127	277	10	problem	problem	NOUN
cana-6127	277	11	of	of	ADP
cana-6127	277	12	heat	heat	NOUN
cana-6127	277	13	conduction	conduction	NOUN
cana-6127	277	14	,	,	PUNCT
cana-6127	277	15	international	international	ADJ
cana-6127	277	16	textbook	textbook	NOUN
cana-6127	277	17	company	company	NOUN
cana-6127	277	18	,	,	PUNCT
cana-6127	277	19	scranton	scranton	PROPN
cana-6127	277	20	,	,	PUNCT
cana-6127	277	21	pennsylvania	pennsylvania	PROPN
cana-6127	277	22	,	,	PUNCT
cana-6127	277	23	1968	1968	NUM
cana-6127	277	24	.	.	PUNCT
cana-6127	278	1	[	[	X
cana-6127	278	2	36	36	NUM
cana-6127	278	3	]	]	PUNCT
cana-6127	278	4	i.	i.	PROPN
cana-6127	278	5	n.	n.	PROPN
cana-6127	278	6	sneddon	sneddon	PROPN
cana-6127	278	7	,	,	PUNCT
cana-6127	278	8	the	the	DET
cana-6127	278	9	use	use	NOUN
cana-6127	278	10	of	of	ADP
cana-6127	278	11	integral	integral	ADJ
cana-6127	278	12	transform	transform	NOUN
cana-6127	278	13	,	,	PUNCT
cana-6127	278	14	mcgraw	mcgraw	PROPN
cana-6127	278	15	hill	hill	PROPN
cana-6127	278	16	,	,	PUNCT
cana-6127	278	17	new	new	PROPN
cana-6127	278	18	york	york	PROPN
cana-6127	278	19	,	,	PUNCT
cana-6127	278	20	1972	1972	NUM
cana-6127	278	21	.	.	PUNCT
cana-6127	279	1	[	[	X
cana-6127	279	2	37	37	NUM
cana-6127	279	3	]	]	PUNCT
cana-6127	279	4	i.	i.	NOUN
cana-6127	279	5	podlubny	podlubny	PROPN
cana-6127	279	6	,	,	PUNCT
cana-6127	279	7	fractional	fractional	ADJ
cana-6127	279	8	differential	differential	NOUN
cana-6127	279	9	equation	equation	NOUN
cana-6127	279	10	,	,	PUNCT
cana-6127	279	11	academic	academic	ADJ
cana-6127	279	12	press	press	NOUN
cana-6127	279	13	,	,	PUNCT
cana-6127	279	14	san	san	PROPN
cana-6127	279	15	diego	diego	PROPN
cana-6127	279	16	,	,	PUNCT
cana-6127	279	17	1999	1999	NUM
cana-6127	279	18	.	.	PUNCT
cana-6127	280	1	[	[	X
cana-6127	280	2	38	38	NUM
cana-6127	280	3	]	]	PUNCT
cana-6127	280	4	b.	b.	PROPN
cana-6127	280	5	g.	g.	PROPN
cana-6127	280	6	korenev	korenev	PROPN
cana-6127	280	7	,	,	PUNCT
cana-6127	280	8	bessel	bessel	NOUN
cana-6127	280	9	functions	function	NOUN
cana-6127	280	10	and	and	CCONJ
cana-6127	280	11	their	their	PRON
cana-6127	280	12	applications	application	NOUN
cana-6127	280	13	.	.	PUNCT
cana-6127	281	1	boca	boca	PROPN
cana-6127	281	2	raton	raton	PROPN
cana-6127	281	3	:	:	PUNCT
cana-6127	281	4	crc	crc	PROPN
cana-6127	281	5	press	press	PROPN
cana-6127	281	6	,	,	PUNCT
cana-6127	281	7	2003	2003	NUM
cana-6127	281	8	.	.	PUNCT
cana-6127	282	1	[	[	X
cana-6127	282	2	39	39	NUM
cana-6127	282	3	]	]	PUNCT
cana-6127	282	4	y.	y.	PROPN
cana-6127	282	5	z.	z.	PROPN
cana-6127	282	6	povstenko	povstenko	PROPN
cana-6127	282	7	,	,	PUNCT
cana-6127	282	8	fractional	fractional	ADJ
cana-6127	282	9	thermoelasticity	thermoelasticity	NOUN
cana-6127	282	10	,	,	PUNCT
cana-6127	282	11	new	new	PROPN
cana-6127	282	12	york	york	PROPN
cana-6127	282	13	:	:	PUNCT
cana-6127	282	14	springer	springer	NOUN
cana-6127	282	15	,	,	PUNCT
cana-6127	282	16	2015	2015	NUM
cana-6127	282	17	.	.	PUNCT
cana-6127	283	1	[	[	X
cana-6127	283	2	40	40	NUM
cana-6127	283	3	]	]	PUNCT
cana-6127	283	4	ptc	ptc	PROPN
cana-6127	283	5	mathcad	mathcad	PROPN
cana-6127	283	6	prime-7.0.0.0	prime-7.0.0.0	NOUN
cana-6127	283	7	,	,	PUNCT
cana-6127	283	8	[	[	X
cana-6127	283	9	online	online	X
cana-6127	283	10	]	]	X
cana-6127	283	11	.	.	PUNCT
cana-6127	284	1	available	available	ADJ
cana-6127	284	2	:	:	PUNCT
cana-6127	284	3	https://support.ptc.com/help/mathcad/r7.0/en/	https://support.ptc.com/help/mathcad/r7.0/en/	NOUN
cana-6127	284	4	(	(	PUNCT
cana-6127	284	5	accessed	access	VERB
cana-6127	284	6	sep	sep	PROPN
cana-6127	284	7	.	.	PROPN
cana-6127	284	8	1	1	NUM
cana-6127	284	9	,	,	PUNCT
cana-6127	284	10	2022	2022	NUM
cana-6127	284	11	)	)	PUNCT
cana-6127	284	12	.	.	PUNCT