id	sid	tid	token	lemma	pos
cana-6099	1	1	communications	communication	NOUN
cana-6099	1	2	on	on	ADP
cana-6099	1	3	applied	apply	VERB
cana-6099	1	4	nonlinear	nonlinear	ADJ
cana-6099	1	5	analysis	analysis	NOUN
cana-6099	1	6	issn	issn	NOUN
cana-6099	1	7	:	:	PUNCT
cana-6099	1	8	1074	1074	NUM
cana-6099	1	9	-	-	PUNCT
cana-6099	1	10	133x	133x	NUM
cana-6099	1	11	vol	vol	VERB
cana-6099	1	12	32	32	NUM
cana-6099	1	13	no	no	NOUN
cana-6099	1	14	.	.	PUNCT
cana-6099	2	1	10s	10	NOUN
cana-6099	2	2	(	(	PUNCT
cana-6099	2	3	2025	2025	NUM
cana-6099	2	4	)	)	PUNCT
cana-6099	2	5	3351	3351	NUM
cana-6099	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	2	7	direct	direct	ADJ
cana-6099	2	8	approach	approach	NOUN
cana-6099	2	9	to	to	ADP
cana-6099	2	10	a	a	DET
cana-6099	2	11	generalized	generalized	ADJ
cana-6099	2	12	fractionalorder	fractionalorder	ADJ
cana-6099	2	13	thermoelastic	thermoelastic	ADJ
cana-6099	2	14	problem	problem	NOUN
cana-6099	2	15	for	for	ADP
cana-6099	2	16	a	a	DET
cana-6099	2	17	thickcircular	thickcircular	ADJ
cana-6099	2	18	plate	plate	NOUN
cana-6099	2	19	with	with	ADP
cana-6099	2	20	lord	lord	PROPN
cana-6099	2	21	-	-	PUNCT
cana-6099	2	22	shulman	shulman	PROPN
cana-6099	2	23	and	and	CCONJ
cana-6099	2	24	classical	classical	ADJ
cana-6099	2	25	coupledthermoelastic	coupledthermoelastic	ADJ
cana-6099	2	26	model	model	NOUN
cana-6099	2	27	vidhya	vidhya	PROPN
cana-6099	2	28	g.	g.	PROPN
cana-6099	2	29	bhandwalkar1	bhandwalkar1	PROPN
cana-6099	3	1	[	[	X
cana-6099	3	2	0000−0003−4132−2527	0000−0003−4132−2527	X
cana-6099	3	3	]	]	X
cana-6099	3	4	,	,	PUNCT
cana-6099	3	5	satish	satish	PROPN
cana-6099	3	6	g.	g.	PROPN
cana-6099	3	7	khavale2	khavale2	PUNCT
cana-6099	4	1	[	[	X
cana-6099	4	2	0000−0003−1281−6261	0000−0003−1281−6261	X
cana-6099	4	3	]	]	PUNCT
cana-6099	4	4	,	,	PUNCT
cana-6099	4	5	kishor	kishor	PROPN
cana-6099	4	6	r.	r.	PROPN
cana-6099	4	7	gaikwad3*[0000−0003−3551−301x	gaikwad3*[0000−0003−3551−301x	PROPN
cana-6099	4	8	]	]	PUNCT
cana-6099	4	9	1	1	NUM
cana-6099	4	10	f.y	f.y	PROPN
cana-6099	4	11	.	.	PROPN
cana-6099	4	12	engineering	engineering	PROPN
cana-6099	4	13	department	department	PROPN
cana-6099	4	14	of	of	ADP
cana-6099	4	15	mathematics	mathematics	PROPN
cana-6099	4	16	,	,	PUNCT
cana-6099	4	17	d.	d.	PROPN
cana-6099	4	18	y.	y.	PROPN
cana-6099	4	19	patil	patil	PROPN
cana-6099	4	20	college	college	PROPN
cana-6099	4	21	of	of	ADP
cana-6099	4	22	engineering	engineering	PROPN
cana-6099	4	23	,	,	PUNCT
cana-6099	4	24	akurdi	akurdi	PROPN
cana-6099	4	25	,	,	PUNCT
cana-6099	4	26	pune	pune	NOUN
cana-6099	4	27	,	,	PUNCT
cana-6099	4	28	maharashtra	maharashtra	PROPN
cana-6099	4	29	,	,	PUNCT
cana-6099	4	30	india	india	PROPN
cana-6099	4	31	411044	411044	NUM
cana-6099	4	32	.	.	PUNCT
cana-6099	5	1	2	2	NUM
cana-6099	5	2	department	department	NOUN
cana-6099	5	3	of	of	ADP
cana-6099	5	4	mathematics	mathematic	NOUN
cana-6099	5	5	,	,	PUNCT
cana-6099	5	6	chetana	chetana	PROPN
cana-6099	5	7	’s	’s	PART
cana-6099	5	8	hazarimal	hazarimal	NOUN
cana-6099	5	9	somani	somani	PROPN
cana-6099	5	10	college	college	PROPN
cana-6099	5	11	of	of	ADP
cana-6099	5	12	commerce	commerce	PROPN
cana-6099	5	13	and	and	CCONJ
cana-6099	5	14	economics	economic	NOUN
cana-6099	5	15	,	,	PUNCT
cana-6099	5	16	smt	smt	PROPN
cana-6099	5	17	.	.	PUNCT
cana-6099	6	1	kusumtai	kusumtai	PROPN
cana-6099	6	2	chaudhari	chaudhari	PROPN
cana-6099	6	3	college	college	PROPN
cana-6099	6	4	of	of	ADP
cana-6099	6	5	art	art	NOUN
cana-6099	6	6	,	,	PUNCT
cana-6099	6	7	(	(	PUNCT
cana-6099	6	8	bandre	bandre	PROPN
cana-6099	6	9	east	east	PROPN
cana-6099	6	10	)	)	PUNCT
cana-6099	6	11	,	,	PUNCT
cana-6099	6	12	mumbai	mumbai	PROPN
cana-6099	6	13	,	,	PUNCT
cana-6099	6	14	maharashtra	maharashtra	PROPN
cana-6099	6	15	,	,	PUNCT
cana-6099	6	16	india	india	PROPN
cana-6099	6	17	400051	400051	NUM
cana-6099	6	18	.	.	PUNCT
cana-6099	7	1	3	3	NUM
cana-6099	7	2	p.	p.	NOUN
cana-6099	7	3	g.	g.	PROPN
cana-6099	7	4	department	department	PROPN
cana-6099	7	5	of	of	ADP
cana-6099	7	6	mathematics	mathematics	PROPN
cana-6099	7	7	,	,	PUNCT
cana-6099	7	8	n.	n.	PROPN
cana-6099	7	9	e.	e.	PROPN
cana-6099	7	10	s.	s.	PROPN
cana-6099	7	11	,	,	PUNCT
cana-6099	7	12	science	science	PROPN
cana-6099	7	13	college	college	PROPN
cana-6099	7	14	,	,	PUNCT
cana-6099	7	15	nanded	nanded	PROPN
cana-6099	7	16	,	,	PUNCT
cana-6099	7	17	maharashtra	maharashtra	PROPN
cana-6099	7	18	,	,	PUNCT
cana-6099	7	19	india	india	PROPN
cana-6099	7	20	431605	431605	NUM
cana-6099	7	21	.	.	PUNCT
cana-6099	8	1	emailvidhyabhandwalkar@gmail.com	emailvidhyabhandwalkar@gmail.com	X
cana-6099	8	2	,	,	PUNCT
cana-6099	8	3	khavalesatish8@gmail.com,drkr.gaikwad@yahoo.in	khavalesatish8@gmail.com,drkr.gaikwad@yahoo.in	ADP
cana-6099	8	4	article	article	NOUN
cana-6099	8	5	history	history	NOUN
cana-6099	8	6	:	:	PUNCT
cana-6099	8	7	received	receive	VERB
cana-6099	8	8	:	:	PUNCT
cana-6099	8	9	06	06	NUM
cana-6099	8	10	-	-	SYM
cana-6099	8	11	07	07	NUM
cana-6099	8	12	-	-	PUNCT
cana-6099	8	13	2025	2025	NUM
cana-6099	8	14	revised	revise	VERB
cana-6099	8	15	:	:	PUNCT
cana-6099	8	16	15	15	NUM
cana-6099	8	17	-	-	SYM
cana-6099	8	18	08	08	NUM
cana-6099	8	19	-	-	PUNCT
cana-6099	8	20	2025	2025	NUM
cana-6099	8	21	accepted	accept	VERB
cana-6099	8	22	:	:	PUNCT
cana-6099	8	23	30	30	NUM
cana-6099	8	24	-	-	SYM
cana-6099	8	25	09	09	NUM
cana-6099	8	26	-	-	PUNCT
cana-6099	8	27	2025	2025	NUM
cana-6099	8	28	abstract	abstract	NOUN
cana-6099	8	29	:	:	PUNCT
cana-6099	8	30	in	in	ADP
cana-6099	8	31	the	the	DET
cana-6099	8	32	present	present	ADJ
cana-6099	8	33	article	article	NOUN
cana-6099	8	34	,	,	PUNCT
cana-6099	8	35	we	we	PRON
cana-6099	8	36	discussed	discuss	VERB
cana-6099	8	37	the	the	DET
cana-6099	8	38	mathematical	mathematical	ADJ
cana-6099	8	39	solution	solution	NOUN
cana-6099	8	40	of	of	ADP
cana-6099	8	41	generalized	generalized	ADJ
cana-6099	8	42	fractional	fractional	ADJ
cana-6099	8	43	order	order	NOUN
cana-6099	8	44	thermoelastic	thermoelastic	ADJ
cana-6099	8	45	problem	problem	NOUN
cana-6099	8	46	for	for	ADP
cana-6099	8	47	a	a	DET
cana-6099	8	48	thick	thick	ADJ
cana-6099	8	49	circular	circular	ADJ
cana-6099	8	50	plate	plate	NOUN
cana-6099	8	51	of	of	ADP
cana-6099	8	52	finite	finite	PROPN
cana-6099	8	53	thickness	thickness	NOUN
cana-6099	8	54	2b	2b	NOUN
cana-6099	8	55	occupying	occupy	VERB
cana-6099	8	56	the	the	DET
cana-6099	8	57	space	space	NOUN
cana-6099	9	1	d	d	NOUN
cana-6099	9	2	defined	define	VERB
cana-6099	9	3	by	by	ADP
cana-6099	9	4	0	0	NUM
cana-6099	9	5	≤	≤	NOUN
cana-6099	9	6	r	r	NOUN
cana-6099	9	7	≤∞	≤∞	PROPN
cana-6099	9	8	,	,	PUNCT
cana-6099	9	9	−b	−b	ADJ
cana-6099	9	10	≤	≤	NUM
cana-6099	9	11	z	z	NOUN
cana-6099	9	12	≤	≤	PROPN
cana-6099	9	13	b.	b.	PROPN
cana-6099	10	1	the	the	DET
cana-6099	10	2	problem	problem	NOUN
cana-6099	10	3	is	be	AUX
cana-6099	10	4	discussed	discuss	VERB
cana-6099	10	5	within	within	ADP
cana-6099	10	6	the	the	DET
cana-6099	10	7	context	context	NOUN
cana-6099	10	8	of	of	ADP
cana-6099	10	9	the	the	DET
cana-6099	10	10	theory	theory	NOUN
cana-6099	10	11	of	of	ADP
cana-6099	10	12	generalized	generalized	ADJ
cana-6099	10	13	thermoelastic	thermoelastic	ADJ
cana-6099	10	14	diffusion	diffusion	NOUN
cana-6099	10	15	with	with	ADP
cana-6099	10	16	one	one	NUM
cana-6099	10	17	relaxation	relaxation	NOUN
cana-6099	10	18	time	time	NOUN
cana-6099	10	19	.	.	PUNCT
cana-6099	11	1	the	the	DET
cana-6099	11	2	upper	upper	ADJ
cana-6099	11	3	and	and	CCONJ
cana-6099	11	4	the	the	DET
cana-6099	11	5	lower	low	ADJ
cana-6099	11	6	surfaces	surface	NOUN
cana-6099	11	7	of	of	ADP
cana-6099	11	8	the	the	DET
cana-6099	11	9	thick	thick	ADJ
cana-6099	11	10	plate	plate	NOUN
cana-6099	11	11	are	be	AUX
cana-6099	11	12	traction	traction	NOUN
cana-6099	11	13	free	free	ADJ
cana-6099	11	14	and	and	CCONJ
cana-6099	11	15	subjected	subject	VERB
cana-6099	11	16	to	to	ADP
cana-6099	11	17	an	an	DET
cana-6099	11	18	axi	axi	NOUN
cana-6099	11	19	-	-	PUNCT
cana-6099	11	20	symmetric	symmetric	ADJ
cana-6099	11	21	heat	heat	NOUN
cana-6099	11	22	supply	supply	NOUN
cana-6099	11	23	.	.	PUNCT
cana-6099	12	1	the	the	DET
cana-6099	12	2	solution	solution	NOUN
cana-6099	12	3	is	be	AUX
cana-6099	12	4	carried	carry	VERB
cana-6099	12	5	out	out	ADP
cana-6099	12	6	by	by	ADP
cana-6099	12	7	using	use	VERB
cana-6099	12	8	integral	integral	ADJ
cana-6099	12	9	transform	transform	NOUN
cana-6099	12	10	technique	technique	NOUN
cana-6099	12	11	and	and	CCONJ
cana-6099	12	12	a	a	DET
cana-6099	12	13	direct	direct	ADJ
cana-6099	12	14	approach	approach	NOUN
cana-6099	12	15	.	.	PUNCT
cana-6099	13	1	the	the	DET
cana-6099	13	2	most	most	ADV
cana-6099	13	3	general	general	ADJ
cana-6099	13	4	solutions	solution	NOUN
cana-6099	13	5	are	be	AUX
cana-6099	13	6	obtained	obtain	VERB
cana-6099	13	7	and	and	CCONJ
cana-6099	13	8	represented	represent	VERB
cana-6099	13	9	graphically	graphically	ADV
cana-6099	13	10	using	use	VERB
cana-6099	13	11	mathcad	mathcad	PROPN
cana-6099	13	12	.	.	PUNCT
cana-6099	14	1	the	the	DET
cana-6099	14	2	validity	validity	NOUN
cana-6099	14	3	of	of	ADP
cana-6099	14	4	this	this	DET
cana-6099	14	5	intended	intend	VERB
cana-6099	14	6	model	model	NOUN
cana-6099	14	7	is	be	AUX
cana-6099	14	8	assessed	assess	VERB
cana-6099	14	9	by	by	ADP
cana-6099	14	10	comparing	compare	VERB
cana-6099	14	11	it	it	PRON
cana-6099	14	12	with	with	ADP
cana-6099	14	13	previously	previously	ADV
cana-6099	14	14	published	publish	VERB
cana-6099	14	15	results	result	NOUN
cana-6099	14	16	.	.	PUNCT
cana-6099	15	1	according	accord	VERB
cana-6099	15	2	to	to	ADP
cana-6099	15	3	the	the	DET
cana-6099	15	4	authors	author	NOUN
cana-6099	15	5	this	this	DET
cana-6099	15	6	model	model	NOUN
cana-6099	15	7	is	be	AUX
cana-6099	15	8	explicitly	explicitly	ADV
cana-6099	15	9	useful	useful	ADJ
cana-6099	15	10	for	for	ADP
cana-6099	15	11	the	the	DET
cana-6099	15	12	researchers	researcher	NOUN
cana-6099	15	13	those	those	PRON
cana-6099	15	14	studying	study	VERB
cana-6099	15	15	development	development	NOUN
cana-6099	15	16	in	in	ADP
cana-6099	15	17	theory	theory	NOUN
cana-6099	15	18	of	of	ADP
cana-6099	15	19	hyperbolic	hyperbolic	ADJ
cana-6099	15	20	thermoelastic	thermoelastic	ADJ
cana-6099	15	21	diffusion	diffusion	NOUN
cana-6099	15	22	,	,	PUNCT
cana-6099	15	23	in	in	ADP
cana-6099	15	24	material	material	NOUN
cana-6099	15	25	science	science	NOUN
cana-6099	15	26	and	and	CCONJ
cana-6099	15	27	designers	designer	NOUN
cana-6099	15	28	of	of	ADP
cana-6099	15	29	new	new	ADJ
cana-6099	15	30	materials	material	NOUN
cana-6099	15	31	.	.	PUNCT
cana-6099	16	1	introduction	introduction	NOUN
cana-6099	16	2	:	:	PUNCT
cana-6099	16	3	this	this	DET
cana-6099	16	4	paper	paper	NOUN
cana-6099	16	5	presents	present	VERB
cana-6099	16	6	an	an	DET
cana-6099	16	7	analytical	analytical	ADJ
cana-6099	16	8	solution	solution	NOUN
cana-6099	16	9	to	to	ADP
cana-6099	16	10	a	a	DET
cana-6099	16	11	generalized	generalize	VERB
cana-6099	16	12	fractional	fractional	ADJ
cana-6099	16	13	order	order	NOUN
cana-6099	16	14	thermoelastic	thermoelastic	ADJ
cana-6099	16	15	problem	problem	NOUN
cana-6099	16	16	in	in	ADP
cana-6099	16	17	a	a	DET
cana-6099	16	18	thick	thick	ADJ
cana-6099	16	19	circular	circular	ADJ
cana-6099	16	20	plate	plate	NOUN
cana-6099	16	21	using	use	VERB
cana-6099	16	22	both	both	CCONJ
cana-6099	16	23	the	the	DET
cana-6099	16	24	lord	lord	PROPN
cana-6099	16	25	–	–	PUNCT
cana-6099	16	26	shulman	shulman	PROPN
cana-6099	16	27	(	(	PUNCT
cana-6099	16	28	ls	ls	PROPN
cana-6099	16	29	)	)	PUNCT
cana-6099	16	30	and	and	CCONJ
cana-6099	16	31	classical	classical	ADJ
cana-6099	16	32	coupled	couple	VERB
cana-6099	16	33	thermoelasticity	thermoelasticity	NOUN
cana-6099	16	34	(	(	PUNCT
cana-6099	16	35	cte	cte	NOUN
cana-6099	16	36	)	)	PUNCT
cana-6099	16	37	models	model	NOUN
cana-6099	16	38	.	.	PUNCT
cana-6099	17	1	the	the	DET
cana-6099	17	2	analysis	analysis	NOUN
cana-6099	17	3	considers	consider	VERB
cana-6099	17	4	a	a	DET
cana-6099	17	5	finite	finite	ADJ
cana-6099	17	6	plate	plate	NOUN
cana-6099	17	7	of	of	ADP
cana-6099	17	8	thickness	thickness	NOUN
cana-6099	17	9	2b	2b	NOUN
cana-6099	17	10	,	,	PUNCT
cana-6099	17	11	subjected	subject	VERB
cana-6099	17	12	to	to	ADP
cana-6099	17	13	axisymmetric	axisymmetric	VERB
cana-6099	17	14	thermal	thermal	ADJ
cana-6099	17	15	loading	loading	NOUN
cana-6099	17	16	on	on	ADP
cana-6099	17	17	its	its	PRON
cana-6099	17	18	traction	traction	NOUN
cana-6099	17	19	-	-	PUNCT
cana-6099	17	20	free	free	ADJ
cana-6099	17	21	upper	upper	ADJ
cana-6099	17	22	and	and	CCONJ
cana-6099	17	23	lower	low	ADJ
cana-6099	17	24	surfaces	surface	NOUN
cana-6099	17	25	.	.	PUNCT
cana-6099	18	1	employing	employ	VERB
cana-6099	18	2	a	a	DET
cana-6099	18	3	direct	direct	ADJ
cana-6099	18	4	approach	approach	NOUN
cana-6099	18	5	along	along	ADP
cana-6099	18	6	with	with	ADP
cana-6099	18	7	integral	integral	ADJ
cana-6099	18	8	transforms	transform	NOUN
cana-6099	18	9	,	,	PUNCT
cana-6099	18	10	we	we	PRON
cana-6099	18	11	derive	derive	VERB
cana-6099	18	12	general	general	ADJ
cana-6099	18	13	solutions	solution	NOUN
cana-6099	18	14	in	in	ADP
cana-6099	18	15	the	the	DET
cana-6099	18	16	laplace	laplace	NOUN
cana-6099	18	17	domain	domain	NOUN
cana-6099	18	18	without	without	ADP
cana-6099	18	19	introducing	introduce	VERB
cana-6099	18	20	potential	potential	ADJ
cana-6099	18	21	functions	function	NOUN
cana-6099	18	22	.	.	PUNCT
cana-6099	19	1	numerical	numerical	ADJ
cana-6099	19	2	evaluations	evaluation	NOUN
cana-6099	19	3	are	be	AUX
cana-6099	19	4	carried	carry	VERB
cana-6099	19	5	out	out	ADP
cana-6099	19	6	using	use	VERB
cana-6099	19	7	mathcad	mathcad	PROPN
cana-6099	19	8	,	,	PUNCT
cana-6099	19	9	and	and	CCONJ
cana-6099	19	10	results	result	NOUN
cana-6099	19	11	are	be	AUX
cana-6099	19	12	graphically	graphically	ADV
cana-6099	19	13	depicted	depict	VERB
cana-6099	19	14	to	to	PART
cana-6099	19	15	highlight	highlight	VERB
cana-6099	19	16	variations	variation	NOUN
cana-6099	19	17	in	in	ADP
cana-6099	19	18	temperature	temperature	NOUN
cana-6099	19	19	,	,	PUNCT
cana-6099	19	20	displacement	displacement	NOUN
cana-6099	19	21	,	,	PUNCT
cana-6099	19	22	stress	stress	NOUN
cana-6099	19	23	,	,	PUNCT
cana-6099	19	24	concentration	concentration	NOUN
cana-6099	19	25	,	,	PUNCT
cana-6099	19	26	and	and	CCONJ
cana-6099	19	27	chemical	chemical	NOUN
cana-6099	19	28	potential	potential	NOUN
cana-6099	19	29	.	.	PUNCT
cana-6099	20	1	the	the	DET
cana-6099	20	2	obtained	obtain	VERB
cana-6099	20	3	outcomes	outcome	NOUN
cana-6099	20	4	show	show	VERB
cana-6099	20	5	consistency	consistency	NOUN
cana-6099	20	6	with	with	ADP
cana-6099	20	7	established	establish	VERB
cana-6099	20	8	results	result	NOUN
cana-6099	20	9	and	and	CCONJ
cana-6099	20	10	illustrate	illustrate	VERB
cana-6099	20	11	the	the	DET
cana-6099	20	12	influence	influence	NOUN
cana-6099	20	13	of	of	ADP
cana-6099	20	14	fractional	fractional	ADJ
cana-6099	20	15	order	order	NOUN
cana-6099	20	16	and	and	CCONJ
cana-6099	20	17	time	time	NOUN
cana-6099	20	18	on	on	ADP
cana-6099	20	19	the	the	DET
cana-6099	20	20	thermoelastic	thermoelastic	ADJ
cana-6099	20	21	behaviour	behaviour	NOUN
cana-6099	20	22	.	.	PUNCT
cana-6099	21	1	this	this	DET
cana-6099	21	2	model	model	NOUN
cana-6099	21	3	proves	prove	VERB
cana-6099	21	4	valuable	valuable	ADJ
cana-6099	21	5	for	for	ADP
cana-6099	21	6	advancing	advance	VERB
cana-6099	21	7	the	the	DET
cana-6099	21	8	study	study	NOUN
cana-6099	21	9	of	of	ADP
cana-6099	21	10	hyperbolic	hyperbolic	ADJ
cana-6099	21	11	thermoelastic	thermoelastic	ADJ
cana-6099	21	12	diffusion	diffusion	NOUN
cana-6099	21	13	,	,	PUNCT
cana-6099	21	14	material	material	NOUN
cana-6099	21	15	science	science	NOUN
cana-6099	21	16	,	,	PUNCT
cana-6099	21	17	and	and	CCONJ
cana-6099	21	18	innovative	innovative	ADJ
cana-6099	21	19	material	material	NOUN
cana-6099	21	20	design	design	NOUN
cana-6099	21	21	.	.	PUNCT
cana-6099	22	1	objectives	objective	NOUN
cana-6099	22	2	:	:	PUNCT
cana-6099	22	3	to	to	PART
cana-6099	22	4	evaluate	evaluate	VERB
cana-6099	22	5	numerical	numerical	ADJ
cana-6099	22	6	solutions	solution	NOUN
cana-6099	22	7	for	for	ADP
cana-6099	22	8	temperature	temperature	NOUN
cana-6099	22	9	,	,	PUNCT
cana-6099	22	10	displacement	displacement	NOUN
cana-6099	22	11	,	,	PUNCT
cana-6099	22	12	stress	stress	NOUN
cana-6099	22	13	,	,	PUNCT
cana-6099	22	14	concentration	concentration	NOUN
cana-6099	22	15	,	,	PUNCT
cana-6099	22	16	and	and	CCONJ
cana-6099	22	17	chemical	chemical	NOUN
cana-6099	22	18	potential	potential	NOUN
cana-6099	22	19	and	and	CCONJ
cana-6099	22	20	observe	observe	VERB
cana-6099	22	21	the	the	DET
cana-6099	22	22	variations	variation	NOUN
cana-6099	22	23	graphically	graphically	ADV
cana-6099	22	24	by	by	ADP
cana-6099	22	25	employing	employ	VERB
cana-6099	22	26	mathcad	mathcad	PROPN
cana-6099	22	27	software	software	NOUN
cana-6099	22	28	for	for	ADP
cana-6099	22	29	two	two	NUM
cana-6099	22	30	distinct	distinct	ADJ
cana-6099	22	31	models	model	NOUN
cana-6099	22	32	namely	namely	ADV
cana-6099	22	33	communications	communication	VERB
cana-6099	22	34	on	on	ADP
cana-6099	22	35	applied	apply	VERB
cana-6099	22	36	nonlinear	nonlinear	ADJ
cana-6099	22	37	analysis	analysis	NOUN
cana-6099	22	38	issn	issn	NOUN
cana-6099	22	39	:	:	PUNCT
cana-6099	22	40	1074	1074	NUM
cana-6099	22	41	-	-	PUNCT
cana-6099	22	42	133x	133x	NUM
cana-6099	22	43	vol	vol	VERB
cana-6099	22	44	32	32	NUM
cana-6099	22	45	no	no	NOUN
cana-6099	22	46	.	.	PUNCT
cana-6099	23	1	10s	10	NOUN
cana-6099	23	2	(	(	PUNCT
cana-6099	23	3	2025	2025	NUM
cana-6099	23	4	)	)	PUNCT
cana-6099	23	5	3352	3352	NUM
cana-6099	23	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	23	7	lord	lord	PROPN
cana-6099	23	8	-	-	PUNCT
cana-6099	23	9	shulman	shulman	PROPN
cana-6099	23	10	&	&	CCONJ
cana-6099	23	11	classical	classical	ADJ
cana-6099	23	12	coupled	couple	VERB
cana-6099	23	13	thermoelastic	thermoelastic	ADJ
cana-6099	23	14	model	model	NOUN
cana-6099	23	15	.	.	PUNCT
cana-6099	24	1	methods	method	NOUN
cana-6099	24	2	:	:	PUNCT
cana-6099	24	3	concerned	concerned	ADJ
cana-6099	24	4	problem	problem	NOUN
cana-6099	24	5	is	be	AUX
cana-6099	24	6	solved	solve	VERB
cana-6099	24	7	by	by	ADP
cana-6099	24	8	employing	employ	VERB
cana-6099	24	9	an	an	DET
cana-6099	24	10	effective	effective	ADJ
cana-6099	24	11	method	method	NOUN
cana-6099	24	12	of	of	ADP
cana-6099	24	13	direct	direct	ADJ
cana-6099	24	14	approach	approach	NOUN
cana-6099	24	15	along	along	ADP
cana-6099	24	16	with	with	ADP
cana-6099	24	17	integral	integral	ADJ
cana-6099	24	18	transforms	transform	NOUN
cana-6099	24	19	without	without	ADP
cana-6099	24	20	introducing	introduce	VERB
cana-6099	24	21	potential	potential	ADJ
cana-6099	24	22	function	function	NOUN
cana-6099	24	23	.	.	PUNCT
cana-6099	25	1	results	result	NOUN
cana-6099	25	2	:	:	PUNCT
cana-6099	25	3	evaluated	evaluate	VERB
cana-6099	25	4	numerical	numerical	ADJ
cana-6099	25	5	solutions	solution	NOUN
cana-6099	25	6	for	for	ADP
cana-6099	25	7	the	the	DET
cana-6099	25	8	field	field	NOUN
cana-6099	25	9	functions	function	NOUN
cana-6099	25	10	such	such	ADJ
cana-6099	25	11	as	as	ADP
cana-6099	25	12	temperature	temperature	NOUN
cana-6099	25	13	,	,	PUNCT
cana-6099	25	14	displacement	displacement	NOUN
cana-6099	25	15	,	,	PUNCT
cana-6099	25	16	stress	stress	NOUN
cana-6099	25	17	,	,	PUNCT
cana-6099	25	18	concentration	concentration	NOUN
cana-6099	25	19	,	,	PUNCT
cana-6099	25	20	and	and	CCONJ
cana-6099	25	21	chemical	chemical	NOUN
cana-6099	25	22	potential	potential	NOUN
cana-6099	25	23	.	.	PUNCT
cana-6099	26	1	conclusions	conclusion	NOUN
cana-6099	26	2	:	:	PUNCT
cana-6099	26	3	in	in	ADP
cana-6099	26	4	this	this	DET
cana-6099	26	5	paper	paper	NOUN
cana-6099	26	6	,	,	PUNCT
cana-6099	26	7	we	we	PRON
cana-6099	26	8	analytically	analytically	ADV
cana-6099	26	9	solved	solve	VERB
cana-6099	26	10	the	the	DET
cana-6099	26	11	generalized	generalize	VERB
cana-6099	26	12	fractional	fractional	ADJ
cana-6099	26	13	order	order	NOUN
cana-6099	26	14	thermoelastic	thermoelastic	ADJ
cana-6099	26	15	problem	problem	NOUN
cana-6099	26	16	for	for	ADP
cana-6099	26	17	a	a	DET
cana-6099	26	18	thick	thick	ADJ
cana-6099	26	19	circular	circular	ADJ
cana-6099	26	20	plate	plate	NOUN
cana-6099	26	21	using	use	VERB
cana-6099	26	22	a	a	DET
cana-6099	26	23	direct	direct	ADJ
cana-6099	26	24	approach	approach	NOUN
cana-6099	26	25	and	and	CCONJ
cana-6099	26	26	integral	integral	ADJ
cana-6099	26	27	transform	transform	NOUN
cana-6099	26	28	techniques	technique	NOUN
cana-6099	26	29	.	.	PUNCT
cana-6099	27	1	the	the	DET
cana-6099	27	2	used	use	VERB
cana-6099	27	3	approach	approach	NOUN
cana-6099	27	4	avoids	avoid	VERB
cana-6099	27	5	the	the	DET
cana-6099	27	6	use	use	NOUN
cana-6099	27	7	of	of	ADP
cana-6099	27	8	potential	potential	ADJ
cana-6099	27	9	function	function	NOUN
cana-6099	27	10	,	,	PUNCT
cana-6099	27	11	offering	offer	VERB
cana-6099	27	12	a	a	DET
cana-6099	27	13	simplified	simplified	ADJ
cana-6099	27	14	and	and	CCONJ
cana-6099	27	15	efficient	efficient	ADJ
cana-6099	27	16	route	route	NOUN
cana-6099	27	17	to	to	PART
cana-6099	27	18	obtain	obtain	VERB
cana-6099	27	19	exact	exact	ADJ
cana-6099	27	20	solution	solution	NOUN
cana-6099	27	21	in	in	ADP
cana-6099	27	22	the	the	DET
cana-6099	27	23	laplace	laplace	NOUN
cana-6099	27	24	domain	domain	NOUN
cana-6099	27	25	.	.	PUNCT
cana-6099	28	1	the	the	DET
cana-6099	28	2	findings	finding	NOUN
cana-6099	28	3	have	have	VERB
cana-6099	28	4	significant	significant	ADJ
cana-6099	28	5	implications	implication	NOUN
cana-6099	28	6	for	for	ADP
cana-6099	28	7	researchers	researcher	NOUN
cana-6099	28	8	exploring	explore	VERB
cana-6099	28	9	fractional	fractional	ADJ
cana-6099	28	10	thermoelasticity	thermoelasticity	NOUN
cana-6099	28	11	,	,	PUNCT
cana-6099	28	12	particularly	particularly	ADV
cana-6099	28	13	in	in	ADP
cana-6099	28	14	the	the	DET
cana-6099	28	15	design	design	NOUN
cana-6099	28	16	of	of	ADP
cana-6099	28	17	advanced	advanced	ADJ
cana-6099	28	18	materials	material	NOUN
cana-6099	28	19	and	and	CCONJ
cana-6099	28	20	systems	system	NOUN
cana-6099	28	21	subjected	subject	VERB
cana-6099	28	22	to	to	ADP
cana-6099	28	23	thermal	thermal	ADJ
cana-6099	28	24	and	and	CCONJ
cana-6099	28	25	diffusion	diffusion	NOUN
cana-6099	28	26	effects	effect	NOUN
cana-6099	28	27	.	.	PUNCT
cana-6099	29	1	keywords	keyword	NOUN
cana-6099	29	2	:	:	PUNCT
cana-6099	29	3	circular	circular	ADJ
cana-6099	29	4	plate	plate	NOUN
cana-6099	29	5	,	,	PUNCT
cana-6099	29	6	fractional	fractional	ADJ
cana-6099	29	7	order	order	NOUN
cana-6099	29	8	derivative	derivative	NOUN
cana-6099	29	9	,	,	PUNCT
cana-6099	29	10	axisymmetric	axisymmetric	ADJ
cana-6099	29	11	temperature	temperature	NOUN
cana-6099	29	12	,	,	PUNCT
cana-6099	29	13	thermoelasticity	thermoelasticity	NOUN
cana-6099	29	14	,	,	PUNCT
cana-6099	29	15	lord	lord	PROPN
cana-6099	29	16	-	-	PUNCT
cana-6099	29	17	shulman	shulman	PROPN
cana-6099	29	18	model	model	PROPN
cana-6099	29	19	,	,	PUNCT
cana-6099	29	20	classical	classical	ADJ
cana-6099	29	21	coupled	couple	VERB
cana-6099	29	22	theory	theory	NOUN
cana-6099	29	23	.	.	PUNCT
cana-6099	30	1	1	1	X
cana-6099	30	2	.	.	X
cana-6099	30	3	introduction	introduction	NOUN
cana-6099	30	4	y.	y.	PROPN
cana-6099	30	5	z.	z.	PROPN
cana-6099	30	6	povstenko	povstenko	PROPN
cana-6099	31	1	[	[	X
cana-6099	31	2	1,3	1,3	NUM
cana-6099	31	3	]	]	PUNCT
cana-6099	31	4	,	,	PUNCT
cana-6099	31	5	solved	solve	VERB
cana-6099	31	6	some	some	DET
cana-6099	31	7	thermoelastic	thermoelastic	ADJ
cana-6099	31	8	problems	problem	NOUN
cana-6099	31	9	based	base	VERB
cana-6099	31	10	on	on	ADP
cana-6099	31	11	the	the	DET
cana-6099	31	12	equation	equation	NOUN
cana-6099	31	13	of	of	ADP
cana-6099	31	14	heat	heat	NOUN
cana-6099	31	15	conduction	conduction	NOUN
cana-6099	31	16	in	in	ADP
cana-6099	31	17	1d	1d	NUM
cana-6099	31	18	as	as	ADV
cana-6099	31	19	well	well	ADV
cana-6099	31	20	as	as	ADP
cana-6099	31	21	2d	2d	NOUN
cana-6099	31	22	with	with	ADP
cana-6099	31	23	a	a	DET
cana-6099	31	24	time	time	NOUN
cana-6099	31	25	-	-	PUNCT
cana-6099	31	26	fractional	fractional	ADJ
cana-6099	31	27	derivative	derivative	ADJ
cana-6099	31	28	and	and	CCONJ
cana-6099	31	29	associated	associated	ADJ
cana-6099	31	30	thermal	thermal	ADJ
cana-6099	31	31	stresses	stress	NOUN
cana-6099	31	32	.	.	PUNCT
cana-6099	32	1	in	in	ADP
cana-6099	32	2	four	four	NUM
cana-6099	32	3	distinct	distinct	ADJ
cana-6099	32	4	thermoelasticity	thermoelasticity	NOUN
cana-6099	32	5	theories	theory	NOUN
cana-6099	32	6	,	,	PUNCT
cana-6099	32	7	s.	s.	PROPN
cana-6099	32	8	mukhopadhyay	mukhopadhyay	PROPN
cana-6099	32	9	et.al	et.al	PROPN
cana-6099	32	10	.	.	PUNCT
cana-6099	33	1	[	[	X
cana-6099	33	2	2	2	NUM
cana-6099	33	3	]	]	PUNCT
cana-6099	33	4	,	,	PUNCT
cana-6099	33	5	explored	explore	VERB
cana-6099	33	6	the	the	DET
cana-6099	33	7	general	general	ADJ
cana-6099	33	8	thermoelastic	thermoelastic	ADJ
cana-6099	33	9	interactions	interaction	NOUN
cana-6099	33	10	in	in	ADP
cana-6099	33	11	unbounded	unbounded	ADJ
cana-6099	33	12	elastic	elastic	ADJ
cana-6099	33	13	media	medium	NOUN
cana-6099	33	14	and	and	CCONJ
cana-6099	33	15	spherical	spherical	ADJ
cana-6099	33	16	cavities	cavity	NOUN
cana-6099	33	17	.	.	PUNCT
cana-6099	34	1	a.	a.	NOUN
cana-6099	34	2	kar	kar	PROPN
cana-6099	34	3	et.al	et.al	PROPN
cana-6099	34	4	.	.	PUNCT
cana-6099	35	1	[	[	X
cana-6099	35	2	4	4	NUM
cana-6099	35	3	]	]	PUNCT
cana-6099	35	4	,	,	PUNCT
cana-6099	35	5	presented	present	VERB
cana-6099	35	6	thermoelasticity	thermoelasticity	NOUN
cana-6099	35	7	theories	theory	NOUN
cana-6099	35	8	for	for	ADP
cana-6099	35	9	a	a	DET
cana-6099	35	10	hollow	hollow	ADJ
cana-6099	35	11	sphere	sphere	NOUN
cana-6099	35	12	with	with	ADP
cana-6099	35	13	a	a	DET
cana-6099	35	14	thermal	thermal	ADJ
cana-6099	35	15	shock	shock	NOUN
cana-6099	35	16	problem	problem	NOUN
cana-6099	35	17	.	.	PUNCT
cana-6099	36	1	in	in	ADP
cana-6099	36	2	the	the	DET
cana-6099	36	3	fractional	fractional	ADJ
cana-6099	36	4	calculus	calculus	NOUN
cana-6099	36	5	technique	technique	NOUN
cana-6099	36	6	,	,	PUNCT
cana-6099	36	7	h.	h.	PROPN
cana-6099	36	8	h.	h.	PROPN
cana-6099	36	9	sherief	sherief	PROPN
cana-6099	36	10	et.al	et.al	PROPN
cana-6099	36	11	.	.	PUNCT
cana-6099	37	1	[	[	X
cana-6099	37	2	5	5	NUM
cana-6099	37	3	]	]	PUNCT
cana-6099	37	4	,	,	PUNCT
cana-6099	37	5	introduced	introduce	VERB
cana-6099	37	6	the	the	DET
cana-6099	37	7	novel	novel	NOUN
cana-6099	37	8	coupling	coupling	NOUN
cana-6099	37	9	between	between	ADP
cana-6099	37	10	thermoelasticity	thermoelasticity	NOUN
cana-6099	37	11	and	and	CCONJ
cana-6099	37	12	widespread	widespread	ADJ
cana-6099	37	13	thermoelasticity	thermoelasticity	NOUN
cana-6099	37	14	with	with	ADP
cana-6099	37	15	one	one	NUM
cana-6099	37	16	relaxation	relaxation	NOUN
cana-6099	37	17	cycle	cycle	NOUN
cana-6099	37	18	.	.	PUNCT
cana-6099	38	1	a.	a.	PROPN
cana-6099	38	2	sur	sur	PROPN
cana-6099	38	3	et.al	et.al	PROPN
cana-6099	38	4	.	.	PUNCT
cana-6099	39	1	[	[	X
cana-6099	39	2	6	6	NUM
cana-6099	39	3	]	]	PUNCT
cana-6099	39	4	,	,	PUNCT
cana-6099	39	5	developed	develop	VERB
cana-6099	39	6	the	the	DET
cana-6099	39	7	new	new	ADJ
cana-6099	39	8	theory	theory	NOUN
cana-6099	39	9	of	of	ADP
cana-6099	39	10	thermoelastic	thermoelastic	ADJ
cana-6099	39	11	distribution	distribution	NOUN
cana-6099	39	12	of	of	ADP
cana-6099	39	13	two	two	NUM
cana-6099	39	14	temperature	temperature	NOUN
cana-6099	39	15	with	with	ADP
cana-6099	39	16	new	new	ADJ
cana-6099	39	17	heat	heat	NOUN
cana-6099	39	18	conduction	conduction	NOUN
cana-6099	39	19	equation	equation	NOUN
cana-6099	39	20	with	with	ADP
cana-6099	39	21	fractional	fractional	ADJ
cana-6099	39	22	order	order	NOUN
cana-6099	39	23	.	.	PUNCT
cana-6099	40	1	h.	h.	PROPN
cana-6099	40	2	m.	m.	PROPN
cana-6099	40	3	youssef	youssef	PROPN
cana-6099	41	1	[	[	X
cana-6099	41	2	7	7	NUM
cana-6099	41	3	]	]	PUNCT
cana-6099	41	4	,	,	PUNCT
cana-6099	41	5	solved	solve	VERB
cana-6099	41	6	the	the	DET
cana-6099	41	7	generalized	generalized	ADJ
cana-6099	41	8	thermoelasticity	thermoelasticity	NOUN
cana-6099	41	9	theory	theory	NOUN
cana-6099	41	10	of	of	ADP
cana-6099	41	11	a	a	DET
cana-6099	41	12	half	half	NOUN
cana-6099	41	13	space	space	NOUN
cana-6099	41	14	filled	fill	VERB
cana-6099	41	15	with	with	ADP
cana-6099	41	16	an	an	DET
cana-6099	41	17	elastic	elastic	ADJ
cana-6099	41	18	material	material	NOUN
cana-6099	41	19	,	,	PUNCT
cana-6099	41	20	which	which	PRON
cana-6099	41	21	has	have	VERB
cana-6099	41	22	constant	constant	ADJ
cana-6099	41	23	elastic	elastic	ADJ
cana-6099	41	24	parameters	parameter	NOUN
cana-6099	41	25	in	in	ADP
cana-6099	41	26	the	the	DET
cana-6099	41	27	context	context	NOUN
cana-6099	41	28	of	of	ADP
cana-6099	41	29	the	the	DET
cana-6099	41	30	fractional	fractional	ADJ
cana-6099	41	31	order	order	NOUN
cana-6099	41	32	derivative	derivative	NOUN
cana-6099	41	33	.	.	PUNCT
cana-6099	42	1	k.	k.	PROPN
cana-6099	42	2	r.	r.	PROPN
cana-6099	42	3	gaikwad	gaikwad	PROPN
cana-6099	42	4	et.al	et.al	PROPN
cana-6099	42	5	.	.	PUNCT
cana-6099	43	1	[	[	X
cana-6099	43	2	8	8	NUM
cana-6099	43	3	]	]	PUNCT
cana-6099	43	4	,	,	PUNCT
cana-6099	43	5	presented	present	VERB
cana-6099	43	6	the	the	DET
cana-6099	43	7	thermoelastic	thermoelastic	ADJ
cana-6099	43	8	problem	problem	NOUN
cana-6099	43	9	for	for	ADP
cana-6099	43	10	the	the	DET
cana-6099	43	11	thick	thick	ADJ
cana-6099	43	12	circular	circular	ADJ
cana-6099	43	13	plate	plate	NOUN
cana-6099	43	14	subjected	subject	VERB
cana-6099	43	15	to	to	ADP
cana-6099	43	16	an	an	DET
cana-6099	43	17	interior	interior	ADJ
cana-6099	43	18	heat	heat	NOUN
cana-6099	43	19	flux	flux	NOUN
cana-6099	43	20	under	under	ADP
cana-6099	43	21	an	an	DET
cana-6099	43	22	unsteady	unsteady	ADJ
cana-6099	43	23	-	-	PUNCT
cana-6099	43	24	state	state	NOUN
cana-6099	43	25	,	,	PUNCT
cana-6099	43	26	the	the	DET
cana-6099	43	27	determination	determination	NOUN
cana-6099	43	28	of	of	ADP
cana-6099	43	29	unknown	unknown	ADJ
cana-6099	43	30	temperature	temperature	NOUN
cana-6099	43	31	,	,	PUNCT
cana-6099	43	32	displacement	displacement	NOUN
cana-6099	43	33	and	and	CCONJ
cana-6099	43	34	thermal	thermal	ADJ
cana-6099	43	35	stresses	stress	NOUN
cana-6099	43	36	on	on	ADP
cana-6099	43	37	the	the	DET
cana-6099	43	38	upper	upper	ADJ
cana-6099	43	39	surface	surface	NOUN
cana-6099	43	40	of	of	ADP
cana-6099	43	41	a	a	DET
cana-6099	43	42	plate	plate	NOUN
cana-6099	43	43	.	.	PUNCT
cana-6099	44	1	k.	k.	PROPN
cana-6099	44	2	r.	r.	PROPN
cana-6099	44	3	gaikwad	gaikwad	PROPN
cana-6099	44	4	et.al	et.al	PROPN
cana-6099	44	5	.	.	PUNCT
cana-6099	45	1	[	[	X
cana-6099	45	2	9	9	NUM
cana-6099	45	3	]	]	PUNCT
cana-6099	45	4	,	,	PUNCT
cana-6099	45	5	studied	study	VERB
cana-6099	45	6	the	the	DET
cana-6099	45	7	nonhomogeneous	nonhomogeneous	ADJ
cana-6099	45	8	heat	heat	NOUN
cana-6099	45	9	conduction	conduction	NOUN
cana-6099	45	10	problem	problem	NOUN
cana-6099	45	11	and	and	CCONJ
cana-6099	45	12	its	its	PRON
cana-6099	45	13	thermal	thermal	ADJ
cana-6099	45	14	deflection	deflection	NOUN
cana-6099	45	15	due	due	ADP
cana-6099	45	16	to	to	ADP
cana-6099	45	17	internal	internal	ADJ
cana-6099	45	18	heat	heat	NOUN
cana-6099	45	19	generation	generation	NOUN
cana-6099	45	20	in	in	ADP
cana-6099	45	21	a	a	DET
cana-6099	45	22	thin	thin	ADJ
cana-6099	45	23	hollow	hollow	ADJ
cana-6099	45	24	circular	circular	ADJ
cana-6099	45	25	disk	disk	NOUN
cana-6099	45	26	.	.	PUNCT
cana-6099	46	1	k.	k.	PROPN
cana-6099	46	2	r.	r.	PROPN
cana-6099	46	3	gaikwad	gaikwad	PROPN
cana-6099	47	1	[	[	X
cana-6099	47	2	10	10	NUM
cana-6099	47	3	]	]	PUNCT
cana-6099	47	4	,	,	PUNCT
cana-6099	47	5	analysed	analyse	VERB
cana-6099	47	6	the	the	DET
cana-6099	47	7	thermoelastic	thermoelastic	ADJ
cana-6099	47	8	deformation	deformation	NOUN
cana-6099	47	9	of	of	ADP
cana-6099	47	10	a	a	DET
cana-6099	47	11	thin	thin	ADJ
cana-6099	47	12	hollow	hollow	ADJ
cana-6099	47	13	circular	circular	ADJ
cana-6099	47	14	disk	disk	NOUN
cana-6099	47	15	due	due	ADP
cana-6099	47	16	to	to	PART
cana-6099	47	17	partially	partially	ADV
cana-6099	47	18	distributed	distribute	VERB
cana-6099	47	19	heat	heat	NOUN
cana-6099	47	20	supply	supply	NOUN
cana-6099	47	21	.	.	PUNCT
cana-6099	48	1	k.	k.	PROPN
cana-6099	48	2	r.	r.	PROPN
cana-6099	48	3	gaikwad	gaikwad	PROPN
cana-6099	49	1	[	[	X
cana-6099	49	2	23	23	NUM
cana-6099	49	3	]	]	PUNCT
cana-6099	49	4	,	,	PUNCT
cana-6099	49	5	analyzed	analyze	VERB
cana-6099	49	6	the	the	DET
cana-6099	49	7	problems	problem	NOUN
cana-6099	49	8	of	of	ADP
cana-6099	49	9	heat	heat	NOUN
cana-6099	49	10	conduction	conduction	NOUN
cana-6099	49	11	for	for	ADP
cana-6099	49	12	temperature	temperature	NOUN
cana-6099	49	13	and	and	CCONJ
cana-6099	49	14	thermal	thermal	ADJ
cana-6099	49	15	stress	stress	NOUN
cana-6099	49	16	.	.	PUNCT
cana-6099	50	1	a.	a.	NOUN
cana-6099	50	2	sur	sur	PROPN
cana-6099	50	3	et.al	et.al	PROPN
cana-6099	50	4	.	.	PUNCT
cana-6099	51	1	[	[	X
cana-6099	51	2	11	11	NUM
cana-6099	51	3	]	]	PUNCT
cana-6099	51	4	,	,	PUNCT
cana-6099	51	5	introduced	introduce	VERB
cana-6099	51	6	the	the	DET
cana-6099	51	7	fractional	fractional	ADJ
cana-6099	51	8	order	order	NOUN
cana-6099	51	9	generalized	generalize	VERB
cana-6099	51	10	thermoelastic	thermoelastic	ADJ
cana-6099	51	11	functionally	functionally	ADV
cana-6099	51	12	graded	grade	VERB
cana-6099	51	13	solid	solid	ADJ
cana-6099	51	14	with	with	ADP
cana-6099	51	15	variable	variable	ADJ
cana-6099	51	16	material	material	NOUN
cana-6099	51	17	properties	property	NOUN
cana-6099	51	18	.	.	PUNCT
cana-6099	52	1	e.	e.	PROPN
cana-6099	52	2	m.	m.	PROPN
cana-6099	52	3	hussain	hussain	PROPN
cana-6099	53	1	[	[	X
cana-6099	53	2	12	12	NUM
cana-6099	53	3	]	]	PUNCT
cana-6099	53	4	,	,	PUNCT
cana-6099	53	5	developed	develop	VERB
cana-6099	53	6	the	the	DET
cana-6099	53	7	fractional	fractional	ADJ
cana-6099	53	8	order	order	NOUN
cana-6099	53	9	thermoelastic	thermoelastic	ADJ
cana-6099	53	10	problem	problem	NOUN
cana-6099	53	11	for	for	ADP
cana-6099	53	12	an	an	DET
cana-6099	53	13	infinitely	infinitely	ADV
cana-6099	53	14	long	long	ADJ
cana-6099	53	15	solid	solid	ADJ
cana-6099	53	16	circular	circular	ADJ
cana-6099	53	17	cylinder	cylinder	NOUN
cana-6099	53	18	.	.	PUNCT
cana-6099	54	1	w.	w.	PROPN
cana-6099	54	2	raslan	raslan	PROPN
cana-6099	54	3	[	[	PRON
cana-6099	54	4	13	13	NUM
cana-6099	54	5	]	]	PUNCT
cana-6099	54	6	,	,	PUNCT
cana-6099	54	7	addressed	address	VERB
cana-6099	54	8	the	the	DET
cana-6099	54	9	1d	1d	NUM
cana-6099	54	10	issue	issue	NOUN
cana-6099	54	11	utilising	utilise	VERB
cana-6099	54	12	the	the	DET
cana-6099	54	13	laplace	laplace	NOUN
cana-6099	54	14	transform	transform	NOUN
cana-6099	54	15	technique	technique	NOUN
cana-6099	54	16	of	of	ADP
cana-6099	54	17	the	the	DET
cana-6099	54	18	thermoelasticity	thermoelasticity	NOUN
cana-6099	54	19	fractional	fractional	ADJ
cana-6099	54	20	order	order	NOUN
cana-6099	54	21	of	of	ADP
cana-6099	54	22	an	an	DET
cana-6099	54	23	infinitely	infinitely	ADV
cana-6099	54	24	long	long	ADJ
cana-6099	54	25	cylindrical	cylindrical	ADJ
cana-6099	54	26	cavity	cavity	NOUN
cana-6099	54	27	.	.	PUNCT
cana-6099	55	1	k.	k.	PROPN
cana-6099	55	2	r.	r.	PROPN
cana-6099	55	3	gaikwad	gaikwad	PROPN
cana-6099	56	1	[	[	X
cana-6099	56	2	14	14	NUM
cana-6099	56	3	]	]	PUNCT
cana-6099	56	4	,	,	PUNCT
cana-6099	56	5	developed	develop	VERB
cana-6099	56	6	the	the	DET
cana-6099	56	7	thermoelastic	thermoelastic	ADJ
cana-6099	56	8	mathematical	mathematical	ADJ
cana-6099	56	9	model	model	NOUN
cana-6099	56	10	for	for	ADP
cana-6099	56	11	circular	circular	ADJ
cana-6099	56	12	communications	communication	NOUN
cana-6099	56	13	on	on	ADP
cana-6099	56	14	applied	apply	VERB
cana-6099	56	15	nonlinear	nonlinear	ADJ
cana-6099	56	16	analysis	analysis	NOUN
cana-6099	56	17	issn	issn	NOUN
cana-6099	56	18	:	:	PUNCT
cana-6099	56	19	1074	1074	NUM
cana-6099	56	20	-	-	PUNCT
cana-6099	56	21	133x	133x	NUM
cana-6099	56	22	vol	vol	VERB
cana-6099	56	23	32	32	NUM
cana-6099	56	24	no	no	NOUN
cana-6099	56	25	.	.	PUNCT
cana-6099	57	1	10s	10	NOUN
cana-6099	57	2	(	(	PUNCT
cana-6099	57	3	2025	2025	NUM
cana-6099	57	4	)	)	PUNCT
cana-6099	57	5	3353	3353	NUM
cana-6099	57	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	57	7	sector	sector	NOUN
cana-6099	57	8	disk	disk	NOUN
cana-6099	57	9	subject	subject	NOUN
cana-6099	57	10	to	to	ADP
cana-6099	57	11	internal	internal	ADJ
cana-6099	57	12	heat	heat	NOUN
cana-6099	57	13	generation	generation	NOUN
cana-6099	57	14	.	.	PUNCT
cana-6099	58	1	a.	a.	NOUN
cana-6099	58	2	bayat	bayat	PROPN
cana-6099	58	3	et.al	et.al	PROPN
cana-6099	58	4	.	.	PUNCT
cana-6099	59	1	[	[	X
cana-6099	59	2	15	15	NUM
cana-6099	59	3	]	]	PUNCT
cana-6099	59	4	,	,	PUNCT
cana-6099	59	5	analysed	analyse	VERB
cana-6099	59	6	the	the	DET
cana-6099	59	7	unsteady	unsteady	ADJ
cana-6099	59	8	state	state	NOUN
cana-6099	59	9	thermo	thermo	NOUN
cana-6099	59	10	-	-	PUNCT
cana-6099	59	11	mechanical	mechanical	ADJ
cana-6099	59	12	problem	problem	NOUN
cana-6099	59	13	of	of	ADP
cana-6099	59	14	the	the	DET
cana-6099	59	15	fgm	fgm	PROPN
cana-6099	59	16	thick	thick	PROPN
cana-6099	59	17	sphere	sphere	PROPN
cana-6099	59	18	.	.	PUNCT
cana-6099	60	1	w.	w.	PROPN
cana-6099	60	2	raslan	raslan	PROPN
cana-6099	60	3	[	[	X
cana-6099	60	4	16	16	NUM
cana-6099	60	5	]	]	PUNCT
cana-6099	60	6	,	,	PUNCT
cana-6099	60	7	resolved	resolve	VERB
cana-6099	60	8	a	a	DET
cana-6099	60	9	2d	2d	NUM
cana-6099	60	10	problem	problem	NOUN
cana-6099	60	11	of	of	ADP
cana-6099	60	12	an	an	DET
cana-6099	60	13	axi	axi	NOUN
cana-6099	60	14	-	-	PUNCT
cana-6099	60	15	symmetric	symmetric	ADJ
cana-6099	60	16	temperature	temperature	NOUN
cana-6099	60	17	distribution	distribution	NOUN
cana-6099	60	18	fractional	fractional	ADJ
cana-6099	60	19	thermoelasticity	thermoelasticity	NOUN
cana-6099	60	20	order	order	NOUN
cana-6099	60	21	theory	theory	NOUN
cana-6099	60	22	of	of	ADP
cana-6099	60	23	a	a	DET
cana-6099	60	24	thick	thick	ADJ
cana-6099	60	25	plate	plate	NOUN
cana-6099	60	26	.	.	PUNCT
cana-6099	61	1	j.	j.	PROPN
cana-6099	61	2	j.	j.	PROPN
cana-6099	61	3	tripathi	tripathi	PROPN
cana-6099	62	1	[	[	X
cana-6099	62	2	17	17	NUM
cana-6099	62	3	]	]	PUNCT
cana-6099	62	4	,	,	PUNCT
cana-6099	62	5	showed	show	VERB
cana-6099	62	6	the	the	DET
cana-6099	62	7	impact	impact	NOUN
cana-6099	62	8	of	of	ADP
cana-6099	62	9	an	an	DET
cana-6099	62	10	axisymmetric	axisymmetric	ADJ
cana-6099	62	11	supply	supply	NOUN
cana-6099	62	12	of	of	ADP
cana-6099	62	13	heat	heat	NOUN
cana-6099	62	14	on	on	ADP
cana-6099	62	15	the	the	DET
cana-6099	62	16	diffusion	diffusion	NOUN
cana-6099	62	17	phenomena	phenomenon	NOUN
cana-6099	62	18	of	of	ADP
cana-6099	62	19	an	an	DET
cana-6099	62	20	infinite	infinite	ADJ
cana-6099	62	21	and	and	CCONJ
cana-6099	62	22	finite	finite	VERB
cana-6099	62	23	thick	thick	ADJ
cana-6099	62	24	thermoelastic	thermoelastic	ADJ
cana-6099	62	25	platform	platform	NOUN
cana-6099	62	26	and	and	CCONJ
cana-6099	62	27	the	the	DET
cana-6099	62	28	theory	theory	NOUN
cana-6099	62	29	of	of	ADP
cana-6099	62	30	widespread	widespread	ADJ
cana-6099	62	31	thermoelastic	thermoelastic	ADJ
cana-6099	62	32	diffusion	diffusion	NOUN
cana-6099	62	33	with	with	ADP
cana-6099	62	34	a	a	DET
cana-6099	62	35	one	one	NUM
cana-6099	62	36	-	-	PUNCT
cana-6099	62	37	time	time	NOUN
cana-6099	62	38	interval	interval	NOUN
cana-6099	62	39	of	of	ADP
cana-6099	62	40	relaxation	relaxation	NOUN
cana-6099	62	41	.	.	PUNCT
cana-6099	63	1	m.	m.	NOUN
cana-6099	63	2	a.	a.	PROPN
cana-6099	63	3	ezzat	ezzat	PROPN
cana-6099	64	1	[	[	X
cana-6099	64	2	18	18	NUM
cana-6099	64	3	]	]	PUNCT
cana-6099	64	4	,	,	PUNCT
cana-6099	64	5	developed	develop	VERB
cana-6099	64	6	a	a	DET
cana-6099	64	7	3d	3d	NUM
cana-6099	64	8	thermoelasticity	thermoelasticity	NOUN
cana-6099	64	9	model	model	NOUN
cana-6099	64	10	with	with	ADP
cana-6099	64	11	time	time	NOUN
cana-6099	64	12	-	-	PUNCT
cana-6099	64	13	dependent	dependent	ADJ
cana-6099	64	14	thermal	thermal	ADJ
cana-6099	64	15	shock	shock	NOUN
cana-6099	64	16	issue	issue	NOUN
cana-6099	64	17	,	,	PUNCT
cana-6099	64	18	utilising	utilise	VERB
cana-6099	64	19	a	a	DET
cana-6099	64	20	fractional	fractional	ADJ
cana-6099	64	21	thermoelasticity	thermoelasticity	NOUN
cana-6099	64	22	order	order	NOUN
cana-6099	64	23	theory	theory	NOUN
cana-6099	64	24	for	for	ADP
cana-6099	64	25	a	a	DET
cana-6099	64	26	half	half	ADJ
cana-6099	64	27	-	-	PUNCT
cana-6099	64	28	space	space	NOUN
cana-6099	64	29	.	.	PUNCT
cana-6099	65	1	k.	k.	PROPN
cana-6099	65	2	r.	r.	PROPN
cana-6099	65	3	gaikwad	gaikwad	PROPN
cana-6099	65	4	et.al	et.al	PROPN
cana-6099	65	5	.	.	PUNCT
cana-6099	66	1	[	[	X
cana-6099	66	2	27	27	NUM
cana-6099	66	3	]	]	PUNCT
cana-6099	66	4	,	,	PUNCT
cana-6099	66	5	analyzed	analyze	VERB
cana-6099	66	6	the	the	DET
cana-6099	66	7	various	various	ADJ
cana-6099	66	8	non	non	ADJ
cana-6099	66	9	-	-	ADJ
cana-6099	66	10	integer	integer	ADJ
cana-6099	66	11	order	order	NOUN
cana-6099	66	12	problems	problem	NOUN
cana-6099	66	13	of	of	ADP
cana-6099	66	14	thermoelasticity	thermoelasticity	NOUN
cana-6099	66	15	with	with	ADP
cana-6099	66	16	different	different	ADJ
cana-6099	66	17	approaches	approach	NOUN
cana-6099	66	18	and	and	CCONJ
cana-6099	66	19	got	get	VERB
cana-6099	66	20	wonderful	wonderful	ADJ
cana-6099	66	21	results	result	NOUN
cana-6099	66	22	.	.	PUNCT
cana-6099	67	1	v.	v.	ADP
cana-6099	67	2	g.	g.	PROPN
cana-6099	67	3	bhandwalkar	bhandwalkar	PROPN
cana-6099	67	4	et.al	et.al	PROPN
cana-6099	67	5	.	.	PUNCT
cana-6099	68	1	[	[	X
cana-6099	68	2	34	34	NUM
cana-6099	68	3	]	]	PUNCT
cana-6099	68	4	,	,	PUNCT
cana-6099	68	5	proposed	propose	VERB
cana-6099	68	6	the	the	DET
cana-6099	68	7	1d	1d	NUM
cana-6099	68	8	fractional	fractional	ADJ
cana-6099	68	9	order	order	NOUN
cana-6099	68	10	generalized	generalize	VERB
cana-6099	68	11	thermoelastic	thermoelastic	ADJ
cana-6099	68	12	model	model	NOUN
cana-6099	68	13	for	for	ADP
cana-6099	68	14	half	half	ADJ
cana-6099	68	15	-	-	PUNCT
cana-6099	68	16	space	space	NOUN
cana-6099	68	17	in	in	ADP
cana-6099	68	18	the	the	DET
cana-6099	68	19	context	context	NOUN
cana-6099	68	20	of	of	ADP
cana-6099	68	21	two	two	NUM
cana-6099	68	22	models	model	NOUN
cana-6099	68	23	,	,	PUNCT
cana-6099	68	24	viz	viz	PROPN
cana-6099	68	25	.	.	PROPN
cana-6099	68	26	,	,	PUNCT
cana-6099	68	27	ls	ls	PROPN
cana-6099	68	28	and	and	CCONJ
cana-6099	68	29	dpl	dpl	NOUN
cana-6099	68	30	.	.	PUNCT
cana-6099	69	1	in	in	ADP
cana-6099	69	2	which	which	DET
cana-6099	69	3	effect	effect	NOUN
cana-6099	69	4	of	of	ADP
cana-6099	69	5	exponentially	exponentially	ADV
cana-6099	69	6	varying	vary	VERB
cana-6099	69	7	heat	heat	NOUN
cana-6099	69	8	source	source	NOUN
cana-6099	69	9	and	and	CCONJ
cana-6099	69	10	the	the	DET
cana-6099	69	11	fractional	fractional	ADJ
cana-6099	69	12	order	order	NOUN
cana-6099	69	13	parameter	parameter	NOUN
cana-6099	69	14	has	have	AUX
cana-6099	69	15	been	be	AUX
cana-6099	69	16	investigated	investigate	VERB
cana-6099	69	17	on	on	ADP
cana-6099	69	18	field	field	NOUN
cana-6099	69	19	variables	variable	NOUN
cana-6099	69	20	such	such	ADJ
cana-6099	69	21	as	as	ADP
cana-6099	69	22	temperature	temperature	NOUN
cana-6099	69	23	,	,	PUNCT
cana-6099	69	24	displacement	displacement	NOUN
cana-6099	69	25	and	and	CCONJ
cana-6099	69	26	stress	stress	NOUN
cana-6099	69	27	.	.	PUNCT
cana-6099	70	1	v.	v.	ADP
cana-6099	70	2	g.	g.	PROPN
cana-6099	70	3	bhandwalkar	bhandwalkar	PROPN
cana-6099	70	4	et.al	et.al	PROPN
cana-6099	70	5	.	.	PUNCT
cana-6099	71	1	[	[	X
cana-6099	71	2	35	35	NUM
cana-6099	71	3	]	]	PUNCT
cana-6099	71	4	,	,	PUNCT
cana-6099	71	5	constructed	construct	VERB
cana-6099	71	6	the	the	DET
cana-6099	71	7	caputofabrizio	caputofabrizio	NOUN
cana-6099	71	8	fractional	fractional	ADJ
cana-6099	71	9	order	order	NOUN
cana-6099	71	10	model	model	NOUN
cana-6099	71	11	to	to	PART
cana-6099	71	12	study	study	VERB
cana-6099	71	13	effects	effect	NOUN
cana-6099	71	14	of	of	ADP
cana-6099	71	15	thermal	thermal	ADJ
cana-6099	71	16	diffusion	diffusion	NOUN
cana-6099	71	17	in	in	ADP
cana-6099	71	18	human	human	ADJ
cana-6099	71	19	head	head	NOUN
cana-6099	71	20	skin	skin	NOUN
cana-6099	71	21	tissue	tissue	NOUN
cana-6099	71	22	.	.	PUNCT
cana-6099	72	1	where	where	SCONJ
cana-6099	72	2	the	the	DET
cana-6099	72	3	accumulation	accumulation	NOUN
cana-6099	72	4	of	of	ADP
cana-6099	72	5	heat	heat	NOUN
cana-6099	72	6	over	over	ADP
cana-6099	72	7	time	time	NOUN
cana-6099	72	8	by	by	ADP
cana-6099	72	9	the	the	DET
cana-6099	72	10	skin	skin	NOUN
cana-6099	72	11	tissue	tissue	NOUN
cana-6099	72	12	is	be	AUX
cana-6099	72	13	realistically	realistically	ADV
cana-6099	72	14	modeled	model	VERB
cana-6099	72	15	.	.	PUNCT
cana-6099	73	1	in	in	ADP
cana-6099	73	2	which	which	PRON
cana-6099	73	3	the	the	DET
cana-6099	73	4	infinite	infinite	ADJ
cana-6099	73	5	memory	memory	NOUN
cana-6099	73	6	effects	effect	NOUN
cana-6099	73	7	have	have	AUX
cana-6099	73	8	been	be	AUX
cana-6099	73	9	avoided	avoid	VERB
cana-6099	73	10	with	with	ADP
cana-6099	73	11	the	the	DET
cana-6099	73	12	help	help	NOUN
cana-6099	73	13	of	of	ADP
cana-6099	73	14	non	non	ADJ
cana-6099	73	15	-	-	ADJ
cana-6099	73	16	singular	singular	ADJ
cana-6099	73	17	kernel	kernel	NOUN
cana-6099	73	18	.	.	PUNCT
cana-6099	74	1	k.r	k.r	PROPN
cana-6099	74	2	.	.	PROPN
cana-6099	74	3	gaikwad	gaikwad	PROPN
cana-6099	75	1	[	[	X
cana-6099	75	2	19	19	NUM
cana-6099	75	3	]	]	PUNCT
cana-6099	75	4	,	,	PUNCT
cana-6099	75	5	studied	study	VERB
cana-6099	75	6	two	two	NUM
cana-6099	75	7	-	-	PUNCT
cana-6099	75	8	dimensional	dimensional	ADJ
cana-6099	75	9	steady	steady	ADJ
cana-6099	75	10	state	state	NOUN
cana-6099	75	11	problem	problem	NOUN
cana-6099	75	12	for	for	ADP
cana-6099	75	13	thin	thin	ADJ
cana-6099	75	14	circular	circular	ADJ
cana-6099	75	15	plate	plate	NOUN
cana-6099	75	16	under	under	ADP
cana-6099	75	17	uniform	uniform	ADJ
cana-6099	75	18	internal	internal	ADJ
cana-6099	75	19	energy	energy	NOUN
cana-6099	75	20	generation	generation	NOUN
cana-6099	75	21	.	.	PUNCT
cana-6099	76	1	finite	finite	VERB
cana-6099	76	2	hankel	hankel	NOUN
cana-6099	76	3	transform	transform	NOUN
cana-6099	76	4	technique	technique	NOUN
cana-6099	76	5	to	to	PART
cana-6099	76	6	solve	solve	VERB
cana-6099	76	7	governing	govern	VERB
cana-6099	76	8	heat	heat	NOUN
cana-6099	76	9	conduction	conduction	NOUN
cana-6099	76	10	equation	equation	NOUN
cana-6099	76	11	.	.	PUNCT
cana-6099	77	1	in	in	ADP
cana-6099	77	2	2019	2019	NUM
cana-6099	77	3	k.	k.	PROPN
cana-6099	77	4	r.	r.	PROPN
cana-6099	77	5	gaikwad	gaikwad	PROPN
cana-6099	77	6	[	[	X
cana-6099	77	7	20	20	NUM
cana-6099	77	8	]	]	PUNCT
cana-6099	77	9	,	,	PUNCT
cana-6099	77	10	a	a	DET
cana-6099	77	11	2d	2d	NUM
cana-6099	77	12	problem	problem	NOUN
cana-6099	77	13	of	of	ADP
cana-6099	77	14	thin	thin	ADJ
cana-6099	77	15	hollow	hollow	ADJ
cana-6099	77	16	circular	circular	ADJ
cana-6099	77	17	disk	disk	NOUN
cana-6099	77	18	is	be	AUX
cana-6099	77	19	analyzed	analyze	VERB
cana-6099	77	20	in	in	ADP
cana-6099	77	21	the	the	DET
cana-6099	77	22	context	context	NOUN
cana-6099	77	23	of	of	ADP
cana-6099	77	24	fractional	fractional	ADJ
cana-6099	77	25	order	order	NOUN
cana-6099	77	26	derivative	derivative	NOUN
cana-6099	77	27	of	of	ADP
cana-6099	77	28	order	order	NOUN
cana-6099	77	29	0	0	PUNCT
cana-6099	77	30	<	<	X
cana-6099	77	31	α	α	PROPN
cana-6099	77	32	≤	≤	ADJ
cana-6099	77	33	2	2	NUM
cana-6099	77	34	.	.	PUNCT
cana-6099	77	35	by	by	ADP
cana-6099	77	36	applying	apply	VERB
cana-6099	77	37	laplace	laplace	NOUN
cana-6099	77	38	,	,	PUNCT
cana-6099	77	39	finite	finite	ADJ
cana-6099	77	40	fourier	fourier	NOUN
cana-6099	77	41	and	and	CCONJ
cana-6099	77	42	hankel	hankel	NOUN
cana-6099	77	43	transforms	transform	VERB
cana-6099	77	44	results	result	NOUN
cana-6099	77	45	have	have	AUX
cana-6099	77	46	been	be	AUX
cana-6099	77	47	obtained	obtain	VERB
cana-6099	77	48	and	and	CCONJ
cana-6099	77	49	illustrated	illustrate	VERB
cana-6099	77	50	graphically	graphically	ADV
cana-6099	77	51	using	use	VERB
cana-6099	77	52	ptc	ptc	PROPN
cana-6099	77	53	mathcad	mathcad	PROPN
cana-6099	77	54	.	.	PUNCT
cana-6099	78	1	in	in	ADP
cana-6099	78	2	2020	2020	NUM
cana-6099	78	3	s.	s.	PROPN
cana-6099	78	4	g.	g.	PROPN
cana-6099	78	5	khavale	khavale	PROPN
cana-6099	78	6	et.al	et.al	PROPN
cana-6099	78	7	.	.	PUNCT
cana-6099	79	1	[	[	X
cana-6099	79	2	21	21	NUM
cana-6099	79	3	]	]	PUNCT
cana-6099	79	4	,	,	PUNCT
cana-6099	79	5	constructed	construct	VERB
cana-6099	79	6	the	the	DET
cana-6099	79	7	fractional	fractional	ADJ
cana-6099	79	8	order	order	NOUN
cana-6099	79	9	model	model	NOUN
cana-6099	79	10	of	of	ADP
cana-6099	79	11	magneto	magneto	NOUN
cana-6099	79	12	-	-	PUNCT
cana-6099	79	13	thermo	thermo	NOUN
cana-6099	79	14	-	-	PUNCT
cana-6099	79	15	viscoelastic	viscoelastic	ADJ
cana-6099	79	16	spherical	spherical	ADJ
cana-6099	79	17	cavity	cavity	NOUN
cana-6099	79	18	and	and	CCONJ
cana-6099	79	19	field	field	NOUN
cana-6099	79	20	variables	variable	NOUN
cana-6099	79	21	have	have	AUX
cana-6099	79	22	obtained	obtain	VERB
cana-6099	79	23	.	.	PUNCT
cana-6099	80	1	the	the	DET
cana-6099	80	2	general	general	ADJ
cana-6099	80	3	solution	solution	NOUN
cana-6099	80	4	is	be	AUX
cana-6099	80	5	derived	derive	VERB
cana-6099	80	6	using	use	VERB
cana-6099	80	7	laplace	laplace	NOUN
cana-6099	80	8	transform	transform	NOUN
cana-6099	80	9	technique	technique	NOUN
cana-6099	80	10	and	and	CCONJ
cana-6099	80	11	state	state	NOUN
cana-6099	80	12	space	space	NOUN
cana-6099	80	13	approach	approach	NOUN
cana-6099	80	14	.	.	PUNCT
cana-6099	81	1	the	the	DET
cana-6099	81	2	time	time	NOUN
cana-6099	81	3	-	-	PUNCT
cana-6099	81	4	fractional	fractional	ADJ
cana-6099	81	5	two	two	NUM
cana-6099	81	6	-	-	PUNCT
cana-6099	81	7	dimensional	dimensional	ADJ
cana-6099	81	8	thermoelastic	thermoelastic	ADJ
cana-6099	81	9	problem	problem	NOUN
cana-6099	81	10	for	for	ADP
cana-6099	81	11	a	a	DET
cana-6099	81	12	thin	thin	ADJ
cana-6099	81	13	hollow	hollow	ADJ
cana-6099	81	14	circular	circular	ADJ
cana-6099	81	15	disk	disk	NOUN
cana-6099	81	16	has	have	AUX
cana-6099	81	17	analyzed	analyze	VERB
cana-6099	81	18	by	by	ADP
cana-6099	81	19	k.	k.	PROPN
cana-6099	81	20	r.	r.	PROPN
cana-6099	81	21	gaikwad	gaikwad	PROPN
cana-6099	81	22	et.al	et.al	PROPN
cana-6099	81	23	.	.	PUNCT
cana-6099	82	1	[	[	X
cana-6099	82	2	22	22	NUM
cana-6099	82	3	]	]	PUNCT
cana-6099	82	4	,	,	PUNCT
cana-6099	82	5	to	to	PART
cana-6099	82	6	study	study	VERB
cana-6099	82	7	its	its	PRON
cana-6099	82	8	thermal	thermal	ADJ
cana-6099	82	9	stresses	stress	NOUN
cana-6099	82	10	in	in	ADP
cana-6099	82	11	nonhomogeneous	nonhomogeneous	ADJ
cana-6099	82	12	medium	medium	NOUN
cana-6099	82	13	under	under	ADP
cana-6099	82	14	four	four	NUM
cana-6099	82	15	boundary	boundary	ADJ
cana-6099	82	16	conditions	condition	NOUN
cana-6099	82	17	.	.	PUNCT
cana-6099	83	1	the	the	DET
cana-6099	83	2	results	result	NOUN
cana-6099	83	3	have	have	AUX
cana-6099	83	4	been	be	AUX
cana-6099	83	5	computed	compute	VERB
cana-6099	83	6	and	and	CCONJ
cana-6099	83	7	illustrated	illustrate	VERB
cana-6099	83	8	graphically	graphically	ADV
cana-6099	83	9	using	use	VERB
cana-6099	83	10	ptc	ptc	PROPN
cana-6099	83	11	mathcad	mathcad	PROPN
cana-6099	83	12	software	software	PROPN
cana-6099	83	13	.	.	PUNCT
cana-6099	84	1	also	also	ADV
cana-6099	84	2	,	,	PUNCT
cana-6099	84	3	some	some	DET
cana-6099	84	4	contributions	contribution	NOUN
cana-6099	84	5	to	to	ADP
cana-6099	84	6	this	this	DET
cana-6099	84	7	theory	theory	NOUN
cana-6099	84	8	are	be	AUX
cana-6099	84	9	the	the	DET
cana-6099	84	10	work	work	NOUN
cana-6099	84	11	in	in	ADP
cana-6099	84	12	[	[	X
cana-6099	84	13	24–26	24–26	NUM
cana-6099	84	14	,	,	PUNCT
cana-6099	84	15	28–33	28–33	NUM
cana-6099	84	16	]	]	PUNCT
cana-6099	84	17	.	.	PUNCT
cana-6099	85	1	this	this	DET
cana-6099	85	2	paper	paper	NOUN
cana-6099	85	3	presents	present	VERB
cana-6099	85	4	an	an	DET
cana-6099	85	5	analytical	analytical	ADJ
cana-6099	85	6	solution	solution	NOUN
cana-6099	85	7	to	to	ADP
cana-6099	85	8	a	a	DET
cana-6099	85	9	generalized	generalize	VERB
cana-6099	85	10	fractional	fractional	ADJ
cana-6099	85	11	order	order	NOUN
cana-6099	85	12	thermoelastic	thermoelastic	ADJ
cana-6099	85	13	problem	problem	NOUN
cana-6099	85	14	in	in	ADP
cana-6099	85	15	a	a	DET
cana-6099	85	16	thick	thick	ADJ
cana-6099	85	17	circular	circular	ADJ
cana-6099	85	18	plate	plate	NOUN
cana-6099	85	19	using	use	VERB
cana-6099	85	20	both	both	CCONJ
cana-6099	85	21	the	the	DET
cana-6099	85	22	lord	lord	PROPN
cana-6099	85	23	–	–	PUNCT
cana-6099	85	24	shulman	shulman	PROPN
cana-6099	85	25	(	(	PUNCT
cana-6099	85	26	ls	ls	PROPN
cana-6099	85	27	)	)	PUNCT
cana-6099	85	28	and	and	CCONJ
cana-6099	85	29	classical	classical	ADJ
cana-6099	85	30	coupled	couple	VERB
cana-6099	85	31	thermoelasticity	thermoelasticity	NOUN
cana-6099	85	32	(	(	PUNCT
cana-6099	85	33	cte	cte	NOUN
cana-6099	85	34	)	)	PUNCT
cana-6099	85	35	models	model	NOUN
cana-6099	85	36	.	.	PUNCT
cana-6099	86	1	the	the	DET
cana-6099	86	2	analysis	analysis	NOUN
cana-6099	86	3	considers	consider	VERB
cana-6099	86	4	a	a	DET
cana-6099	86	5	finite	finite	ADJ
cana-6099	86	6	plate	plate	NOUN
cana-6099	86	7	of	of	ADP
cana-6099	86	8	thickness	thickness	NOUN
cana-6099	86	9	2b	2b	NOUN
cana-6099	86	10	,	,	PUNCT
cana-6099	86	11	subjected	subject	VERB
cana-6099	86	12	to	to	ADP
cana-6099	86	13	axisymmetric	axisymmetric	VERB
cana-6099	86	14	thermal	thermal	ADJ
cana-6099	86	15	loading	loading	NOUN
cana-6099	86	16	on	on	ADP
cana-6099	86	17	its	its	PRON
cana-6099	86	18	traction	traction	NOUN
cana-6099	86	19	-	-	PUNCT
cana-6099	86	20	free	free	ADJ
cana-6099	86	21	upper	upper	ADJ
cana-6099	86	22	and	and	CCONJ
cana-6099	86	23	lower	low	ADJ
cana-6099	86	24	surfaces	surface	NOUN
cana-6099	86	25	.	.	PUNCT
cana-6099	87	1	employing	employ	VERB
cana-6099	87	2	a	a	DET
cana-6099	87	3	direct	direct	ADJ
cana-6099	87	4	approach	approach	NOUN
cana-6099	87	5	along	along	ADP
cana-6099	87	6	with	with	ADP
cana-6099	87	7	integral	integral	ADJ
cana-6099	87	8	transforms	transform	NOUN
cana-6099	87	9	,	,	PUNCT
cana-6099	87	10	we	we	PRON
cana-6099	87	11	derive	derive	VERB
cana-6099	87	12	general	general	ADJ
cana-6099	87	13	solutions	solution	NOUN
cana-6099	87	14	in	in	ADP
cana-6099	87	15	the	the	DET
cana-6099	87	16	laplace	laplace	NOUN
cana-6099	87	17	domain	domain	NOUN
cana-6099	87	18	without	without	ADP
cana-6099	87	19	introducing	introduce	VERB
cana-6099	87	20	potential	potential	ADJ
cana-6099	87	21	functions	function	NOUN
cana-6099	87	22	.	.	PUNCT
cana-6099	88	1	numerical	numerical	ADJ
cana-6099	88	2	evaluations	evaluation	NOUN
cana-6099	88	3	are	be	AUX
cana-6099	88	4	carried	carry	VERB
cana-6099	88	5	out	out	ADP
cana-6099	88	6	using	use	VERB
cana-6099	88	7	mathcad	mathcad	PROPN
cana-6099	88	8	,	,	PUNCT
cana-6099	88	9	and	and	CCONJ
cana-6099	88	10	results	result	NOUN
cana-6099	88	11	are	be	AUX
cana-6099	88	12	graphically	graphically	ADV
cana-6099	88	13	depicted	depict	VERB
cana-6099	88	14	to	to	PART
cana-6099	88	15	highlight	highlight	VERB
cana-6099	88	16	variations	variation	NOUN
cana-6099	88	17	in	in	ADP
cana-6099	88	18	temperature	temperature	NOUN
cana-6099	88	19	,	,	PUNCT
cana-6099	88	20	displacement	displacement	NOUN
cana-6099	88	21	,	,	PUNCT
cana-6099	88	22	stress	stress	NOUN
cana-6099	88	23	,	,	PUNCT
cana-6099	88	24	concentration	concentration	NOUN
cana-6099	88	25	,	,	PUNCT
cana-6099	88	26	and	and	CCONJ
cana-6099	88	27	chemical	chemical	NOUN
cana-6099	88	28	potential	potential	NOUN
cana-6099	88	29	.	.	PUNCT
cana-6099	89	1	the	the	DET
cana-6099	89	2	obtained	obtain	VERB
cana-6099	89	3	outcomes	outcome	NOUN
cana-6099	89	4	show	show	VERB
cana-6099	89	5	consistency	consistency	NOUN
cana-6099	89	6	with	with	ADP
cana-6099	89	7	established	establish	VERB
cana-6099	89	8	results	result	NOUN
cana-6099	89	9	and	and	CCONJ
cana-6099	89	10	illustrate	illustrate	VERB
cana-6099	89	11	the	the	DET
cana-6099	89	12	influence	influence	NOUN
cana-6099	89	13	of	of	ADP
cana-6099	89	14	fractional	fractional	ADJ
cana-6099	89	15	order	order	NOUN
cana-6099	89	16	and	and	CCONJ
cana-6099	89	17	time	time	NOUN
cana-6099	89	18	on	on	ADP
cana-6099	89	19	the	the	DET
cana-6099	89	20	thermoelastic	thermoelastic	ADJ
cana-6099	89	21	behaviour	behaviour	NOUN
cana-6099	89	22	.	.	PUNCT
cana-6099	90	1	this	this	DET
cana-6099	90	2	model	model	NOUN
cana-6099	90	3	proves	prove	VERB
cana-6099	90	4	valuable	valuable	ADJ
cana-6099	90	5	for	for	ADP
cana-6099	90	6	advancing	advance	VERB
cana-6099	90	7	the	the	DET
cana-6099	90	8	study	study	NOUN
cana-6099	90	9	of	of	ADP
cana-6099	90	10	hyperbolic	hyperbolic	ADJ
cana-6099	90	11	thermoelastic	thermoelastic	ADJ
cana-6099	90	12	diffusion	diffusion	NOUN
cana-6099	90	13	,	,	PUNCT
cana-6099	90	14	material	material	NOUN
cana-6099	90	15	science	science	NOUN
cana-6099	90	16	,	,	PUNCT
cana-6099	90	17	and	and	CCONJ
cana-6099	90	18	innovative	innovative	ADJ
cana-6099	90	19	material	material	NOUN
cana-6099	90	20	design	design	NOUN
cana-6099	90	21	.	.	PUNCT
cana-6099	91	1	communications	communication	NOUN
cana-6099	91	2	on	on	ADP
cana-6099	91	3	applied	apply	VERB
cana-6099	91	4	nonlinear	nonlinear	ADJ
cana-6099	91	5	analysis	analysis	NOUN
cana-6099	91	6	issn	issn	NOUN
cana-6099	91	7	:	:	PUNCT
cana-6099	91	8	1074	1074	NUM
cana-6099	91	9	-	-	PUNCT
cana-6099	91	10	133x	133x	NUM
cana-6099	91	11	vol	vol	VERB
cana-6099	91	12	32	32	NUM
cana-6099	91	13	no	no	NOUN
cana-6099	91	14	.	.	PUNCT
cana-6099	92	1	10s	10	NOUN
cana-6099	92	2	(	(	PUNCT
cana-6099	92	3	2025	2025	NUM
cana-6099	92	4	)	)	PUNCT
cana-6099	92	5	3354	3354	NUM
cana-6099	92	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	92	7	2	2	NUM
cana-6099	92	8	.	.	PUNCT
cana-6099	92	9	basic	basic	ADJ
cana-6099	92	10	equations	equation	NOUN
cana-6099	92	11	&	&	CCONJ
cana-6099	92	12	relations	relation	NOUN
cana-6099	92	13	the	the	DET
cana-6099	92	14	field	field	NOUN
cana-6099	92	15	equations	equation	NOUN
cana-6099	92	16	for	for	ADP
cana-6099	92	17	the	the	DET
cana-6099	92	18	generalized	generalize	VERB
cana-6099	92	19	thermoelastic	thermoelastic	ADJ
cana-6099	92	20	diffusion	diffusion	NOUN
cana-6099	92	21	in	in	ADP
cana-6099	92	22	an	an	DET
cana-6099	92	23	isotropic	isotropic	ADJ
cana-6099	92	24	medium	medium	NOUN
cana-6099	92	25	in	in	ADP
cana-6099	92	26	the	the	DET
cana-6099	92	27	absence	absence	NOUN
cana-6099	92	28	of	of	ADP
cana-6099	92	29	body	body	NOUN
cana-6099	92	30	forces	force	NOUN
cana-6099	92	31	and	and	CCONJ
cana-6099	92	32	heat	heat	NOUN
cana-6099	92	33	source	source	NOUN
cana-6099	92	34	are	be	AUX
cana-6099	92	35	as	as	SCONJ
cana-6099	92	36	follows	follow	VERB
cana-6099	92	37	:	:	PUNCT
cana-6099	92	38	(	(	PUNCT
cana-6099	92	39	1	1	X
cana-6099	92	40	)	)	PUNCT
cana-6099	92	41	equation	equation	NOUN
cana-6099	92	42	of	of	ADP
cana-6099	92	43	motion	motion	NOUN
cana-6099	92	44	[	[	X
cana-6099	92	45	17	17	NUM
cana-6099	92	46	]	]	X
cana-6099	92	47	:	:	PUNCT
cana-6099	92	48	𝜌𝑢𝑖̈	𝜌𝑢𝑖̈	PROPN
cana-6099	92	49	=	=	SYM
cana-6099	93	1	µ𝑢𝑖,𝑗𝑗	µ𝑢𝑖,𝑗𝑗	PROPN
cana-6099	93	2	+	+	X
cana-6099	93	3	(	(	PUNCT
cana-6099	93	4	𝜆	𝜆	PRON
cana-6099	93	5	+	+	X
cana-6099	93	6	µ)𝑢𝑖,𝑗𝑗	µ)𝑢𝑖,𝑗𝑗	PROPN
cana-6099	93	7	−	−	NOUN
cana-6099	93	8	𝜉1𝑇,𝑖	𝜉1𝑇,𝑖	NOUN
cana-6099	93	9	−	−	PROPN
cana-6099	93	10	𝜉1	𝜉1	NOUN
cana-6099	93	11	𝐶,𝑖	𝐶,𝑖	NOUN
cana-6099	93	12	(	(	PUNCT
cana-6099	93	13	1	1	X
cana-6099	93	14	)	)	PUNCT
cana-6099	93	15	where	where	SCONJ
cana-6099	93	16	ξ1	ξ1	NOUN
cana-6099	93	17	and	and	CCONJ
cana-6099	93	18	ξ2	ξ2	NOUN
cana-6099	93	19	are	be	AUX
cana-6099	93	20	material	material	NOUN
cana-6099	93	21	constants	constant	NOUN
cana-6099	93	22	.	.	PUNCT
cana-6099	94	1	(	(	PUNCT
cana-6099	94	2	2	2	X
cana-6099	94	3	)	)	PUNCT
cana-6099	94	4	equation	equation	NOUN
cana-6099	94	5	of	of	ADP
cana-6099	94	6	heat	heat	NOUN
cana-6099	94	7	conduction	conduction	NOUN
cana-6099	94	8	[	[	X
cana-6099	94	9	7	7	NUM
cana-6099	94	10	]	]	X
cana-6099	94	11	:	:	PUNCT
cana-6099	94	12	𝑘𝑇,𝑖𝑖	𝑘𝑇,𝑖𝑖	PROPN
cana-6099	94	13	=	=	SYM
cana-6099	94	14	𝜕	𝜕	PROPN
cana-6099	94	15	𝜕𝑡	𝜕𝑡	PROPN
cana-6099	94	16	(	(	PUNCT
cana-6099	94	17	1	1	NUM
cana-6099	94	18	+	+	NUM
cana-6099	94	19	𝜏0	𝜏0	PROPN
cana-6099	94	20	𝜕𝛼	𝜕𝛼	NOUN
cana-6099	94	21	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6099	94	22	)	)	PUNCT
cana-6099	94	23	(	(	PUNCT
cana-6099	94	24	𝜌𝐶𝐸𝑇	𝜌𝐶𝐸𝑇	X
cana-6099	94	25	+	+	CCONJ
cana-6099	94	26	𝑇0𝜉1𝑒	𝑇0𝜉1𝑒	NOUN
cana-6099	94	27	+	+	X
cana-6099	94	28	𝑇0𝛽𝑡𝐶	𝑇0𝛽𝑡𝐶	PROPN
cana-6099	94	29	)	)	PUNCT
cana-6099	94	30	(	(	PUNCT
cana-6099	94	31	2	2	NUM
cana-6099	94	32	)	)	PUNCT
cana-6099	94	33	(	(	PUNCT
cana-6099	94	34	3	3	X
cana-6099	94	35	)	)	PUNCT
cana-6099	94	36	equation	equation	NOUN
cana-6099	94	37	of	of	ADP
cana-6099	94	38	mass	mass	ADJ
cana-6099	94	39	diffusion	diffusion	NOUN
cana-6099	94	40	[	[	X
cana-6099	94	41	7	7	NUM
cana-6099	94	42	]	]	NUM
cana-6099	94	43	:	:	PUNCT
cana-6099	94	44	(	(	PUNCT
cana-6099	94	45	3	3	X
cana-6099	94	46	)	)	PUNCT
cana-6099	94	47	(	(	PUNCT
cana-6099	94	48	4	4	X
cana-6099	94	49	)	)	PUNCT
cana-6099	94	50	constitutive	constitutive	ADJ
cana-6099	94	51	equations	equation	NOUN
cana-6099	95	1	[	[	X
cana-6099	95	2	17	17	NUM
cana-6099	95	3	]	]	X
cana-6099	95	4	:	:	PUNCT
cana-6099	95	5	𝜎𝑖𝑗	𝜎𝑖𝑗	PROPN
cana-6099	95	6	=	=	SYM
cana-6099	95	7	2µ휀𝑖𝑗	2µ휀𝑖𝑗	NUM
cana-6099	95	8	+	+	NUM
cana-6099	95	9	𝛿𝑖𝑗(𝜆𝑒	𝛿𝑖𝑗(𝜆𝑒	X
cana-6099	95	10	−	−	PROPN
cana-6099	95	11	𝜉1(𝑇	𝜉1(𝑇	PROPN
cana-6099	95	12	−	−	PROPN
cana-6099	95	13	𝑇0	𝑇0	NOUN
cana-6099	95	14	)	)	PUNCT
cana-6099	95	15	−	−	PROPN
cana-6099	95	16	𝜉2𝐶	𝜉2𝐶	NOUN
cana-6099	95	17	)	)	PUNCT
cana-6099	95	18	,	,	PUNCT
cana-6099	95	19	(	(	PUNCT
cana-6099	95	20	4	4	X
cana-6099	95	21	)	)	PUNCT
cana-6099	95	22	𝑃	𝑃	NOUN
cana-6099	95	23	=	=	PUNCT
cana-6099	95	24	−𝜉2𝑒	−𝜉2𝑒	PROPN
cana-6099	95	25	+	+	CCONJ
cana-6099	95	26	𝛽𝐶	𝛽𝐶	NOUN
cana-6099	95	27	−	−	NOUN
cana-6099	95	28	𝛽𝑡(𝑇	𝛽𝑡(𝑇	NOUN
cana-6099	95	29	−	−	NOUN
cana-6099	95	30	𝑇0	𝑇0	NOUN
cana-6099	95	31	)	)	PUNCT
cana-6099	95	32	(	(	PUNCT
cana-6099	95	33	5	5	X
cana-6099	95	34	)	)	PUNCT
cana-6099	95	35	where	where	SCONJ
cana-6099	95	36	휀𝑖𝑗	휀𝑖𝑗	ADV
cana-6099	95	37	,	,	PUNCT
cana-6099	95	38	i	i	PRON
cana-6099	95	39	,	,	PUNCT
cana-6099	95	40	j	j	PROPN
cana-6099	95	41	=	=	SYM
cana-6099	95	42	1,2,3	1,2,3	NUM
cana-6099	95	43	...	...	PUNCT
cana-6099	95	44	are	be	AUX
cana-6099	95	45	the	the	DET
cana-6099	95	46	components	component	NOUN
cana-6099	95	47	of	of	ADP
cana-6099	95	48	the	the	DET
cana-6099	95	49	strain	strain	NOUN
cana-6099	95	50	tensor	tensor	NOUN
cana-6099	95	51	given	give	VERB
cana-6099	95	52	by	by	ADP
cana-6099	95	53	(	(	PUNCT
cana-6099	95	54	6	6	NUM
cana-6099	95	55	)	)	PUNCT
cana-6099	95	56	3	3	NUM
cana-6099	95	57	.	.	X
cana-6099	95	58	two	two	NUM
cana-6099	95	59	dimensional	dimensional	ADJ
cana-6099	95	60	fractional	fractional	ADJ
cana-6099	95	61	order	order	NOUN
cana-6099	95	62	formulation	formulation	NOUN
cana-6099	95	63	we	we	PRON
cana-6099	95	64	take	take	VERB
cana-6099	95	65	the	the	DET
cana-6099	95	66	axis	axis	NOUN
cana-6099	95	67	of	of	ADP
cana-6099	95	68	symmetry	symmetry	NOUN
cana-6099	95	69	as	as	ADP
cana-6099	95	70	the	the	DET
cana-6099	95	71	z	z	NOUN
cana-6099	95	72	axis	axis	NOUN
cana-6099	95	73	,	,	PUNCT
cana-6099	95	74	and	and	CCONJ
cana-6099	95	75	the	the	DET
cana-6099	95	76	origin	origin	NOUN
cana-6099	95	77	of	of	ADP
cana-6099	95	78	the	the	DET
cana-6099	95	79	system	system	NOUN
cana-6099	95	80	of	of	ADP
cana-6099	95	81	co	co	NOUN
cana-6099	95	82	-	-	NOUN
cana-6099	95	83	ordinates	ordinate	NOUN
cana-6099	95	84	is	be	AUX
cana-6099	95	85	at	at	ADP
cana-6099	95	86	the	the	DET
cana-6099	95	87	middle	middle	ADJ
cana-6099	95	88	plane	plane	NOUN
cana-6099	95	89	between	between	ADP
cana-6099	95	90	the	the	DET
cana-6099	95	91	upper	upper	ADJ
cana-6099	95	92	and	and	CCONJ
cana-6099	95	93	lower	low	ADJ
cana-6099	95	94	faces	face	NOUN
cana-6099	95	95	of	of	ADP
cana-6099	95	96	the	the	DET
cana-6099	95	97	plate	plate	NOUN
cana-6099	95	98	.	.	PUNCT
cana-6099	96	1	the	the	DET
cana-6099	96	2	problem	problem	NOUN
cana-6099	96	3	is	be	AUX
cana-6099	96	4	studied	study	VERB
cana-6099	96	5	using	use	VERB
cana-6099	96	6	the	the	DET
cana-6099	96	7	cylindrical	cylindrical	ADJ
cana-6099	96	8	polar	polar	ADJ
cana-6099	96	9	co	co	NOUN
cana-6099	96	10	-	-	NOUN
cana-6099	96	11	ordinates	ordinate	NOUN
cana-6099	96	12	(	(	PUNCT
cana-6099	96	13	r	r	NOUN
cana-6099	96	14	,	,	PUNCT
cana-6099	96	15	φ	φ	NOUN
cana-6099	96	16	,	,	PUNCT
cana-6099	96	17	z	z	NOUN
cana-6099	96	18	)	)	PUNCT
cana-6099	96	19	.	.	PUNCT
cana-6099	97	1	due	due	ADP
cana-6099	97	2	to	to	ADP
cana-6099	97	3	the	the	DET
cana-6099	97	4	rotational	rotational	ADJ
cana-6099	97	5	symmetry	symmetry	NOUN
cana-6099	97	6	about	about	ADP
cana-6099	97	7	the	the	DET
cana-6099	97	8	z	z	NOUN
cana-6099	97	9	axis	axis	NOUN
cana-6099	97	10	of	of	ADP
cana-6099	97	11	the	the	DET
cana-6099	97	12	problem	problem	NOUN
cana-6099	97	13	,	,	PUNCT
cana-6099	97	14	all	all	DET
cana-6099	97	15	quantities	quantity	NOUN
cana-6099	97	16	are	be	AUX
cana-6099	97	17	independent	independent	ADJ
cana-6099	97	18	of	of	ADP
cana-6099	97	19	the	the	DET
cana-6099	97	20	co	co	NOUN
cana-6099	97	21	-	-	NOUN
cana-6099	97	22	ordinate	ordinate	NOUN
cana-6099	97	23	φ	φ	NOUN
cana-6099	97	24	.	.	PUNCT
cana-6099	98	1	for	for	ADP
cana-6099	98	2	the	the	DET
cana-6099	98	3	2d	2d	PROPN
cana-6099	98	4	problem	problem	NOUN
cana-6099	98	5	,	,	PUNCT
cana-6099	98	6	the	the	DET
cana-6099	98	7	displacement	displacement	ADJ
cana-6099	98	8	vector	vector	NOUN
cana-6099	98	9	u	u	NOUN
cana-6099	98	10	has	have	VERB
cana-6099	98	11	the	the	DET
cana-6099	98	12	form	form	NOUN
cana-6099	98	13	u	u	NOUN
cana-6099	98	14	=	=	PUNCT
cana-6099	98	15	(	(	PUNCT
cana-6099	98	16	u	u	NOUN
cana-6099	98	17	,	,	PUNCT
cana-6099	98	18	0	0	NUM
cana-6099	98	19	,	,	PUNCT
cana-6099	98	20	w	w	NOUN
cana-6099	98	21	)	)	PUNCT
cana-6099	98	22	.	.	PUNCT
cana-6099	99	1	hence	hence	ADV
cana-6099	99	2	,	,	PUNCT
cana-6099	99	3	the	the	DET
cana-6099	99	4	components	component	NOUN
cana-6099	99	5	of	of	ADP
cana-6099	99	6	the	the	DET
cana-6099	99	7	strain	strain	NOUN
cana-6099	99	8	tensor	tensor	NOUN
cana-6099	99	9	of	of	ADP
cana-6099	99	10	eq	eq	PROPN
cana-6099	99	11	.	.	PUNCT
cana-6099	100	1	(	(	PUNCT
cana-6099	100	2	6	6	NUM
cana-6099	100	3	)	)	PUNCT
cana-6099	100	4	can	can	AUX
cana-6099	100	5	be	be	AUX
cana-6099	100	6	written	write	VERB
cana-6099	100	7	in	in	ADP
cana-6099	100	8	the	the	DET
cana-6099	100	9	form	form	NOUN
cana-6099	100	10	:	:	PUNCT
cana-6099	100	11	𝑒𝑟𝑟	𝑒𝑟𝑟	NOUN
cana-6099	100	12	=	=	PUNCT
cana-6099	101	1	𝜕𝑢	𝜕𝑢	NOUN
cana-6099	101	2	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	101	3	,	,	PUNCT
cana-6099	101	4	𝑒𝜙𝜙	𝑒𝜙𝜙	NOUN
cana-6099	101	5	=	=	SYM
cana-6099	101	6	𝑢	𝑢	PART
cana-6099	101	7	𝑟	𝑟	NOUN
cana-6099	101	8	,	,	PUNCT
cana-6099	101	9	𝑒𝑧𝑧	𝑒𝑧𝑧	ADJ
cana-6099	101	10	=	=	PUNCT
cana-6099	101	11	𝜕𝑤	𝜕𝑤	VERB
cana-6099	101	12	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	101	13	,	,	PUNCT
cana-6099	101	14	𝑒𝑟𝑧	𝑒𝑟𝑧	X
cana-6099	101	15	=	=	NOUN
cana-6099	101	16	1	1	NUM
cana-6099	101	17	2	2	NUM
cana-6099	101	18	(	(	PUNCT
cana-6099	101	19	𝜕𝑢	𝜕𝑢	NOUN
cana-6099	101	20	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	101	21	+	+	CCONJ
cana-6099	101	22	𝜕𝑤	𝜕𝑤	NOUN
cana-6099	101	23	𝜕𝑟	𝜕𝑟	ADV
cana-6099	101	24	)	)	PUNCT
cana-6099	101	25	(	(	PUNCT
cana-6099	101	26	7	7	X
cana-6099	101	27	)	)	PUNCT
cana-6099	101	28	𝑒	𝑒	NOUN
cana-6099	101	29	=	=	SYM
cana-6099	101	30	𝑢	𝑢	PART
cana-6099	101	31	𝑟	𝑟	X
cana-6099	101	32	+	+	CCONJ
cana-6099	101	33	𝜕𝑢	𝜕𝑢	NOUN
cana-6099	101	34	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	101	35	+	+	CCONJ
cana-6099	101	36	𝜕𝑤	𝜕𝑤	VERB
cana-6099	101	37	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	101	38	=	=	SYM
cana-6099	101	39	1	1	NUM
cana-6099	101	40	𝑟	𝑟	NOUN
cana-6099	101	41	𝜕	𝜕	PROPN
cana-6099	101	42	𝜕𝑟	𝜕𝑟	PROPN
cana-6099	101	43	+	+	CCONJ
cana-6099	101	44	𝜕2	𝜕2	NOUN
cana-6099	101	45	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6099	101	46	(	(	PUNCT
cana-6099	101	47	8)	8)	NUM
cana-6099	101	48	the	the	DET
cana-6099	101	49	laplacian	laplacian	ADJ
cana-6099	101	50	operator	operator	NOUN
cana-6099	101	51	[	[	X
cana-6099	101	52	17	17	NUM
cana-6099	101	53	]	]	SYM
cana-6099	101	54	:	:	PUNCT
cana-6099	101	55	(	(	PUNCT
cana-6099	101	56	9	9	X
cana-6099	101	57	)	)	PUNCT
cana-6099	101	58	the	the	DET
cana-6099	101	59	governing	govern	VERB
cana-6099	101	60	equations	equation	NOUN
cana-6099	101	61	(	(	PUNCT
cana-6099	101	62	1	1	NUM
cana-6099	101	63	)	)	PUNCT
cana-6099	101	64	to	to	ADP
cana-6099	101	65	(	(	PUNCT
cana-6099	101	66	5	5	X
cana-6099	101	67	)	)	PUNCT
cana-6099	101	68	will	will	AUX
cana-6099	101	69	take	take	VERB
cana-6099	101	70	the	the	DET
cana-6099	101	71	form	form	NOUN
cana-6099	101	72	:	:	PUNCT
cana-6099	101	73	communications	communication	NOUN
cana-6099	101	74	on	on	ADP
cana-6099	101	75	applied	apply	VERB
cana-6099	101	76	nonlinear	nonlinear	ADJ
cana-6099	101	77	analysis	analysis	NOUN
cana-6099	101	78	issn	issn	NOUN
cana-6099	101	79	:	:	PUNCT
cana-6099	101	80	1074	1074	NUM
cana-6099	101	81	-	-	PUNCT
cana-6099	101	82	133x	133x	NUM
cana-6099	101	83	vol	vol	VERB
cana-6099	101	84	32	32	NUM
cana-6099	101	85	no	no	NOUN
cana-6099	101	86	.	.	PUNCT
cana-6099	102	1	10s	10	NOUN
cana-6099	102	2	(	(	PUNCT
cana-6099	102	3	2025	2025	NUM
cana-6099	102	4	)	)	PUNCT
cana-6099	102	5	3355	3355	NUM
cana-6099	102	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	103	1	𝜇∇2𝑢	𝜇∇2𝑢	NOUN
cana-6099	103	2	−	−	NOUN
cana-6099	103	3	𝜇	𝜇	ADP
cana-6099	103	4	𝑟2	𝑟2	NOUN
cana-6099	103	5	𝑢	𝑢	X
cana-6099	103	6	+	+	X
cana-6099	103	7	(	(	PUNCT
cana-6099	103	8	𝜆	𝜆	NOUN
cana-6099	103	9	+	+	X
cana-6099	103	10	𝜇	𝜇	NOUN
cana-6099	103	11	)	)	PUNCT
cana-6099	103	12	𝜕𝑒	𝜕𝑒	NOUN
cana-6099	103	13	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	103	14	−	−	PROPN
cana-6099	103	15	𝜉1	𝜉1	PROPN
cana-6099	103	16	𝜕𝑇	𝜕𝑇	NOUN
cana-6099	103	17	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	103	18	−	−	VERB
cana-6099	103	19	𝜉2	𝜉2	PROPN
cana-6099	103	20	𝜕𝐶	𝜕𝐶	PROPN
cana-6099	103	21	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	103	22	=	=	SYM
cana-6099	103	23	𝜌	𝜌	ADP
cana-6099	103	24	𝜕2𝑢	𝜕2𝑢	PROPN
cana-6099	103	25	𝜕𝑡2	𝜕𝑡2	NOUN
cana-6099	103	26	(	(	PUNCT
cana-6099	103	27	10	10	NUM
cana-6099	103	28	)	)	PUNCT
cana-6099	103	29	𝜇∇2𝑤	𝜇∇2𝑤	NOUN
cana-6099	103	30	+	+	CCONJ
cana-6099	103	31	(	(	PUNCT
cana-6099	103	32	𝜆	𝜆	NOUN
cana-6099	103	33	+	+	X
cana-6099	103	34	𝜇	𝜇	NOUN
cana-6099	103	35	)	)	PUNCT
cana-6099	103	36	𝜕𝑒	𝜕𝑒	ADP
cana-6099	103	37	𝜕𝑧	𝜕𝑧	NUM
cana-6099	103	38	−	−	PROPN
cana-6099	103	39	𝜉1	𝜉1	PROPN
cana-6099	103	40	𝜕𝑇	𝜕𝑇	PROPN
cana-6099	103	41	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	103	42	−	−	NOUN
cana-6099	103	43	𝜉2	𝜉2	PROPN
cana-6099	103	44	𝜕𝐶	𝜕𝐶	PROPN
cana-6099	103	45	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	103	46	=	=	SYM
cana-6099	103	47	𝜌	𝜌	ADP
cana-6099	103	48	𝜕2𝑢	𝜕2𝑢	PROPN
cana-6099	103	49	𝜕𝑡2	𝜕𝑡2	NOUN
cana-6099	103	50	(	(	PUNCT
cana-6099	103	51	11	11	NUM
cana-6099	103	52	)	)	PUNCT
cana-6099	103	53	𝑘∇2𝑇	𝑘∇2𝑇	PROPN
cana-6099	104	1	=	=	SYM
cana-6099	104	2	𝜕	𝜕	PROPN
cana-6099	104	3	𝜕𝑡	𝜕𝑡	PROPN
cana-6099	104	4	(	(	PUNCT
cana-6099	104	5	1	1	NUM
cana-6099	104	6	+	+	NUM
cana-6099	104	7	𝜏0	𝜏0	PROPN
cana-6099	104	8	𝜕𝛼	𝜕𝛼	NOUN
cana-6099	104	9	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6099	104	10	)	)	PUNCT
cana-6099	104	11	(	(	PUNCT
cana-6099	104	12	𝜌𝐶𝐸𝑇	𝜌𝐶𝐸𝑇	X
cana-6099	104	13	+	+	CCONJ
cana-6099	104	14	𝑇0𝜉1𝑒	𝑇0𝜉1𝑒	NOUN
cana-6099	104	15	+	+	X
cana-6099	104	16	𝑇0𝛽𝑡𝐶	𝑇0𝛽𝑡𝐶	PROPN
cana-6099	104	17	)	)	PUNCT
cana-6099	104	18	(	(	PUNCT
cana-6099	104	19	12	12	NUM
cana-6099	104	20	)	)	PUNCT
cana-6099	104	21	𝐷𝜉2∇2𝑒	𝐷𝜉2∇2𝑒	VERB
cana-6099	105	1	+	+	CCONJ
cana-6099	105	2	𝐷𝛽𝑡∇2𝑇	𝐷𝛽𝑡∇2𝑇	PROPN
cana-6099	105	3	+	+	CCONJ
cana-6099	105	4	(	(	PUNCT
cana-6099	105	5	𝜕	𝜕	PROPN
cana-6099	105	6	𝜕𝑡	𝜕𝑡	PROPN
cana-6099	105	7	+	+	CCONJ
cana-6099	105	8	𝜏0	𝜏0	PROPN
cana-6099	105	9	𝜕2	𝜕2	ADJ
cana-6099	105	10	𝜕𝑡2	𝜕𝑡2	NOUN
cana-6099	105	11	)	)	PUNCT
cana-6099	105	12	𝐶	𝐶	PROPN
cana-6099	105	13	−	−	PROPN
cana-6099	105	14	𝐷𝛽∇2𝐶	𝐷𝛽∇2𝐶	PROPN
cana-6099	105	15	=	=	SYM
cana-6099	105	16	0	0	NUM
cana-6099	105	17	(	(	PUNCT
cana-6099	105	18	13	13	NUM
cana-6099	105	19	)	)	PUNCT
cana-6099	105	20	𝜎𝜙𝜙	𝜎𝜙𝜙	ADJ
cana-6099	105	21	=	=	SYM
cana-6099	105	22	2𝜇𝑒𝜙𝜙	2𝜇𝑒𝜙𝜙	NUM
cana-6099	106	1	+	+	CCONJ
cana-6099	106	2	𝜆𝑒	𝜆𝑒	VERB
cana-6099	106	3	−	−	PROPN
cana-6099	106	4	𝜉1(𝑇	𝜉1(𝑇	PROPN
cana-6099	106	5	−	−	PROPN
cana-6099	106	6	𝑇0	𝑇0	NOUN
cana-6099	106	7	)	)	PUNCT
cana-6099	106	8	−	−	PROPN
cana-6099	106	9	𝜉2𝐶	𝜉2𝐶	PRON
cana-6099	106	10	(	(	PUNCT
cana-6099	106	11	14	14	NUM
cana-6099	106	12	)	)	PUNCT
cana-6099	106	13	𝜎𝑟𝑟	𝜎𝑟𝑟	VERB
cana-6099	106	14	=	=	SYM
cana-6099	106	15	2𝜇𝑒𝑟𝑟	2𝜇𝑒𝑟𝑟	NUM
cana-6099	107	1	+	+	CCONJ
cana-6099	107	2	𝜆𝑒	𝜆𝑒	VERB
cana-6099	107	3	−	−	PROPN
cana-6099	107	4	𝜉1(𝑇	𝜉1(𝑇	PROPN
cana-6099	107	5	−	−	PROPN
cana-6099	107	6	𝑇0	𝑇0	NOUN
cana-6099	107	7	)	)	PUNCT
cana-6099	107	8	−	−	PROPN
cana-6099	107	9	𝜉2𝐶	𝜉2𝐶	X
cana-6099	107	10	(	(	PUNCT
cana-6099	107	11	15	15	NUM
cana-6099	107	12	)	)	PUNCT
cana-6099	107	13	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6099	107	14	=	=	PUNCT
cana-6099	108	1	2𝜇𝑒𝑧𝑧	2𝜇𝑒𝑧𝑧	NUM
cana-6099	108	2	+	+	CCONJ
cana-6099	108	3	𝜆𝑒	𝜆𝑒	VERB
cana-6099	108	4	−	−	PROPN
cana-6099	108	5	𝜉1(𝑇	𝜉1(𝑇	PROPN
cana-6099	108	6	−	−	PROPN
cana-6099	108	7	𝑇0	𝑇0	NOUN
cana-6099	108	8	)	)	PUNCT
cana-6099	108	9	−	−	PROPN
cana-6099	108	10	𝜉2𝐶	𝜉2𝐶	PROPN
cana-6099	108	11	(	(	PUNCT
cana-6099	108	12	16	16	NUM
cana-6099	108	13	)	)	PUNCT
cana-6099	108	14	𝜎𝑟𝑧	𝜎𝑟𝑧	NOUN
cana-6099	108	15	=	=	PUNCT
cana-6099	108	16	𝜇𝑒𝑟𝑧	𝜇𝑒𝑟𝑧	NOUN
cana-6099	108	17	(	(	PUNCT
cana-6099	108	18	17	17	NUM
cana-6099	108	19	)	)	PUNCT
cana-6099	108	20	𝜎𝑟𝜑	𝜎𝑟𝜑	NOUN
cana-6099	108	21	=	=	SYM
cana-6099	108	22	𝜎𝑧𝜑	𝜎𝑧𝜑	X
cana-6099	108	23	=	=	SYM
cana-6099	108	24	0	0	NUM
cana-6099	108	25	(	(	PUNCT
cana-6099	108	26	18	18	NUM
cana-6099	108	27	)	)	PUNCT
cana-6099	108	28	𝑃	𝑃	NOUN
cana-6099	108	29	=	=	PUNCT
cana-6099	108	30	−𝜉2𝑒	−𝜉2𝑒	PROPN
cana-6099	108	31	+	+	CCONJ
cana-6099	108	32	𝛽𝐶	𝛽𝐶	NOUN
cana-6099	108	33	−	−	NOUN
cana-6099	108	34	𝛽𝑡(𝑇	𝛽𝑡(𝑇	NOUN
cana-6099	108	35	−	−	NOUN
cana-6099	108	36	𝑇0	𝑇0	NOUN
cana-6099	108	37	)	)	PUNCT
cana-6099	108	38	(	(	PUNCT
cana-6099	108	39	19	19	NUM
cana-6099	108	40	)	)	PUNCT
cana-6099	108	41	the	the	DET
cana-6099	108	42	following	follow	VERB
cana-6099	108	43	are	be	AUX
cana-6099	108	44	the	the	DET
cana-6099	108	45	non	non	ADJ
cana-6099	108	46	-	-	ADJ
cana-6099	108	47	dimensional	dimensional	ADJ
cana-6099	108	48	variables	variable	NOUN
cana-6099	108	49	which	which	PRON
cana-6099	108	50	are	be	AUX
cana-6099	108	51	expressed	express	VERB
cana-6099	108	52	as	as	ADP
cana-6099	108	53	:	:	PUNCT
cana-6099	108	54	where	where	SCONJ
cana-6099	108	55	,	,	PUNCT
cana-6099	108	56	putting	put	VERB
cana-6099	108	57	non	non	ADJ
cana-6099	108	58	-	-	ADJ
cana-6099	108	59	dimensional	dimensional	ADJ
cana-6099	108	60	quantities	quantity	NOUN
cana-6099	108	61	in	in	ADP
cana-6099	108	62	equations	equation	NOUN
cana-6099	108	63	(	(	PUNCT
cana-6099	108	64	10	10	NUM
cana-6099	108	65	)	)	PUNCT
cana-6099	108	66	to	to	ADP
cana-6099	108	67	(	(	PUNCT
cana-6099	108	68	19	19	NUM
cana-6099	108	69	)	)	PUNCT
cana-6099	108	70	,	,	PUNCT
cana-6099	108	71	the	the	DET
cana-6099	108	72	stress	stress	NOUN
cana-6099	108	73	components	component	NOUN
cana-6099	108	74	&	&	CCONJ
cana-6099	108	75	governing	govern	VERB
cana-6099	108	76	equations	equation	NOUN
cana-6099	108	77	adopt	adopt	VERB
cana-6099	108	78	the	the	DET
cana-6099	108	79	form	form	NOUN
cana-6099	108	80	:	:	PUNCT
cana-6099	108	81	∇2𝑢	∇2𝑢	NOUN
cana-6099	108	82	−	−	NUM
cana-6099	108	83	1	1	NUM
cana-6099	108	84	𝑟2	𝑟2	NOUN
cana-6099	108	85	𝑢	𝑢	PART
cana-6099	108	86	+	+	X
cana-6099	108	87	(	(	PUNCT
cana-6099	108	88	𝜉2	𝜉2	ADJ
cana-6099	108	89	−	−	PROPN
cana-6099	108	90	1	1	NUM
cana-6099	108	91	)	)	PUNCT
cana-6099	108	92	𝜕𝑒	𝜕𝑒	NOUN
cana-6099	108	93	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	108	94	−	−	PROPN
cana-6099	108	95	𝜉2	𝜉2	PROPN
cana-6099	108	96	𝜕𝑇	𝜕𝑇	PROPN
cana-6099	108	97	𝜕𝑟	𝜕𝑟	VERB
cana-6099	108	98	−	−	VERB
cana-6099	108	99	𝜉2	𝜉2	PROPN
cana-6099	108	100	𝜕𝐶	𝜕𝐶	PROPN
cana-6099	108	101	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	108	102	=	=	SYM
cana-6099	108	103	𝜉2	𝜉2	ADJ
cana-6099	108	104	𝜕2𝑢	𝜕2𝑢	PROPN
cana-6099	108	105	𝜕𝑡2	𝜕𝑡2	NOUN
cana-6099	108	106	(	(	PUNCT
cana-6099	108	107	20	20	NUM
cana-6099	108	108	)	)	PUNCT
cana-6099	108	109	∇2𝑤	∇2𝑤	PROPN
cana-6099	109	1	+	+	CCONJ
cana-6099	109	2	(	(	PUNCT
cana-6099	109	3	𝜉2	𝜉2	ADJ
cana-6099	109	4	−	−	PROPN
cana-6099	109	5	1	1	NUM
cana-6099	109	6	)	)	PUNCT
cana-6099	109	7	𝜕𝑒	𝜕𝑒	NOUN
cana-6099	109	8	𝜕𝑧	𝜕𝑧	PRON
cana-6099	109	9	−	−	PROPN
cana-6099	109	10	𝜉2	𝜉2	PROPN
cana-6099	109	11	𝜕𝑇	𝜕𝑇	PROPN
cana-6099	109	12	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	109	13	−	−	NOUN
cana-6099	109	14	𝜉2	𝜉2	PROPN
cana-6099	109	15	𝜕𝐶	𝜕𝐶	PROPN
cana-6099	109	16	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	109	17	=	=	SYM
cana-6099	109	18	𝜉2	𝜉2	PROPN
cana-6099	109	19	𝜕2𝑤	𝜕2𝑤	ADP
cana-6099	109	20	𝜕𝑡2	𝜕𝑡2	PROPN
cana-6099	109	21	(	(	PUNCT
cana-6099	109	22	21	21	NUM
cana-6099	109	23	)	)	PUNCT
cana-6099	109	24	∇2𝜃	∇2𝜃	VERB
cana-6099	110	1	=	=	SYM
cana-6099	110	2	𝜕	𝜕	PROPN
cana-6099	110	3	𝜕𝑡	𝜕𝑡	NOUN
cana-6099	110	4	(	(	PUNCT
cana-6099	110	5	1	1	NUM
cana-6099	110	6	+	+	NUM
cana-6099	110	7	𝜏0	𝜏0	PROPN
cana-6099	110	8	𝜕𝛼	𝜕𝛼	NOUN
cana-6099	110	9	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6099	110	10	)	)	PUNCT
cana-6099	111	1	(	(	PUNCT
cana-6099	111	2	𝜃	𝜃	X
cana-6099	111	3	+	+	X
cana-6099	111	4	𝜖𝑒	𝜖𝑒	ADP
cana-6099	111	5	+	+	ADJ
cana-6099	111	6	𝜖𝛽1𝐶	𝜖𝛽1𝐶	PROPN
cana-6099	111	7	)	)	PUNCT
cana-6099	111	8	(	(	PUNCT
cana-6099	111	9	22	22	NUM
cana-6099	111	10	)	)	PUNCT
cana-6099	111	11	∇2𝑒	∇2𝑒	PROPN
cana-6099	112	1	+	+	CCONJ
cana-6099	112	2	𝛽1∇2𝜃	𝛽1∇2𝜃	ADJ
cana-6099	112	3	+	+	CCONJ
cana-6099	112	4	𝛽2	𝛽2	NOUN
cana-6099	112	5	(	(	PUNCT
cana-6099	112	6	𝜕	𝜕	PROPN
cana-6099	112	7	𝜕𝑡	𝜕𝑡	PROPN
cana-6099	112	8	+	+	CCONJ
cana-6099	112	9	𝜏0	𝜏0	PROPN
cana-6099	112	10	𝜕2	𝜕2	ADJ
cana-6099	112	11	𝜕𝑡2	𝜕𝑡2	NOUN
cana-6099	112	12	)	)	PUNCT
cana-6099	112	13	𝐶	𝐶	PROPN
cana-6099	112	14	−	−	PROPN
cana-6099	112	15	𝛽3∇2𝐶	𝛽3∇2𝐶	X
cana-6099	113	1	=	=	SYM
cana-6099	113	2	0	0	NUM
cana-6099	113	3	(	(	PUNCT
cana-6099	113	4	23	23	NUM
cana-6099	113	5	)	)	PUNCT
cana-6099	113	6	𝜎𝜙𝜙	𝜎𝜙𝜙	ADJ
cana-6099	113	7	=	=	SYM
cana-6099	113	8	2	2	NUM
cana-6099	113	9	𝜉2	𝜉2	PROPN
cana-6099	113	10	𝑢	𝑢	PART
cana-6099	113	11	𝑟	𝑟	NOUN
cana-6099	113	12	+	+	CCONJ
cana-6099	113	13	(	(	PUNCT
cana-6099	113	14	𝜉2	𝜉2	ADJ
cana-6099	113	15	−	−	PROPN
cana-6099	113	16	2	2	X
cana-6099	113	17	)	)	PUNCT
cana-6099	113	18	𝜉2	𝜉2	PROPN
cana-6099	113	19	𝑒	𝑒	PROPN
cana-6099	113	20	−	−	PROPN
cana-6099	114	1	𝜃	𝜃	SYM
cana-6099	115	1	−	−	PROPN
cana-6099	116	1	𝐶	𝐶	PROPN
cana-6099	116	2	(	(	PUNCT
cana-6099	116	3	24	24	NUM
cana-6099	116	4	)	)	PUNCT
cana-6099	116	5	𝜎𝑟𝑟	𝜎𝑟𝑟	VERB
cana-6099	116	6	=	=	SYM
cana-6099	116	7	2	2	NUM
cana-6099	116	8	𝜉2	𝜉2	PROPN
cana-6099	116	9	𝜕𝑢	𝜕𝑢	NOUN
cana-6099	116	10	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	116	11	+	+	CCONJ
cana-6099	116	12	(	(	PUNCT
cana-6099	116	13	𝜉2	𝜉2	ADJ
cana-6099	116	14	−	−	PROPN
cana-6099	116	15	2	2	X
cana-6099	116	16	)	)	PUNCT
cana-6099	116	17	𝜉2	𝜉2	PROPN
cana-6099	116	18	𝑒	𝑒	PROPN
cana-6099	116	19	−	−	PROPN
cana-6099	117	1	𝜃	𝜃	SYM
cana-6099	117	2	−	−	PROPN
cana-6099	117	3	𝐶	𝐶	PROPN
cana-6099	117	4	(	(	PUNCT
cana-6099	117	5	25	25	NUM
cana-6099	117	6	)	)	PUNCT
cana-6099	117	7	communications	communication	NOUN
cana-6099	117	8	on	on	ADP
cana-6099	117	9	applied	apply	VERB
cana-6099	117	10	nonlinear	nonlinear	ADJ
cana-6099	117	11	analysis	analysis	NOUN
cana-6099	117	12	issn	issn	NOUN
cana-6099	117	13	:	:	PUNCT
cana-6099	117	14	1074	1074	NUM
cana-6099	117	15	-	-	PUNCT
cana-6099	117	16	133x	133x	NUM
cana-6099	117	17	vol	vol	VERB
cana-6099	117	18	32	32	NUM
cana-6099	117	19	no	no	NOUN
cana-6099	117	20	.	.	PUNCT
cana-6099	118	1	10s	10	NOUN
cana-6099	118	2	(	(	PUNCT
cana-6099	118	3	2025	2025	NUM
cana-6099	118	4	)	)	PUNCT
cana-6099	118	5	3356	3356	NUM
cana-6099	118	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	118	7	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6099	118	8	=	=	SYM
cana-6099	118	9	2	2	NUM
cana-6099	118	10	𝜉2	𝜉2	PROPN
cana-6099	118	11	𝜕𝑤	𝜕𝑤	VERB
cana-6099	118	12	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	118	13	+	+	CCONJ
cana-6099	118	14	(	(	PUNCT
cana-6099	118	15	𝜉2	𝜉2	ADJ
cana-6099	118	16	−	−	PROPN
cana-6099	118	17	2	2	X
cana-6099	118	18	)	)	PUNCT
cana-6099	118	19	𝜉2	𝜉2	PROPN
cana-6099	118	20	𝑒	𝑒	PROPN
cana-6099	118	21	−	−	PROPN
cana-6099	119	1	𝜃	𝜃	SYM
cana-6099	120	1	−	−	PROPN
cana-6099	121	1	𝐶	𝐶	PROPN
cana-6099	121	2	(	(	PUNCT
cana-6099	121	3	26	26	NUM
cana-6099	121	4	)	)	PUNCT
cana-6099	121	5	𝜎𝑟𝑧	𝜎𝑟𝑧	NOUN
cana-6099	121	6	=	=	SYM
cana-6099	121	7	1	1	NUM
cana-6099	121	8	𝜉2	𝜉2	NOUN
cana-6099	121	9	(	(	PUNCT
cana-6099	121	10	𝜕𝑢	𝜕𝑢	NOUN
cana-6099	121	11	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	121	12	+	+	CCONJ
cana-6099	121	13	𝜕𝑤	𝜕𝑤	NOUN
cana-6099	121	14	𝜕𝑟	𝜕𝑟	ADV
cana-6099	121	15	)	)	PUNCT
cana-6099	121	16	(	(	PUNCT
cana-6099	121	17	27	27	NUM
cana-6099	121	18	)	)	PUNCT
cana-6099	121	19	𝑃	𝑃	NOUN
cana-6099	121	20	=	=	PUNCT
cana-6099	121	21	−𝑒	−𝑒	NOUN
cana-6099	121	22	+	+	PUNCT
cana-6099	121	23	𝛽3𝐶	𝛽3𝐶	NOUN
cana-6099	121	24	−	−	PROPN
cana-6099	121	25	𝛽1𝜃	𝛽1𝜃	NOUN
cana-6099	121	26	(	(	PUNCT
cana-6099	121	27	28	28	NUM
cana-6099	121	28	)	)	PUNCT
cana-6099	121	29	where	where	SCONJ
cana-6099	121	30	,	,	PUNCT
cana-6099	121	31	4	4	X
cana-6099	121	32	.	.	NOUN
cana-6099	121	33	initial	initial	ADJ
cana-6099	121	34	&	&	CCONJ
cana-6099	121	35	boundary	boundary	ADJ
cana-6099	121	36	conditions	condition	NOUN
cana-6099	121	37	•	•	ADP
cana-6099	121	38	initial	initial	ADJ
cana-6099	121	39	conditions	condition	NOUN
cana-6099	121	40	:	:	PUNCT
cana-6099	121	41	the	the	DET
cana-6099	121	42	initial	initial	ADJ
cana-6099	121	43	conditions	condition	NOUN
cana-6099	121	44	are	be	AUX
cana-6099	121	45	assumed	assume	VERB
cana-6099	121	46	as	as	ADP
cana-6099	121	47	:	:	PUNCT
cana-6099	121	48	(	(	PUNCT
cana-6099	121	49	29	29	NUM
cana-6099	121	50	)	)	PUNCT
cana-6099	121	51	(	(	PUNCT
cana-6099	121	52	30	30	NUM
cana-6099	121	53	)	)	PUNCT
cana-6099	121	54	(	(	PUNCT
cana-6099	121	55	31	31	NUM
cana-6099	121	56	)	)	PUNCT
cana-6099	121	57	(	(	PUNCT
cana-6099	121	58	32	32	NUM
cana-6099	121	59	)	)	PUNCT
cana-6099	121	60	•	•	NUM
cana-6099	121	61	boundary	boundary	ADJ
cana-6099	121	62	conditions	condition	NOUN
cana-6099	121	63	:	:	PUNCT
cana-6099	121	64	the	the	DET
cana-6099	121	65	boundary	boundary	ADJ
cana-6099	121	66	conditions	condition	NOUN
cana-6099	121	67	are	be	AUX
cana-6099	121	68	assumed	assume	VERB
cana-6099	121	69	as	as	ADP
cana-6099	121	70	:	:	PUNCT
cana-6099	121	71	𝜕𝜃	𝜕𝜃	NOUN
cana-6099	121	72	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	121	73	=	=	SYM
cana-6099	121	74	±𝑔0𝐹(𝑟	±𝑔0𝐹(𝑟	NOUN
cana-6099	121	75	,	,	PUNCT
cana-6099	121	76	𝑧	𝑧	NOUN
cana-6099	121	77	)	)	PUNCT
cana-6099	121	78	,	,	PUNCT
cana-6099	121	79	𝑧	𝑧	X
cana-6099	121	80	=	=	SYM
cana-6099	121	81	±𝑏	±𝑏	PROPN
cana-6099	121	82	,	,	PUNCT
cana-6099	121	83	(	(	PUNCT
cana-6099	121	84	33	33	NUM
cana-6099	121	85	)	)	PUNCT
cana-6099	121	86	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6099	121	87	=	=	SYM
cana-6099	121	88	0	0	NUM
cana-6099	121	89	,	,	PUNCT
cana-6099	121	90	𝑧	𝑧	X
cana-6099	121	91	=	=	SYM
cana-6099	121	92	±𝑏	±𝑏	PROPN
cana-6099	121	93	,	,	PUNCT
cana-6099	121	94	(	(	PUNCT
cana-6099	121	95	34	34	NUM
cana-6099	121	96	)	)	PUNCT
cana-6099	121	97	𝜎𝑟𝑧	𝜎𝑟𝑧	NOUN
cana-6099	121	98	=	=	SYM
cana-6099	121	99	0	0	NUM
cana-6099	121	100	,	,	PUNCT
cana-6099	121	101	𝑧	𝑧	X
cana-6099	121	102	=	=	SYM
cana-6099	121	103	±𝑏	±𝑏	PROPN
cana-6099	121	104	,	,	PUNCT
cana-6099	121	105	(	(	PUNCT
cana-6099	121	106	35	35	NUM
cana-6099	121	107	)	)	PUNCT
cana-6099	121	108	𝑃	𝑃	NOUN
cana-6099	121	109	=	=	PUNCT
cana-6099	121	110	𝐻(𝑡)𝑓(𝑟	𝐻(𝑡)𝑓(𝑟	NOUN
cana-6099	121	111	)	)	PUNCT
cana-6099	121	112	,	,	PUNCT
cana-6099	121	113	𝑧	𝑧	NOUN
cana-6099	121	114	=	=	SYM
cana-6099	121	115	𝑏	𝑏	NOUN
cana-6099	121	116	,	,	PUNCT
cana-6099	121	117	(	(	PUNCT
cana-6099	121	118	36	36	NUM
cana-6099	121	119	)	)	PUNCT
cana-6099	121	120	where	where	SCONJ
cana-6099	121	121	,	,	PUNCT
cana-6099	121	122	f(r	f(r	PROPN
cana-6099	121	123	)	)	PUNCT
cana-6099	121	124	is	be	AUX
cana-6099	121	125	a	a	DET
cana-6099	121	126	known	know	VERB
cana-6099	121	127	function	function	NOUN
cana-6099	121	128	of	of	ADP
cana-6099	121	129	r	r	NOUN
cana-6099	121	130	and	and	CCONJ
cana-6099	121	131	h(t	h(t	PROPN
cana-6099	121	132	)	)	PUNCT
cana-6099	121	133	is	be	AUX
cana-6099	121	134	a	a	DET
cana-6099	121	135	heaviside	heaviside	ADJ
cana-6099	121	136	unit	unit	NOUN
cana-6099	121	137	step	step	NOUN
cana-6099	121	138	function	function	NOUN
cana-6099	121	139	.	.	PUNCT
cana-6099	122	1	equations	equation	NOUN
cana-6099	122	2	(	(	PUNCT
cana-6099	122	3	7	7	NUM
cana-6099	122	4	)	)	PUNCT
cana-6099	122	5	to	to	ADP
cana-6099	122	6	(	(	PUNCT
cana-6099	122	7	28	28	NUM
cana-6099	122	8	)	)	PUNCT
cana-6099	122	9	and	and	CCONJ
cana-6099	122	10	(	(	PUNCT
cana-6099	122	11	29	29	NUM
cana-6099	122	12	)	)	PUNCT
cana-6099	122	13	to	to	ADP
cana-6099	122	14	(	(	PUNCT
cana-6099	122	15	36	36	NUM
cana-6099	122	16	)	)	PUNCT
cana-6099	122	17	constitute	constitute	VERB
cana-6099	122	18	the	the	DET
cana-6099	122	19	mathematical	mathematical	ADJ
cana-6099	122	20	formulation	formulation	NOUN
cana-6099	122	21	of	of	ADP
cana-6099	122	22	the	the	DET
cana-6099	122	23	problem	problem	NOUN
cana-6099	122	24	under	under	ADP
cana-6099	122	25	consideration	consideration	NOUN
cana-6099	122	26	.	.	PUNCT
cana-6099	123	1	communications	communication	NOUN
cana-6099	123	2	on	on	ADP
cana-6099	123	3	applied	apply	VERB
cana-6099	123	4	nonlinear	nonlinear	ADJ
cana-6099	123	5	analysis	analysis	NOUN
cana-6099	123	6	issn	issn	NOUN
cana-6099	123	7	:	:	PUNCT
cana-6099	123	8	1074	1074	NUM
cana-6099	123	9	-	-	PUNCT
cana-6099	123	10	133x	133x	NUM
cana-6099	123	11	vol	vol	VERB
cana-6099	123	12	32	32	NUM
cana-6099	123	13	no	no	NOUN
cana-6099	123	14	.	.	PUNCT
cana-6099	124	1	10s	10	NOUN
cana-6099	124	2	(	(	PUNCT
cana-6099	124	3	2025	2025	NUM
cana-6099	124	4	)	)	PUNCT
cana-6099	124	5	3357	3357	NUM
cana-6099	124	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	124	7	5	5	X
cana-6099	124	8	.	.	PUNCT
cana-6099	124	9	geometry	geometry	NOUN
cana-6099	124	10	of	of	ADP
cana-6099	124	11	problem	problem	NOUN
cana-6099	124	12	figure	figure	NOUN
cana-6099	124	13	1	1	NUM
cana-6099	124	14	.	.	PUNCT
cana-6099	124	15	thick	thick	ADJ
cana-6099	124	16	circular	circular	ADJ
cana-6099	124	17	plate	plate	NOUN
cana-6099	124	18	under	under	ADP
cana-6099	124	19	axisymmetric	axisymmetric	ADJ
cana-6099	124	20	heat	heat	NOUN
cana-6099	124	21	supply	supply	NOUN
cana-6099	124	22	6	6	NUM
cana-6099	124	23	.	.	PUNCT
cana-6099	124	24	solution	solution	NOUN
cana-6099	124	25	using	use	VERB
cana-6099	124	26	direct	direct	ADJ
cana-6099	124	27	approach	approach	NOUN
cana-6099	124	28	we	we	PRON
cana-6099	124	29	use	use	VERB
cana-6099	124	30	the	the	DET
cana-6099	124	31	laplace	laplace	NOUN
cana-6099	124	32	transform	transform	NOUN
cana-6099	124	33	defined	define	VERB
cana-6099	124	34	as	as	SCONJ
cana-6099	124	35	follows	follow	VERB
cana-6099	124	36	:	:	PUNCT
cana-6099	124	37	(	(	PUNCT
cana-6099	124	38	37	37	NUM
cana-6099	124	39	)	)	PUNCT
cana-6099	124	40	where	where	SCONJ
cana-6099	124	41	,	,	PUNCT
cana-6099	124	42	p	p	NOUN
cana-6099	124	43	is	be	AUX
cana-6099	124	44	the	the	DET
cana-6099	124	45	laplace	laplace	NOUN
cana-6099	124	46	transform	transform	NOUN
cana-6099	124	47	parameter	parameter	NOUN
cana-6099	124	48	.	.	PUNCT
cana-6099	125	1	applying	apply	VERB
cana-6099	125	2	laplace	laplace	NOUN
cana-6099	125	3	transform	transform	NOUN
cana-6099	125	4	to	to	ADP
cana-6099	125	5	equations	equation	NOUN
cana-6099	125	6	(	(	PUNCT
cana-6099	125	7	20	20	NUM
cana-6099	125	8	)	)	PUNCT
cana-6099	125	9	to	to	ADP
cana-6099	125	10	(	(	PUNCT
cana-6099	125	11	28	28	NUM
cana-6099	125	12	)	)	PUNCT
cana-6099	125	13	and	and	CCONJ
cana-6099	125	14	using	use	VERB
cana-6099	125	15	the	the	DET
cana-6099	125	16	homogeneous	homogeneous	ADJ
cana-6099	125	17	initial	initial	ADJ
cana-6099	125	18	conditions	condition	NOUN
cana-6099	125	19	(	(	PUNCT
cana-6099	125	20	29	29	NUM
cana-6099	125	21	)	)	PUNCT
cana-6099	125	22	to	to	ADP
cana-6099	125	23	(	(	PUNCT
cana-6099	125	24	32	32	NUM
cana-6099	125	25	)	)	PUNCT
cana-6099	125	26	,	,	PUNCT
cana-6099	125	27	ones	one	NOUN
cana-6099	125	28	obtain	obtain	VERB
cana-6099	125	29	:	:	PUNCT
cana-6099	125	30	∇2	∇2	PROPN
cana-6099	125	31	�	�	SYM
cana-6099	125	32	̅	̅	NOUN
cana-6099	125	33	�	�	NOUN
cana-6099	125	34	−	−	NUM
cana-6099	125	35	1	1	NUM
cana-6099	125	36	𝑟2	𝑟2	NOUN
cana-6099	125	37	�	�	NOUN
cana-6099	125	38	̅	̅	NOUN
cana-6099	125	39	�	�	NOUN
cana-6099	125	40	+	+	CCONJ
cana-6099	125	41	(	(	PUNCT
cana-6099	125	42	𝜉2	𝜉2	ADJ
cana-6099	125	43	−	−	PROPN
cana-6099	125	44	1	1	NUM
cana-6099	125	45	)	)	PUNCT
cana-6099	125	46	𝜕	𝜕	NOUN
cana-6099	125	47	�	�	PROPN
cana-6099	125	48	̅	̅	NOUN
cana-6099	125	49	�	�	PROPN
cana-6099	125	50	𝜕𝑟	𝜕𝑟	NUM
cana-6099	125	51	−	−	PROPN
cana-6099	125	52	𝜉2	𝜉2	PROPN
cana-6099	125	53	𝜕	𝜕	PROPN
cana-6099	125	54	�	�	PROPN
cana-6099	125	55	̅	̅	NOUN
cana-6099	125	56	�	�	PROPN
cana-6099	125	57	𝜕𝑟	𝜕𝑟	CCONJ
cana-6099	125	58	−	−	PROPN
cana-6099	125	59	𝜉2	𝜉2	PROPN
cana-6099	125	60	𝜕𝐶̅	𝜕𝐶̅	PROPN
cana-6099	126	1	𝜕𝑟	𝜕𝑟	PROPN
cana-6099	126	2	=	=	SYM
cana-6099	126	3	𝜉2𝑝2	𝜉2𝑝2	PROPN
cana-6099	126	4	�	�	PROPN
cana-6099	126	5	̅	̅	NOUN
cana-6099	126	6	�	�	PROPN
cana-6099	126	7	(	(	PUNCT
cana-6099	126	8	38	38	NUM
cana-6099	126	9	)	)	PUNCT
cana-6099	126	10	∇2	∇2	PROPN
cana-6099	126	11	�	�	SYM
cana-6099	126	12	̅	̅	NOUN
cana-6099	126	13	�	�	NOUN
cana-6099	126	14	+	+	CCONJ
cana-6099	126	15	(	(	PUNCT
cana-6099	126	16	𝜉2	𝜉2	ADJ
cana-6099	126	17	−	−	PROPN
cana-6099	126	18	1	1	NUM
cana-6099	126	19	)	)	PUNCT
cana-6099	126	20	𝜕	𝜕	NOUN
cana-6099	126	21	�	�	NOUN
cana-6099	126	22	̅	̅	NOUN
cana-6099	126	23	�	�	PROPN
cana-6099	126	24	𝜕𝑧	𝜕𝑧	PROPN
cana-6099	126	25	−	−	PROPN
cana-6099	126	26	𝜉2	𝜉2	PROPN
cana-6099	126	27	𝜕	𝜕	PROPN
cana-6099	126	28	�	�	PROPN
cana-6099	126	29	̅	̅	NOUN
cana-6099	126	30	�	�	PROPN
cana-6099	126	31	𝜕𝑧	𝜕𝑧	NOUN
cana-6099	126	32	−	−	PROPN
cana-6099	126	33	𝜉2	𝜉2	PROPN
cana-6099	126	34	𝜕𝐶̅	𝜕𝐶̅	NOUN
cana-6099	126	35	𝜕𝑧	𝜕𝑧	PROPN
cana-6099	126	36	=	=	SYM
cana-6099	126	37	𝜉2𝑝2	𝜉2𝑝2	NOUN
cana-6099	126	38	�	�	PROPN
cana-6099	126	39	̅	̅	NOUN
cana-6099	126	40	�	�	PROPN
cana-6099	126	41	(	(	PUNCT
cana-6099	126	42	39	39	NUM
cana-6099	126	43	)	)	PUNCT
cana-6099	126	44	∇2	∇2	PROPN
cana-6099	126	45	�	�	SYM
cana-6099	126	46	̅	̅	NOUN
cana-6099	126	47	�	�	PROPN
cana-6099	126	48	=	=	SYM
cana-6099	126	49	�	�	PROPN
cana-6099	126	50	̅	̅	NOUN
cana-6099	126	51	�	�	NOUN
cana-6099	126	52	(1	(1	NOUN
cana-6099	126	53	+	+	CCONJ
cana-6099	126	54	𝜏0𝑝𝛼)(	𝜏0𝑝𝛼)(	PROPN
cana-6099	126	55	�	�	NOUN
cana-6099	126	56	̅	̅	NOUN
cana-6099	126	57	�	�	PROPN
cana-6099	126	58	+	+	CCONJ
cana-6099	126	59	𝜖	𝜖	PROPN
cana-6099	126	60	�	�	PROPN
cana-6099	126	61	̅	̅	NOUN
cana-6099	126	62	�	�	NOUN
cana-6099	126	63	+	+	CCONJ
cana-6099	126	64	𝜖𝛽1𝐶̅	𝜖𝛽1𝐶̅	PROPN
cana-6099	126	65	)	)	PUNCT
cana-6099	126	66	(	(	PUNCT
cana-6099	126	67	40	40	NUM
cana-6099	126	68	)	)	PUNCT
cana-6099	126	69	∇2	∇2	PROPN
cana-6099	126	70	�	�	SYM
cana-6099	126	71	̅	̅	NOUN
cana-6099	126	72	�	�	PROPN
cana-6099	126	73	+	+	SYM
cana-6099	126	74	𝛽1∇2	𝛽1∇2	PROPN
cana-6099	126	75	�	�	PROPN
cana-6099	126	76	̅	̅	NOUN
cana-6099	126	77	�	�	NOUN
cana-6099	126	78	+	+	CCONJ
cana-6099	126	79	𝛽2(𝑝	𝛽2(𝑝	NUM
cana-6099	126	80	+	+	CCONJ
cana-6099	126	81	𝜏0𝑝2)𝐶̅	𝜏0𝑝2)𝐶̅	NOUN
cana-6099	126	82	−	−	PROPN
cana-6099	126	83	𝛽3∇2𝐶̅	𝛽3∇2𝐶̅	NOUN
cana-6099	126	84	=	=	SYM
cana-6099	126	85	0	0	NUM
cana-6099	126	86	(	(	PUNCT
cana-6099	126	87	41	41	NUM
cana-6099	126	88	)	)	PUNCT
cana-6099	126	89	𝜎𝜙𝜙	𝜎𝜙𝜙	ADJ
cana-6099	126	90	=	=	SYM
cana-6099	126	91	2	2	NUM
cana-6099	126	92	𝜉2	𝜉2	PROPN
cana-6099	126	93	�	�	PROPN
cana-6099	126	94	̅	̅	NOUN
cana-6099	126	95	�	�	NOUN
cana-6099	126	96	𝑟	𝑟	NOUN
cana-6099	126	97	+	+	CCONJ
cana-6099	126	98	(	(	PUNCT
cana-6099	126	99	𝜉2	𝜉2	ADJ
cana-6099	126	100	−	−	PROPN
cana-6099	126	101	2	2	X
cana-6099	126	102	)	)	PUNCT
cana-6099	126	103	𝜉2	𝜉2	PROPN
cana-6099	126	104	�	�	PROPN
cana-6099	126	105	̅	̅	NOUN
cana-6099	126	106	�	�	PROPN
cana-6099	126	107	−	−	PROPN
cana-6099	126	108	�	�	PROPN
cana-6099	126	109	̅	̅	NOUN
cana-6099	126	110	�	�	PROPN
cana-6099	126	111	−	−	PROPN
cana-6099	126	112	𝐶̅	𝐶̅	NOUN
cana-6099	126	113	(	(	PUNCT
cana-6099	126	114	42	42	NUM
cana-6099	126	115	)	)	PUNCT
cana-6099	126	116	𝜎𝑟𝑟	𝜎𝑟𝑟	VERB
cana-6099	126	117	=	=	SYM
cana-6099	126	118	2	2	NUM
cana-6099	126	119	𝜉2	𝜉2	PROPN
cana-6099	126	120	𝜕	𝜕	PROPN
cana-6099	126	121	�	�	PROPN
cana-6099	126	122	̅	̅	NOUN
cana-6099	126	123	�	�	PROPN
cana-6099	126	124	𝜕𝑟	𝜕𝑟	PROPN
cana-6099	126	125	+	+	CCONJ
cana-6099	126	126	(	(	PUNCT
cana-6099	126	127	𝜉2	𝜉2	ADJ
cana-6099	126	128	−	−	PROPN
cana-6099	126	129	2	2	X
cana-6099	126	130	)	)	PUNCT
cana-6099	126	131	𝜉2	𝜉2	PROPN
cana-6099	126	132	�	�	PROPN
cana-6099	126	133	̅	̅	NOUN
cana-6099	126	134	�	�	PROPN
cana-6099	126	135	−	−	PROPN
cana-6099	126	136	�	�	PROPN
cana-6099	126	137	̅	̅	NOUN
cana-6099	126	138	�	�	PROPN
cana-6099	126	139	−	−	PROPN
cana-6099	126	140	𝐶̅	𝐶̅	NOUN
cana-6099	126	141	(	(	PUNCT
cana-6099	126	142	43	43	NUM
cana-6099	126	143	)	)	PUNCT
cana-6099	127	1	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6099	127	2	=	=	SYM
cana-6099	127	3	2	2	NUM
cana-6099	127	4	𝜉2	𝜉2	PROPN
cana-6099	127	5	𝜕	𝜕	PROPN
cana-6099	127	6	�	�	PROPN
cana-6099	127	7	̅	̅	NOUN
cana-6099	127	8	�	�	PROPN
cana-6099	127	9	𝜕𝑧	𝜕𝑧	PROPN
cana-6099	127	10	+	+	CCONJ
cana-6099	127	11	(	(	PUNCT
cana-6099	127	12	𝜉2	𝜉2	ADJ
cana-6099	127	13	−	−	PROPN
cana-6099	127	14	2	2	X
cana-6099	127	15	)	)	PUNCT
cana-6099	127	16	𝜉2	𝜉2	PROPN
cana-6099	127	17	�	�	PROPN
cana-6099	127	18	̅	̅	NOUN
cana-6099	127	19	�	�	PROPN
cana-6099	127	20	−	−	PROPN
cana-6099	127	21	�	�	PROPN
cana-6099	127	22	̅	̅	NOUN
cana-6099	127	23	�	�	PROPN
cana-6099	127	24	−	−	PROPN
cana-6099	127	25	𝐶̅	𝐶̅	NOUN
cana-6099	127	26	(	(	PUNCT
cana-6099	127	27	44	44	NUM
cana-6099	127	28	)	)	PUNCT
cana-6099	127	29	𝜎𝑟𝑧	𝜎𝑟𝑧	NOUN
cana-6099	127	30	=	=	SYM
cana-6099	127	31	1	1	NUM
cana-6099	127	32	𝜉2	𝜉2	PROPN
cana-6099	127	33	(	(	PUNCT
cana-6099	127	34	𝜕	𝜕	NOUN
cana-6099	127	35	�	�	NOUN
cana-6099	127	36	̅	̅	NOUN
cana-6099	127	37	�	�	PROPN
cana-6099	127	38	𝜕𝑧	𝜕𝑧	PROPN
cana-6099	127	39	+	+	NOUN
cana-6099	127	40	𝜕	𝜕	PROPN
cana-6099	127	41	�	�	NOUN
cana-6099	127	42	̅	̅	NOUN
cana-6099	127	43	�	�	PROPN
cana-6099	127	44	𝜕𝑟	𝜕𝑟	NOUN
cana-6099	127	45	)	)	PUNCT
cana-6099	127	46	(	(	PUNCT
cana-6099	127	47	45	45	NUM
cana-6099	127	48	)	)	PUNCT
cana-6099	127	49	𝑃	𝑃	NOUN
cana-6099	127	50	=	=	PUNCT
cana-6099	127	51	−	−	NOUN
cana-6099	127	52	�	�	NOUN
cana-6099	127	53	̅	̅	NOUN
cana-6099	127	54	�	�	NOUN
cana-6099	127	55	+	+	CCONJ
cana-6099	127	56	𝛽3𝐶̅	𝛽3𝐶̅	ADJ
cana-6099	127	57	−	−	PROPN
cana-6099	127	58	𝛽1	𝛽1	NOUN
cana-6099	127	59	�	�	NOUN
cana-6099	127	60	̅	̅	NOUN
cana-6099	127	61	�	�	PROPN
cana-6099	127	62	(	(	PUNCT
cana-6099	127	63	46	46	NUM
cana-6099	127	64	)	)	PUNCT
cana-6099	127	65	communications	communication	NOUN
cana-6099	127	66	on	on	ADP
cana-6099	127	67	applied	apply	VERB
cana-6099	127	68	nonlinear	nonlinear	ADJ
cana-6099	127	69	analysis	analysis	NOUN
cana-6099	127	70	issn	issn	NOUN
cana-6099	127	71	:	:	PUNCT
cana-6099	127	72	1074	1074	NUM
cana-6099	127	73	-	-	PUNCT
cana-6099	127	74	133x	133x	NUM
cana-6099	127	75	vol	vol	VERB
cana-6099	127	76	32	32	NUM
cana-6099	127	77	no	no	NOUN
cana-6099	127	78	.	.	PUNCT
cana-6099	128	1	10s	10	NOUN
cana-6099	128	2	(	(	PUNCT
cana-6099	128	3	2025	2025	NUM
cana-6099	128	4	)	)	PUNCT
cana-6099	128	5	3358	3358	NUM
cana-6099	128	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	128	7	simplifying	simplify	VERB
cana-6099	128	8	equations	equation	NOUN
cana-6099	128	9	(	(	PUNCT
cana-6099	128	10	37	37	NUM
cana-6099	128	11	)	)	PUNCT
cana-6099	128	12	and	and	CCONJ
cana-6099	128	13	(	(	PUNCT
cana-6099	128	14	38	38	NUM
cana-6099	128	15	)	)	PUNCT
cana-6099	128	16	,	,	PUNCT
cana-6099	128	17	we	we	PRON
cana-6099	128	18	get	get	VERB
cana-6099	128	19	,	,	PUNCT
cana-6099	128	20	(	(	PUNCT
cana-6099	128	21	𝛻2	𝛻2	X
cana-6099	129	1	−	−	PRON
cana-6099	129	2	𝑝2)𝑒	𝑝2)𝑒	NOUN
cana-6099	129	3	=	=	SYM
cana-6099	129	4	𝛻2	𝛻2	NOUN
cana-6099	129	5	�	�	PROPN
cana-6099	129	6	̅	̅	NOUN
cana-6099	129	7	�	�	NOUN
cana-6099	129	8	+	+	CCONJ
cana-6099	129	9	𝛻2𝐶̅	𝛻2𝐶̅	NOUN
cana-6099	129	10	=	=	SYM
cana-6099	129	11	0	0	NUM
cana-6099	129	12	eliminating	eliminate	VERB
cana-6099	129	13	�	�	PROPN
cana-6099	129	14	̅	̅	NOUN
cana-6099	129	15	�	�	PROPN
cana-6099	129	16	and	and	CCONJ
cana-6099	129	17	𝐶̅	𝐶̅	NOUN
cana-6099	129	18	from	from	ADP
cana-6099	129	19	(	(	PUNCT
cana-6099	129	20	39	39	NUM
cana-6099	129	21	)	)	PUNCT
cana-6099	129	22	,	,	PUNCT
cana-6099	129	23	(	(	PUNCT
cana-6099	129	24	40	40	NUM
cana-6099	129	25	)	)	PUNCT
cana-6099	129	26	and	and	CCONJ
cana-6099	129	27	(	(	PUNCT
cana-6099	129	28	46	46	NUM
cana-6099	129	29	)	)	PUNCT
cana-6099	129	30	,	,	PUNCT
cana-6099	129	31	we	we	PRON
cana-6099	129	32	get	get	VERB
cana-6099	129	33	,	,	PUNCT
cana-6099	129	34	(	(	PUNCT
cana-6099	129	35	47	47	NUM
cana-6099	129	36	)	)	PUNCT
cana-6099	129	37	(	(	PUNCT
cana-6099	129	38	𝛻6	𝛻6	NOUN
cana-6099	129	39	−	−	PROPN
cana-6099	129	40	𝐴1𝛻4	𝐴1𝛻4	NOUN
cana-6099	129	41	+	+	CCONJ
cana-6099	129	42	𝐴2𝛻2	𝐴2𝛻2	ADJ
cana-6099	129	43	−	−	PROPN
cana-6099	129	44	𝐴3	𝐴3	PROPN
cana-6099	129	45	)	)	PUNCT
cana-6099	129	46	�	�	PROPN
cana-6099	129	47	̅	̅	NOUN
cana-6099	129	48	�	�	NOUN
cana-6099	129	49	=	=	SYM
cana-6099	129	50	0	0	NUM
cana-6099	130	1	(	(	PUNCT
cana-6099	130	2	48	48	NUM
cana-6099	130	3	)	)	PUNCT
cana-6099	130	4	where	where	SCONJ
cana-6099	130	5	,	,	PUNCT
cana-6099	130	6	,	,	PUNCT
cana-6099	130	7	similarly	similarly	ADV
cana-6099	130	8	we	we	PRON
cana-6099	130	9	can	can	AUX
cana-6099	130	10	show	show	VERB
cana-6099	130	11	that	that	SCONJ
cana-6099	130	12	the	the	DET
cana-6099	130	13	�	�	PROPN
cana-6099	130	14	̅	̅	NOUN
cana-6099	130	15	�	�	PROPN
cana-6099	130	16	and	and	CCONJ
cana-6099	130	17	�	�	PROPN
cana-6099	130	18	̅	̅	NOUN
cana-6099	130	19	�	�	NOUN
cana-6099	130	20	satisfy	satisfy	VERB
cana-6099	130	21	the	the	DET
cana-6099	130	22	equations	equation	NOUN
cana-6099	130	23	,	,	PUNCT
cana-6099	130	24	(	(	PUNCT
cana-6099	130	25	𝛻6	𝛻6	NOUN
cana-6099	130	26	−	−	PROPN
cana-6099	130	27	𝐴1𝛻4	𝐴1𝛻4	NOUN
cana-6099	130	28	+	+	CCONJ
cana-6099	130	29	𝐴2𝛻2	𝐴2𝛻2	ADJ
cana-6099	130	30	−	−	PROPN
cana-6099	130	31	𝐴3	𝐴3	PROPN
cana-6099	130	32	)	)	PUNCT
cana-6099	130	33	�	�	PROPN
cana-6099	130	34	̅	̅	NOUN
cana-6099	130	35	�	�	NOUN
cana-6099	130	36	=	=	SYM
cana-6099	130	37	0	0	NUM
cana-6099	130	38	(	(	PUNCT
cana-6099	130	39	49	49	NUM
cana-6099	130	40	)	)	PUNCT
cana-6099	130	41	(	(	PUNCT
cana-6099	130	42	𝛻6	𝛻6	NOUN
cana-6099	130	43	−	−	PROPN
cana-6099	130	44	𝐴1𝛻4	𝐴1𝛻4	NOUN
cana-6099	130	45	+	+	CCONJ
cana-6099	130	46	𝐴2𝛻2	𝐴2𝛻2	ADJ
cana-6099	130	47	−	−	PROPN
cana-6099	130	48	𝐴3	𝐴3	PROPN
cana-6099	130	49	)	)	PUNCT
cana-6099	130	50	𝐶̅	𝐶̅	NOUN
cana-6099	130	51	=	=	SYM
cana-6099	130	52	0	0	NUM
cana-6099	130	53	(	(	PUNCT
cana-6099	130	54	50	50	NUM
cana-6099	130	55	)	)	PUNCT
cana-6099	130	56	equation	equation	NOUN
cana-6099	130	57	(	(	PUNCT
cana-6099	130	58	48	48	NUM
cana-6099	130	59	)	)	PUNCT
cana-6099	130	60	can	can	AUX
cana-6099	130	61	be	be	AUX
cana-6099	130	62	written	write	VERB
cana-6099	130	63	as	as	ADP
cana-6099	130	64	:	:	PUNCT
cana-6099	130	65	=	=	SYM
cana-6099	130	66	0	0	SYM
cana-6099	130	67	(	(	PUNCT
cana-6099	130	68	51	51	NUM
cana-6099	130	69	)	)	PUNCT
cana-6099	130	70	where	where	SCONJ
cana-6099	130	71	,	,	PUNCT
cana-6099	130	72	k1	k1	PROPN
cana-6099	130	73	,	,	PUNCT
cana-6099	130	74	k2	k2	NOUN
cana-6099	130	75	and	and	CCONJ
cana-6099	130	76	k3	k3	NOUN
cana-6099	130	77	are	be	AUX
cana-6099	130	78	the	the	DET
cana-6099	130	79	roots	root	NOUN
cana-6099	130	80	having	have	VERB
cana-6099	130	81	positive	positive	ADJ
cana-6099	130	82	real	real	ADJ
cana-6099	130	83	parts	part	NOUN
cana-6099	130	84	of	of	ADP
cana-6099	130	85	the	the	DET
cana-6099	130	86	characteristic	characteristic	ADJ
cana-6099	130	87	equation	equation	NOUN
cana-6099	130	88	given	give	VERB
cana-6099	130	89	by	by	ADP
cana-6099	130	90	𝑘6	𝑘6	PROPN
cana-6099	130	91	−	−	PROPN
cana-6099	130	92	𝐴1𝑘4	𝐴1𝑘4	PROPN
cana-6099	130	93	+	+	CCONJ
cana-6099	130	94	𝐴2𝑘2	𝐴2𝑘2	PROPN
cana-6099	130	95	−	−	PROPN
cana-6099	130	96	𝐴3	𝐴3	PROPN
cana-6099	130	97	=	=	SYM
cana-6099	130	98	0	0	NUM
cana-6099	131	1	(	(	PUNCT
cana-6099	131	2	52	52	NUM
cana-6099	131	3	)	)	PUNCT
cana-6099	131	4	the	the	DET
cana-6099	131	5	roots	root	NOUN
cana-6099	131	6	k1	k1	NOUN
cana-6099	131	7	,	,	PUNCT
cana-6099	131	8	k2	k2	NOUN
cana-6099	131	9	and	and	CCONJ
cana-6099	131	10	k3	k3	NOUN
cana-6099	131	11	are	be	AUX
cana-6099	131	12	given	give	VERB
cana-6099	131	13	by	by	ADP
cana-6099	131	14	:	:	PUNCT
cana-6099	131	15	,	,	PUNCT
cana-6099	131	16	where	where	SCONJ
cana-6099	131	17	,	,	PUNCT
cana-6099	131	18	.	.	PUNCT
cana-6099	132	1	7	7	X
cana-6099	132	2	.	.	X
cana-6099	132	3	extraction	extraction	NOUN
cana-6099	132	4	of	of	ADP
cana-6099	132	5	field	field	NOUN
cana-6099	132	6	functions	function	VERB
cana-6099	132	7	the	the	DET
cana-6099	132	8	solution	solution	NOUN
cana-6099	132	9	of	of	ADP
cana-6099	132	10	equation	equation	NOUN
cana-6099	132	11	(	(	PUNCT
cana-6099	132	12	51	51	NUM
cana-6099	132	13	)	)	PUNCT
cana-6099	132	14	can	can	AUX
cana-6099	132	15	be	be	AUX
cana-6099	132	16	written	write	VERB
cana-6099	132	17	in	in	ADP
cana-6099	132	18	the	the	DET
cana-6099	132	19	form	form	NOUN
cana-6099	132	20	:	:	PUNCT
cana-6099	132	21	(	(	PUNCT
cana-6099	132	22	53	53	NUM
cana-6099	132	23	)	)	PUNCT
cana-6099	132	24	communications	communication	NOUN
cana-6099	132	25	on	on	ADP
cana-6099	132	26	applied	apply	VERB
cana-6099	132	27	nonlinear	nonlinear	ADJ
cana-6099	132	28	analysis	analysis	NOUN
cana-6099	132	29	issn	issn	NOUN
cana-6099	132	30	:	:	PUNCT
cana-6099	132	31	1074	1074	NUM
cana-6099	132	32	-	-	PUNCT
cana-6099	132	33	133x	133x	NUM
cana-6099	132	34	vol	vol	VERB
cana-6099	132	35	32	32	NUM
cana-6099	132	36	no	no	NOUN
cana-6099	132	37	.	.	PUNCT
cana-6099	133	1	10s	10	NOUN
cana-6099	133	2	(	(	PUNCT
cana-6099	133	3	2025	2025	NUM
cana-6099	133	4	)	)	PUNCT
cana-6099	133	5	3359	3359	NUM
cana-6099	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	133	7	where	where	SCONJ
cana-6099	133	8	,	,	PUNCT
cana-6099	133	9	𝜃	𝜃	NOUN
cana-6099	133	10	�	�	NOUN
cana-6099	133	11	̅	̅	NOUN
cana-6099	133	12	�	�	NOUN
cana-6099	133	13	is	be	AUX
cana-6099	133	14	a	a	DET
cana-6099	133	15	solution	solution	NOUN
cana-6099	133	16	of	of	ADP
cana-6099	133	17	the	the	DET
cana-6099	133	18	following	follow	VERB
cana-6099	133	19	equation	equation	NOUN
cana-6099	133	20	:	:	PUNCT
cana-6099	133	21	(	(	PUNCT
cana-6099	133	22	𝛻2	𝛻2	X
cana-6099	133	23	−	−	ADP
cana-6099	133	24	𝑘𝑖	𝑘𝑖	NOUN
cana-6099	133	25	2)𝜃	2)𝜃	NUM
cana-6099	133	26	�	�	NOUN
cana-6099	133	27	̅	̅	NOUN
cana-6099	133	28	�	�	NOUN
cana-6099	133	29	=	=	SYM
cana-6099	133	30	0	0	NUM
cana-6099	133	31	,	,	PUNCT
cana-6099	133	32	𝑖	𝑖	NOUN
cana-6099	133	33	=	=	NOUN
cana-6099	133	34	1,2,3	1,2,3	NOUN
cana-6099	133	35	.	.	PUNCT
cana-6099	134	1	taking	take	VERB
cana-6099	134	2	the	the	DET
cana-6099	134	3	hankel	hankel	NOUN
cana-6099	134	4	transform	transform	NOUN
cana-6099	134	5	of	of	ADP
cana-6099	134	6	the	the	DET
cana-6099	134	7	above	above	ADJ
cana-6099	134	8	equation	equation	NOUN
cana-6099	134	9	,	,	PUNCT
cana-6099	134	10	we	we	PRON
cana-6099	134	11	get	get	VERB
cana-6099	134	12	(	(	PUNCT
cana-6099	134	13	54	54	NUM
cana-6099	134	14	)	)	PUNCT
cana-6099	134	15	(	(	PUNCT
cana-6099	134	16	𝐷2	𝐷2	PROPN
cana-6099	134	17	−	−	PROPN
cana-6099	134	18	𝛾2	𝛾2	NOUN
cana-6099	134	19	−	−	NOUN
cana-6099	134	20	𝑘𝑖	𝑘𝑖	NOUN
cana-6099	134	21	2)𝜃𝑖	2)𝜃𝑖	NUM
cana-6099	134	22	∗̅̅	∗̅̅	NOUN
cana-6099	134	23	̅	̅	NOUN
cana-6099	134	24	=	=	SYM
cana-6099	134	25	0	0	NUM
cana-6099	134	26	,	,	PUNCT
cana-6099	134	27	𝑖	𝑖	NOUN
cana-6099	134	28	=	=	NOUN
cana-6099	135	1	1,2,3	1,2,3	NUM
cana-6099	135	2	.	.	PUNCT
cana-6099	136	1	(	(	PUNCT
cana-6099	136	2	55	55	NUM
cana-6099	136	3	)	)	PUNCT
cana-6099	136	4	where	where	SCONJ
cana-6099	136	5	,	,	PUNCT
cana-6099	136	6	the	the	DET
cana-6099	136	7	solution	solution	NOUN
cana-6099	136	8	of	of	ADP
cana-6099	136	9	equation	equation	NOUN
cana-6099	136	10	(	(	PUNCT
cana-6099	136	11	55	55	NUM
cana-6099	136	12	)	)	PUNCT
cana-6099	136	13	has	have	VERB
cana-6099	136	14	the	the	DET
cana-6099	136	15	form	form	NOUN
cana-6099	136	16	𝜃𝑖	𝜃𝑖	ADP
cana-6099	136	17	∗̅̅	∗̅̅	NOUN
cana-6099	136	18	̅	̅	NOUN
cana-6099	136	19	=	=	SYM
cana-6099	136	20	∑	∑	NOUN
cana-6099	136	21	𝐵𝑖(𝛾	𝐵𝑖(𝛾	PROPN
cana-6099	136	22	,	,	PUNCT
cana-6099	136	23	𝑝	𝑝	NOUN
cana-6099	136	24	)	)	PUNCT
cana-6099	136	25	cosh(𝑞𝑖𝑧	cosh(𝑞𝑖𝑧	NOUN
cana-6099	136	26	)	)	PUNCT
cana-6099	136	27	(	(	PUNCT
cana-6099	136	28	56	56	NUM
cana-6099	136	29	)	)	PUNCT
cana-6099	136	30	3	3	NUM
cana-6099	136	31	𝑖=1	𝑖=1	PUNCT
cana-6099	136	32	where	where	SCONJ
cana-6099	136	33	,	,	PUNCT
cana-6099	136	34	𝑞	𝑞	X
cana-6099	136	35	𝑖	𝑖	SYM
cana-6099	136	36	2	2	NUM
cana-6099	136	37	=	=	AUX
cana-6099	136	38	𝛾2	𝛾2	VERB
cana-6099	136	39	+	+	CCONJ
cana-6099	136	40	𝑘𝑖	𝑘𝑖	NOUN
cana-6099	136	41	2	2	NUM
cana-6099	136	42	similarly	similarly	ADV
cana-6099	136	43	𝑒	𝑒	SYM
cana-6099	136	44	∗̅	∗̅	NOUN
cana-6099	136	45	and	and	CCONJ
cana-6099	136	46	𝐶𝑖	𝐶𝑖	PROPN
cana-6099	136	47	∗̅̅	∗̅̅	NOUN
cana-6099	136	48	̅	̅	NOUN
cana-6099	136	49	can	can	AUX
cana-6099	136	50	be	be	AUX
cana-6099	136	51	obtain	obtain	VERB
cana-6099	136	52	form	form	NOUN
cana-6099	136	53	(	(	PUNCT
cana-6099	136	54	49	49	NUM
cana-6099	136	55	)	)	PUNCT
cana-6099	136	56	&	&	CCONJ
cana-6099	137	1	(	(	PUNCT
cana-6099	137	2	50	50	NUM
cana-6099	137	3	)	)	PUNCT
cana-6099	137	4	as	as	ADP
cana-6099	137	5	:	:	PUNCT
cana-6099	137	6	𝑒𝑖	𝑒𝑖	PART
cana-6099	137	7	∗̅	∗̅	NOUN
cana-6099	137	8	=	=	SYM
cana-6099	137	9	∑	∑	PUNCT
cana-6099	137	10	𝐶𝑖(𝛾	𝐶𝑖(𝛾	PROPN
cana-6099	137	11	,	,	PUNCT
cana-6099	137	12	𝑝	𝑝	NOUN
cana-6099	137	13	)	)	PUNCT
cana-6099	137	14	cosh(𝑞𝑖𝑧	cosh(𝑞𝑖𝑧	NOUN
cana-6099	137	15	)	)	PUNCT
cana-6099	137	16	(	(	PUNCT
cana-6099	137	17	57	57	NUM
cana-6099	137	18	)	)	PUNCT
cana-6099	137	19	3	3	NUM
cana-6099	137	20	𝑖=1	𝑖=1	PUNCT
cana-6099	137	21	𝐶𝑖	𝐶𝑖	NOUN
cana-6099	137	22	∗̅̅	∗̅̅	NOUN
cana-6099	137	23	̅	̅	NOUN
cana-6099	137	24	=	=	SYM
cana-6099	137	25	∑	∑	NOUN
cana-6099	137	26	𝐷𝑖(𝛾	𝐷𝑖(𝛾	PROPN
cana-6099	137	27	,	,	PUNCT
cana-6099	137	28	𝑝	𝑝	NOUN
cana-6099	137	29	)	)	PUNCT
cana-6099	137	30	cosh(𝑞𝑖𝑧	cosh(𝑞𝑖𝑧	NOUN
cana-6099	137	31	)	)	PUNCT
cana-6099	137	32	(	(	PUNCT
cana-6099	137	33	58	58	NUM
cana-6099	137	34	)	)	PUNCT
cana-6099	137	35	3	3	NUM
cana-6099	137	36	𝑖=1	𝑖=1	PUNCT
cana-6099	137	37	where	where	SCONJ
cana-6099	137	38	,	,	PUNCT
cana-6099	137	39	𝐵𝑖(𝛾	𝐵𝑖(𝛾	PROPN
cana-6099	137	40	,	,	PUNCT
cana-6099	137	41	𝑝	𝑝	NOUN
cana-6099	137	42	)	)	PUNCT
cana-6099	137	43	,	,	PUNCT
cana-6099	137	44	𝐶𝑖(𝛾	𝐶𝑖(𝛾	NOUN
cana-6099	137	45	,	,	PUNCT
cana-6099	137	46	𝑝	𝑝	NOUN
cana-6099	137	47	)	)	PUNCT
cana-6099	137	48	&	&	CCONJ
cana-6099	137	49	𝐷𝑖(𝛾	𝐷𝑖(𝛾	PROPN
cana-6099	137	50	,	,	PUNCT
cana-6099	137	51	𝑝	𝑝	NOUN
cana-6099	137	52	)	)	PUNCT
cana-6099	137	53	,	,	PUNCT
cana-6099	137	54	𝑖	𝑖	SYM
cana-6099	138	1	=	=	NOUN
cana-6099	138	2	1,2,3	1,2,3	NUM
cana-6099	138	3	are	be	AUX
cana-6099	138	4	parameters	parameter	NOUN
cana-6099	138	5	depending	depend	VERB
cana-6099	138	6	on	on	ADP
cana-6099	138	7	𝛾	𝛾	PROPN
cana-6099	138	8	&	&	CCONJ
cana-6099	138	9	𝑝.	𝑝.	PROPN
cana-6099	138	10	substituting	substituting	NOUN
cana-6099	138	11	(	(	PUNCT
cana-6099	138	12	56	56	NUM
cana-6099	138	13	)	)	PUNCT
cana-6099	138	14	,	,	PUNCT
cana-6099	138	15	(	(	PUNCT
cana-6099	138	16	57	57	NUM
cana-6099	138	17	)	)	PUNCT
cana-6099	138	18	,	,	PUNCT
cana-6099	138	19	(	(	PUNCT
cana-6099	138	20	58	58	NUM
cana-6099	138	21	)	)	PUNCT
cana-6099	138	22	in	in	ADP
cana-6099	138	23	(	(	PUNCT
cana-6099	138	24	40	40	NUM
cana-6099	138	25	)	)	PUNCT
cana-6099	138	26	and	and	CCONJ
cana-6099	138	27	(	(	PUNCT
cana-6099	138	28	47	47	NUM
cana-6099	138	29	)	)	PUNCT
cana-6099	138	30	the	the	DET
cana-6099	138	31	parameters	parameter	NOUN
cana-6099	138	32	𝐶𝑖(𝛾	𝐶𝑖(𝛾	ADV
cana-6099	138	33	,	,	PUNCT
cana-6099	138	34	𝑝	𝑝	NOUN
cana-6099	138	35	)	)	PUNCT
cana-6099	138	36	and	and	CCONJ
cana-6099	138	37	𝐷𝑖(𝛾	𝐷𝑖(𝛾	PROPN
cana-6099	138	38	,	,	PUNCT
cana-6099	138	39	𝑝	𝑝	NOUN
cana-6099	138	40	)	)	PUNCT
cana-6099	138	41	,	,	PUNCT
cana-6099	138	42	𝑖	𝑖	SYM
cana-6099	139	1	=	=	NOUN
cana-6099	139	2	1,2,3	1,2,3	NOUN
cana-6099	139	3	can	can	AUX
cana-6099	139	4	be	be	AUX
cana-6099	139	5	expressed	express	VERB
cana-6099	139	6	in	in	ADP
cana-6099	139	7	terms	term	NOUN
cana-6099	139	8	of	of	ADP
cana-6099	139	9	𝐵𝑖(𝛾	𝐵𝑖(𝛾	NOUN
cana-6099	139	10	,	,	PUNCT
cana-6099	139	11	𝑝	𝑝	NOUN
cana-6099	139	12	)	)	PUNCT
cana-6099	139	13	as	as	ADP
cana-6099	139	14	:	:	PUNCT
cana-6099	139	15	𝐶𝑖(𝛾	𝐶𝑖(𝛾	NOUN
cana-6099	139	16	,	,	PUNCT
cana-6099	139	17	𝑝	𝑝	NOUN
cana-6099	139	18	)	)	PUNCT
cana-6099	139	19	=	=	SYM
cana-6099	139	20	𝑓𝑖𝐵𝑖(𝛾	𝑓𝑖𝐵𝑖(𝛾	NOUN
cana-6099	139	21	,	,	PUNCT
cana-6099	139	22	𝑝	𝑝	NOUN
cana-6099	139	23	)	)	PUNCT
cana-6099	139	24	(	(	PUNCT
cana-6099	139	25	59	59	NUM
cana-6099	139	26	)	)	PUNCT
cana-6099	139	27	𝐷𝑖(𝛾	𝐷𝑖(𝛾	PROPN
cana-6099	139	28	,	,	PUNCT
cana-6099	139	29	𝑝	𝑝	NOUN
cana-6099	139	30	)	)	PUNCT
cana-6099	139	31	=	=	SYM
cana-6099	139	32	𝑑𝑖𝐵𝑖(𝛾	𝑑𝑖𝐵𝑖(𝛾	PROPN
cana-6099	139	33	,	,	PUNCT
cana-6099	139	34	𝑝	𝑝	NOUN
cana-6099	139	35	)	)	PUNCT
cana-6099	139	36	(	(	PUNCT
cana-6099	139	37	60	60	NUM
cana-6099	139	38	)	)	PUNCT
cana-6099	139	39	where	where	SCONJ
cana-6099	139	40	,	,	PUNCT
cana-6099	139	41	and	and	CCONJ
cana-6099	139	42	.	.	PUNCT
cana-6099	140	1	applying	apply	VERB
cana-6099	140	2	the	the	DET
cana-6099	140	3	inversion	inversion	NOUN
cana-6099	140	4	of	of	ADP
cana-6099	140	5	the	the	DET
cana-6099	140	6	hankel	hankel	NOUN
cana-6099	140	7	transform	transform	VERB
cana-6099	140	8	[	[	X
cana-6099	140	9	14	14	NUM
cana-6099	140	10	]	]	PUNCT
cana-6099	140	11	to	to	ADP
cana-6099	140	12	equations	equation	NOUN
cana-6099	140	13	(	(	PUNCT
cana-6099	140	14	56	56	NUM
cana-6099	140	15	)	)	PUNCT
cana-6099	140	16	,	,	PUNCT
cana-6099	140	17	(	(	PUNCT
cana-6099	140	18	57	57	NUM
cana-6099	140	19	)	)	PUNCT
cana-6099	140	20	&	&	CCONJ
cana-6099	140	21	(	(	PUNCT
cana-6099	140	22	58	58	NUM
cana-6099	140	23	)	)	PUNCT
cana-6099	140	24	we	we	PRON
cana-6099	140	25	get	get	VERB
cana-6099	140	26	,	,	PUNCT
cana-6099	140	27	communications	communication	NOUN
cana-6099	140	28	on	on	ADP
cana-6099	140	29	applied	apply	VERB
cana-6099	140	30	nonlinear	nonlinear	ADJ
cana-6099	140	31	analysis	analysis	NOUN
cana-6099	140	32	issn	issn	NOUN
cana-6099	140	33	:	:	PUNCT
cana-6099	140	34	1074	1074	NUM
cana-6099	140	35	-	-	PUNCT
cana-6099	140	36	133x	133x	NUM
cana-6099	140	37	vol	vol	VERB
cana-6099	140	38	32	32	NUM
cana-6099	140	39	no	no	NOUN
cana-6099	140	40	.	.	PUNCT
cana-6099	141	1	10s	10	NOUN
cana-6099	141	2	(	(	PUNCT
cana-6099	141	3	2025	2025	NUM
cana-6099	141	4	)	)	PUNCT
cana-6099	141	5	3360	3360	NUM
cana-6099	141	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	141	7	𝜃𝑖	𝜃𝑖	ADP
cana-6099	141	8	∗̅̅	∗̅̅	NOUN
cana-6099	141	9	̅	̅	NOUN
cana-6099	141	10	=	=	SYM
cana-6099	141	11	∫	∫	X
cana-6099	141	12	{	{	PUNCT
cana-6099	141	13	∑	∑	PROPN
cana-6099	141	14	𝐵𝑖(𝛾	𝐵𝑖(𝛾	PROPN
cana-6099	141	15	,	,	PUNCT
cana-6099	141	16	𝑝	𝑝	NOUN
cana-6099	141	17	)	)	PUNCT
cana-6099	141	18	cosh(𝑞𝑖𝑧	cosh(𝑞𝑖𝑧	NOUN
cana-6099	141	19	)	)	PUNCT
cana-6099	141	20	3	3	NUM
cana-6099	141	21	𝑖=1	𝑖=1	PROPN
cana-6099	141	22	}	}	PUNCT
cana-6099	141	23	𝛾𝐽0(𝛾𝑟)𝑑𝛾	𝛾𝐽0(𝛾𝑟)𝑑𝛾	NOUN
cana-6099	141	24	(	(	PUNCT
cana-6099	141	25	61	61	NUM
cana-6099	141	26	)	)	PUNCT
cana-6099	141	27	∞	∞	NUM
cana-6099	141	28	0	0	NUM
cana-6099	141	29	(	(	PUNCT
cana-6099	141	30	62	62	NUM
cana-6099	141	31	)	)	PUNCT
cana-6099	141	32	𝐶𝑖	𝐶𝑖	PROPN
cana-6099	141	33	∗̅̅	∗̅̅	NOUN
cana-6099	141	34	̅	̅	NOUN
cana-6099	141	35	=	=	SYM
cana-6099	141	36	∫	∫	PROPN
cana-6099	141	37	{	{	PUNCT
cana-6099	141	38	∑	∑	PROPN
cana-6099	141	39	𝐷𝑖(𝛾	𝐷𝑖(𝛾	PROPN
cana-6099	141	40	,	,	PUNCT
cana-6099	141	41	𝑝	𝑝	NOUN
cana-6099	141	42	)	)	PUNCT
cana-6099	141	43	cosh(𝑞𝑖𝑧	cosh(𝑞𝑖𝑧	NOUN
cana-6099	141	44	)	)	PUNCT
cana-6099	141	45	3	3	NUM
cana-6099	141	46	𝑖=1	𝑖=1	PROPN
cana-6099	141	47	}	}	PUNCT
cana-6099	141	48	𝛾𝐽0(𝛾𝑟)𝑑𝛾	𝛾𝐽0(𝛾𝑟)𝑑𝛾	NOUN
cana-6099	141	49	(	(	PUNCT
cana-6099	141	50	63	63	NUM
cana-6099	141	51	)	)	PUNCT
cana-6099	141	52	∞	∞	NUM
cana-6099	141	53	0	0	NUM
cana-6099	141	54	equations	equation	NOUN
cana-6099	141	55	(	(	PUNCT
cana-6099	141	56	38	38	NUM
cana-6099	141	57	)	)	PUNCT
cana-6099	141	58	to	to	ADP
cana-6099	141	59	(	(	PUNCT
cana-6099	141	60	39	39	NUM
cana-6099	141	61	)	)	PUNCT
cana-6099	141	62	and	and	CCONJ
cana-6099	141	63	(	(	PUNCT
cana-6099	141	64	61	61	NUM
cana-6099	141	65	)	)	PUNCT
cana-6099	141	66	to	to	ADP
cana-6099	141	67	(	(	PUNCT
cana-6099	141	68	63	63	NUM
cana-6099	141	69	)	)	PUNCT
cana-6099	142	1	then	then	ADV
cana-6099	142	2	solution	solution	NOUN
cana-6099	142	3	for	for	ADP
cana-6099	142	4	the	the	DET
cana-6099	142	5	displacement	displacement	ADJ
cana-6099	142	6	components	component	NOUN
cana-6099	142	7	in	in	ADP
cana-6099	142	8	the	the	DET
cana-6099	142	9	laplace	laplace	NOUN
cana-6099	142	10	transform	transform	NOUN
cana-6099	142	11	domain	domain	NOUN
cana-6099	142	12	as	as	ADP
cana-6099	142	13	:	:	PUNCT
cana-6099	142	14	where	where	SCONJ
cana-6099	142	15	,	,	PUNCT
cana-6099	142	16	the	the	DET
cana-6099	142	17	parameters	parameter	NOUN
cana-6099	142	18	𝐸(𝛾	𝐸(𝛾	ADP
cana-6099	142	19	,	,	PUNCT
cana-6099	142	20	𝑝	𝑝	NOUN
cana-6099	142	21	)	)	PUNCT
cana-6099	142	22	&	&	CCONJ
cana-6099	142	23	𝐹(𝛾	𝐹(𝛾	PUNCT
cana-6099	142	24	,	,	PUNCT
cana-6099	142	25	𝑝	𝑝	NOUN
cana-6099	142	26	)	)	PUNCT
cana-6099	142	27	depend	depend	VERB
cana-6099	142	28	on	on	ADP
cana-6099	142	29	𝛾	𝛾	PROPN
cana-6099	142	30	and	and	CCONJ
cana-6099	142	31	𝑠	𝑠	INTJ
cana-6099	142	32	only	only	ADV
cana-6099	142	33	and	and	CCONJ
cana-6099	142	34	.	.	PUNCT
cana-6099	143	1	using	use	VERB
cana-6099	143	2	equations	equation	NOUN
cana-6099	143	3	(	(	PUNCT
cana-6099	143	4	42	42	NUM
cana-6099	143	5	)	)	PUNCT
cana-6099	143	6	to	to	ADP
cana-6099	143	7	(	(	PUNCT
cana-6099	143	8	46	46	NUM
cana-6099	143	9	)	)	PUNCT
cana-6099	143	10	&	&	CCONJ
cana-6099	143	11	the	the	DET
cana-6099	143	12	solutions	solution	NOUN
cana-6099	143	13	from	from	ADP
cana-6099	143	14	equations	equation	NOUN
cana-6099	143	15	(	(	PUNCT
cana-6099	143	16	61	61	NUM
cana-6099	143	17	)	)	PUNCT
cana-6099	143	18	to	to	ADP
cana-6099	143	19	(	(	PUNCT
cana-6099	143	20	65	65	NUM
cana-6099	143	21	)	)	PUNCT
cana-6099	143	22	we	we	PRON
cana-6099	143	23	obtain	obtain	VERB
cana-6099	143	24	the	the	DET
cana-6099	143	25	stress	stress	NOUN
cana-6099	143	26	components	component	NOUN
cana-6099	143	27	&	&	CCONJ
cana-6099	143	28	the	the	DET
cana-6099	143	29	chemical	chemical	NOUN
cana-6099	143	30	potential	potential	NOUN
cana-6099	143	31	in	in	ADP
cana-6099	143	32	the	the	DET
cana-6099	143	33	laplace	laplace	NOUN
cana-6099	143	34	transform	transform	NOUN
cana-6099	143	35	domain	domain	NOUN
cana-6099	143	36	as	as	SCONJ
cana-6099	143	37	follows	follow	VERB
cana-6099	143	38	:	:	PUNCT
cana-6099	143	39	communications	communication	NOUN
cana-6099	143	40	on	on	ADP
cana-6099	143	41	applied	apply	VERB
cana-6099	143	42	nonlinear	nonlinear	ADJ
cana-6099	143	43	analysis	analysis	NOUN
cana-6099	143	44	issn	issn	NOUN
cana-6099	143	45	:	:	PUNCT
cana-6099	143	46	1074	1074	NUM
cana-6099	143	47	-	-	PUNCT
cana-6099	143	48	133x	133x	NUM
cana-6099	143	49	vol	vol	VERB
cana-6099	143	50	32	32	NUM
cana-6099	143	51	no	no	NOUN
cana-6099	143	52	.	.	PUNCT
cana-6099	144	1	10s	10	NOUN
cana-6099	144	2	(	(	PUNCT
cana-6099	144	3	2025	2025	NUM
cana-6099	144	4	)	)	PUNCT
cana-6099	144	5	3361	3361	NUM
cana-6099	144	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	145	1	where	where	SCONJ
cana-6099	145	2	,	,	PUNCT
cana-6099	145	3	and	and	CCONJ
cana-6099	145	4	8	8	NUM
cana-6099	145	5	.	.	NOUN
cana-6099	145	6	numerical	numerical	ADJ
cana-6099	145	7	inversion	inversion	NOUN
cana-6099	145	8	the	the	DET
cana-6099	145	9	solutions	solution	NOUN
cana-6099	145	10	of	of	ADP
cana-6099	145	11	concentration	concentration	NOUN
cana-6099	145	12	(	(	PUNCT
cana-6099	145	13	c	c	NOUN
cana-6099	145	14	)	)	PUNCT
cana-6099	145	15	,	,	PUNCT
cana-6099	145	16	temperature	temperature	NOUN
cana-6099	145	17	(	(	PUNCT
cana-6099	145	18	θ	θ	NOUN
cana-6099	145	19	)	)	PUNCT
cana-6099	145	20	,	,	PUNCT
cana-6099	145	21	chemical	chemical	NOUN
cana-6099	145	22	potential	potential	NOUN
cana-6099	145	23	(	(	PUNCT
cana-6099	145	24	p	p	NOUN
cana-6099	145	25	)	)	PUNCT
cana-6099	145	26	,	,	PUNCT
cana-6099	145	27	displacement	displacement	NOUN
cana-6099	145	28	(	(	PUNCT
cana-6099	145	29	u	u	NOUN
cana-6099	145	30	)	)	PUNCT
cana-6099	145	31	and	and	CCONJ
cana-6099	145	32	stresses	stress	NOUN
cana-6099	145	33	(	(	PUNCT
cana-6099	145	34	σrr	σrr	PROPN
cana-6099	145	35	,	,	PUNCT
cana-6099	145	36	σrz	σrz	PROPN
cana-6099	145	37	&	&	CCONJ
cana-6099	145	38	σzz	σzz	PROPN
cana-6099	145	39	)	)	PUNCT
cana-6099	145	40	are	be	AUX
cana-6099	145	41	obtained	obtain	VERB
cana-6099	145	42	numerically	numerically	ADV
cana-6099	145	43	by	by	ADP
cana-6099	145	44	the	the	DET
cana-6099	145	45	inversion	inversion	NOUN
cana-6099	145	46	of	of	ADP
cana-6099	145	47	laplace	laplace	NOUN
cana-6099	145	48	transform	transform	NOUN
cana-6099	145	49	method	method	NOUN
cana-6099	145	50	in	in	ADP
cana-6099	145	51	time	time	NOUN
cana-6099	145	52	domain	domain	NOUN
cana-6099	145	53	[	[	X
cana-6099	145	54	38	38	NUM
cana-6099	145	55	]	]	PUNCT
cana-6099	145	56	.	.	PUNCT
cana-6099	146	1	9	9	X
cana-6099	146	2	.	.	X
cana-6099	146	3	physical	physical	ADJ
cana-6099	146	4	constants	constant	NOUN
cana-6099	146	5	these	these	DET
cana-6099	146	6	material	material	NOUN
cana-6099	146	7	constants	constant	NOUN
cana-6099	146	8	for	for	ADP
cana-6099	146	9	copper	copper	NOUN
cana-6099	146	10	material	material	NOUN
cana-6099	146	11	has	have	AUX
cana-6099	146	12	been	be	AUX
cana-6099	146	13	used	use	VERB
cana-6099	146	14	for	for	ADP
cana-6099	146	15	numerical	numerical	ADJ
cana-6099	146	16	calculation	calculation	NOUN
cana-6099	146	17	as	as	SCONJ
cana-6099	146	18	follows	follow	VERB
cana-6099	146	19	[	[	X
cana-6099	146	20	17	17	NUM
cana-6099	146	21	]	]	NUM
cana-6099	146	22	:	:	PUNCT
cana-6099	146	23	table	table	NOUN
cana-6099	146	24	1	1	NUM
cana-6099	146	25	.	.	PUNCT
cana-6099	147	1	physical	physical	ADJ
cana-6099	147	2	constants	constant	NOUN
cana-6099	147	3	for	for	ADP
cana-6099	147	4	copper	copper	NOUN
cana-6099	147	5	material	material	NOUN
cana-6099	147	6	physical	physical	ADJ
cana-6099	147	7	constants	constant	NOUN
cana-6099	147	8	value	value	NOUN
cana-6099	147	9	lame	lame	NOUN
cana-6099	147	10	’s	’s	PART
cana-6099	147	11	constant	constant	ADJ
cana-6099	147	12	(	(	PUNCT
cana-6099	147	13	𝜆	𝜆	NOUN
cana-6099	147	14	)	)	PUNCT
cana-6099	147	15	7.76	7.76	NUM
cana-6099	147	16	×	×	NOUN
cana-6099	147	17	1010	1010	NUM
cana-6099	147	18	𝑁𝑚−2	𝑁𝑚−2	NOUN
cana-6099	147	19	lame	lame	NOUN
cana-6099	147	20	’s	’s	PART
cana-6099	147	21	constant	constant	ADJ
cana-6099	147	22	(	(	PUNCT
cana-6099	147	23	𝜇	𝜇	NOUN
cana-6099	147	24	)	)	PUNCT
cana-6099	147	25	3.86	3.86	NUM
cana-6099	147	26	×	×	NOUN
cana-6099	147	27	1010	1010	NUM
cana-6099	147	28	𝑘𝑔𝑚−1𝑠−2	𝑘𝑔𝑚−1𝑠−2	PROPN
cana-6099	147	29	density	density	NOUN
cana-6099	147	30	(	(	PUNCT
cana-6099	147	31	𝜌	𝜌	NOUN
cana-6099	147	32	)	)	PUNCT
cana-6099	147	33	8954	8954	NUM
cana-6099	148	1	𝑘𝑔𝑚−3	𝑘𝑔𝑚−3	PROPN
cana-6099	148	2	reference	reference	NOUN
cana-6099	148	3	temperature	temperature	NOUN
cana-6099	148	4	(	(	PUNCT
cana-6099	148	5	𝑇0	𝑇0	NOUN
cana-6099	148	6	)	)	PUNCT
cana-6099	148	7	293	293	NUM
cana-6099	148	8	°	°	X
cana-6099	149	1	𝐾	𝐾	PROPN
cana-6099	149	2	coefficient	coefficient	NOUN
cana-6099	149	3	of	of	ADP
cana-6099	149	4	linear	linear	ADJ
cana-6099	149	5	thermal	thermal	ADJ
cana-6099	149	6	expansion	expansion	NOUN
cana-6099	149	7	(	(	PUNCT
cana-6099	149	8	𝛼𝑡	𝛼𝑡	NOUN
cana-6099	149	9	)	)	PUNCT
cana-6099	149	10	1.78	1.78	NUM
cana-6099	149	11	×	×	NOUN
cana-6099	149	12	10−5	10−5	NUM
cana-6099	149	13	𝐾−1	𝐾−1	NOUN
cana-6099	149	14	thermal	thermal	ADJ
cana-6099	149	15	conductivity	conductivity	NOUN
cana-6099	149	16	(	(	PUNCT
cana-6099	149	17	𝑘	𝑘	NOUN
cana-6099	149	18	)	)	PUNCT
cana-6099	149	19	386	386	NUM
cana-6099	149	20	𝐽𝐾−1𝑚−1𝑠−1	𝐽𝐾−1𝑚−1𝑠−1	X
cana-6099	149	21	specific	specific	ADJ
cana-6099	149	22	heat	heat	NOUN
cana-6099	149	23	per	per	ADP
cana-6099	149	24	unit	unit	NOUN
cana-6099	149	25	mass	mass	NOUN
cana-6099	149	26	(	(	PUNCT
cana-6099	149	27	𝐶𝐸	𝐶𝐸	PROPN
cana-6099	149	28	)	)	PUNCT
cana-6099	149	29	383.1	383.1	NUM
cana-6099	149	30	𝐽𝐾−1𝑚−1𝑠−1	𝐽𝐾−1𝑚−1𝑠−1	NOUN
cana-6099	149	31	coefficient	coefficient	NOUN
cana-6099	149	32	of	of	ADP
cana-6099	149	33	linear	linear	PROPN
cana-6099	149	34	diffusion	diffusion	NOUN
cana-6099	149	35	equation	equation	NOUN
cana-6099	149	36	(	(	PUNCT
cana-6099	149	37	𝛼𝑐	𝛼𝑐	NOUN
cana-6099	149	38	)	)	PUNCT
cana-6099	149	39	1.78	1.78	NUM
cana-6099	149	40	×	×	NOUN
cana-6099	149	41	10−5	10−5	NUM
cana-6099	149	42	𝐾−1	𝐾−1	NOUN
cana-6099	149	43	measure	measure	NOUN
cana-6099	149	44	of	of	ADP
cana-6099	149	45	the	the	DET
cana-6099	149	46	thermo	thermo	NOUN
cana-6099	149	47	-	-	PUNCT
cana-6099	149	48	diffusion	diffusion	NOUN
cana-6099	149	49	effect	effect	NOUN
cana-6099	149	50	(	(	PUNCT
cana-6099	149	51	𝛽𝑡	𝛽𝑡	NOUN
cana-6099	149	52	)	)	PUNCT
cana-6099	149	53	1.2	1.2	NUM
cana-6099	149	54	×	×	NOUN
cana-6099	149	55	104	104	NUM
cana-6099	149	56	𝑚2𝑠−2𝐾−1	𝑚2𝑠−2𝐾−1	NOUN
cana-6099	149	57	communications	communication	NOUN
cana-6099	149	58	on	on	ADP
cana-6099	149	59	applied	apply	VERB
cana-6099	149	60	nonlinear	nonlinear	ADJ
cana-6099	149	61	analysis	analysis	NOUN
cana-6099	149	62	issn	issn	NOUN
cana-6099	149	63	:	:	PUNCT
cana-6099	149	64	1074	1074	NUM
cana-6099	149	65	-	-	PUNCT
cana-6099	149	66	133x	133x	NUM
cana-6099	149	67	vol	vol	VERB
cana-6099	149	68	32	32	NUM
cana-6099	149	69	no	no	NOUN
cana-6099	149	70	.	.	PUNCT
cana-6099	150	1	10s	10	NOUN
cana-6099	150	2	(	(	PUNCT
cana-6099	150	3	2025	2025	NUM
cana-6099	150	4	)	)	PUNCT
cana-6099	150	5	3362	3362	NUM
cana-6099	150	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	150	7	measure	measure	NOUN
cana-6099	150	8	of	of	ADP
cana-6099	150	9	diffusive	diffusive	ADJ
cana-6099	150	10	effect	effect	NOUN
cana-6099	150	11	(	(	PUNCT
cana-6099	150	12	𝛽	𝛽	NOUN
cana-6099	150	13	)	)	PUNCT
cana-6099	150	14	0.9	0.9	NUM
cana-6099	150	15	×	×	NOUN
cana-6099	150	16	106	106	NUM
cana-6099	150	17	≈	≈	NUM
cana-6099	150	18	1	1	NUM
cana-6099	150	19	𝑚5𝑘𝑔−1𝑠−2	𝑚5𝑘𝑔−1𝑠−2	NOUN
cana-6099	150	20	diffusion	diffusion	NOUN
cana-6099	150	21	coefficient	coefficient	NOUN
cana-6099	150	22	(	(	PUNCT
cana-6099	150	23	𝐷	𝐷	NOUN
cana-6099	150	24	)	)	PUNCT
cana-6099	150	25	0.88	0.88	NUM
cana-6099	150	26	×	×	NOUN
cana-6099	150	27	10−8	10−8	NUM
cana-6099	150	28	𝑘𝑔𝑠𝑚−3	𝑘𝑔𝑠𝑚−3	NOUN
cana-6099	150	29	𝜂	𝜂	X
cana-6099	150	30	=	=	VERB
cana-6099	150	31	𝜌𝐶𝐸	𝜌𝐶𝐸	PRON
cana-6099	150	32	𝑘	𝑘	ADP
cana-6099	150	33	8886.73	8886.73	NUM
cana-6099	150	34	𝑠𝑚−2	𝑠𝑚−2	PROPN
cana-6099	150	35	𝜖	𝜖	X
cana-6099	150	36	=	=	SYM
cana-6099	150	37	𝜉1	𝜉1	PROPN
cana-6099	150	38	2𝑇0	2𝑇0	NUM
cana-6099	150	39	𝜌𝐶𝐸(𝜆	𝜌𝐶𝐸(𝜆	PUNCT
cana-6099	151	1	+	+	NUM
cana-6099	151	2	2𝜇	2𝜇	NUM
cana-6099	151	3	)	)	PUNCT
cana-6099	151	4	0.0168	0.0168	NUM
cana-6099	151	5	𝑁𝑚𝐽−1	𝑁𝑚𝐽−1	ADV
cana-6099	151	6	𝛽1	𝛽1	NOUN
cana-6099	151	7	=	=	PUNCT
cana-6099	151	8	𝛽𝑡(𝜆	𝛽𝑡(𝜆	X
cana-6099	151	9	+	+	NUM
cana-6099	151	10	2𝜇	2𝜇	NUM
cana-6099	151	11	)	)	PUNCT
cana-6099	151	12	𝜉1𝜉2	𝜉1𝜉2	VERB
cana-6099	151	13	5.43	5.43	NUM
cana-6099	151	14	𝛽2	𝛽2	NOUN
cana-6099	151	15	=	=	SYM
cana-6099	151	16	(	(	PUNCT
cana-6099	151	17	𝜆	𝜆	NOUN
cana-6099	151	18	+	+	NOUN
cana-6099	151	19	2𝜇	2𝜇	NOUN
cana-6099	151	20	)	)	PUNCT
cana-6099	151	21	𝐷𝜂𝜉2	𝐷𝜂𝜉2	NOUN
cana-6099	151	22	2	2	NUM
cana-6099	151	23	0.533	0.533	NUM
cana-6099	151	24	𝛽3	𝛽3	NOUN
cana-6099	151	25	=	=	SYM
cana-6099	151	26	𝛽𝑡(𝜆	𝛽𝑡(𝜆	X
cana-6099	151	27	+	+	NUM
cana-6099	151	28	2𝜇	2𝜇	NOUN
cana-6099	151	29	)	)	PUNCT
cana-6099	151	30	𝜉2	𝜉2	NOUN
cana-6099	151	31	2	2	NUM
cana-6099	151	32	36.24	36.24	NUM
cana-6099	151	33	𝛽2	𝛽2	NOUN
cana-6099	151	34	4	4	NUM
cana-6099	151	35	10	10	NUM
cana-6099	151	36	.	.	PUNCT
cana-6099	152	1	results	result	NOUN
cana-6099	152	2	&	&	CCONJ
cana-6099	152	3	discussion	discussion	NOUN
cana-6099	152	4	in	in	ADP
cana-6099	152	5	this	this	DET
cana-6099	152	6	chapter	chapter	NOUN
cana-6099	152	7	,	,	PUNCT
cana-6099	152	8	we	we	PRON
cana-6099	152	9	consider	consider	VERB
cana-6099	152	10	a	a	DET
cana-6099	152	11	thick	thick	ADJ
cana-6099	152	12	circular	circular	ADJ
cana-6099	152	13	plate	plate	NOUN
cana-6099	152	14	of	of	ADP
cana-6099	152	15	height	height	NOUN
cana-6099	152	16	b	b	PROPN
cana-6099	152	17	=	=	SYM
cana-6099	152	18	1	1	NUM
cana-6099	152	19	m	m	NOUN
cana-6099	152	20	and	and	CCONJ
cana-6099	152	21	axisymmetric	axisymmetric	ADJ
cana-6099	152	22	heat	heat	NOUN
cana-6099	152	23	is	be	AUX
cana-6099	152	24	supplied	supply	VERB
cana-6099	152	25	to	to	ADP
cana-6099	152	26	its	its	PRON
cana-6099	152	27	upper	upper	ADJ
cana-6099	152	28	and	and	CCONJ
cana-6099	152	29	lower	low	ADJ
cana-6099	152	30	surface	surface	NOUN
cana-6099	152	31	.	.	PUNCT
cana-6099	153	1	the	the	DET
cana-6099	153	2	procured	procure	VERB
cana-6099	153	3	results	result	NOUN
cana-6099	153	4	have	have	AUX
cana-6099	153	5	obtained	obtain	VERB
cana-6099	153	6	for	for	ADP
cana-6099	153	7	concentration	concentration	NOUN
cana-6099	153	8	(	(	PUNCT
cana-6099	153	9	c	c	NOUN
cana-6099	153	10	)	)	PUNCT
cana-6099	153	11	distribution	distribution	NOUN
cana-6099	153	12	,	,	PUNCT
cana-6099	153	13	chemical	chemical	NOUN
cana-6099	153	14	potential	potential	NOUN
cana-6099	153	15	(	(	PUNCT
cana-6099	153	16	p	p	NOUN
cana-6099	153	17	)	)	PUNCT
cana-6099	153	18	distribution	distribution	NOUN
cana-6099	153	19	,	,	PUNCT
cana-6099	153	20	temperature	temperature	NOUN
cana-6099	153	21	(	(	PUNCT
cana-6099	153	22	θ	θ	NOUN
cana-6099	153	23	)	)	PUNCT
cana-6099	153	24	distribution	distribution	NOUN
cana-6099	153	25	,	,	PUNCT
cana-6099	153	26	displacement	displacement	ADJ
cana-6099	153	27	component	component	NOUN
cana-6099	153	28	(	(	PUNCT
cana-6099	153	29	u	u	NOUN
cana-6099	153	30	)	)	PUNCT
cana-6099	153	31	,	,	PUNCT
cana-6099	153	32	radial	radial	ADJ
cana-6099	153	33	(	(	PUNCT
cana-6099	153	34	σrr	σrr	NOUN
cana-6099	153	35	)	)	PUNCT
cana-6099	153	36	stress	stress	NOUN
cana-6099	153	37	,	,	PUNCT
cana-6099	153	38	and	and	CCONJ
cana-6099	153	39	axial	axial	ADJ
cana-6099	153	40	(	(	PUNCT
cana-6099	153	41	σzz	σzz	PROPN
cana-6099	153	42	)	)	PUNCT
cana-6099	153	43	stress	stress	NOUN
cana-6099	153	44	.	.	PUNCT
cana-6099	154	1	the	the	DET
cana-6099	154	2	computations	computation	NOUN
cana-6099	154	3	are	be	AUX
cana-6099	154	4	carried	carry	VERB
cana-6099	154	5	out	out	ADP
cana-6099	154	6	for	for	ADP
cana-6099	154	7	distinct	distinct	ADJ
cana-6099	154	8	values	value	NOUN
cana-6099	154	9	of	of	ADP
cana-6099	154	10	time	time	NOUN
cana-6099	154	11	t	t	PROPN
cana-6099	154	12	=	=	SYM
cana-6099	154	13	0.05s	0.05s	PROPN
cana-6099	154	14	,	,	PUNCT
cana-6099	154	15	0.065s	0.065s	NUM
cana-6099	154	16	,	,	PUNCT
cana-6099	154	17	0.08s	0.08s	NUM
cana-6099	154	18	.	.	PUNCT
cana-6099	155	1	the	the	DET
cana-6099	155	2	results	result	NOUN
cana-6099	155	3	have	have	AUX
cana-6099	155	4	studied	study	VERB
cana-6099	155	5	in	in	ADP
cana-6099	155	6	the	the	DET
cana-6099	155	7	context	context	NOUN
cana-6099	155	8	of	of	ADP
cana-6099	155	9	two	two	NUM
cana-6099	155	10	different	different	ADJ
cana-6099	155	11	theories	theory	NOUN
cana-6099	155	12	lord	lord	PROPN
cana-6099	155	13	-	-	PUNCT
cana-6099	155	14	shulman	shulman	PROPN
cana-6099	155	15	(	(	PUNCT
cana-6099	155	16	ls	ls	PROPN
cana-6099	155	17	)	)	PUNCT
cana-6099	155	18	and	and	CCONJ
cana-6099	155	19	classical	classical	ADJ
cana-6099	155	20	coupled	couple	VERB
cana-6099	155	21	(	(	PUNCT
cana-6099	155	22	cte	cte	NOUN
cana-6099	155	23	)	)	PUNCT
cana-6099	155	24	theory	theory	NOUN
cana-6099	155	25	.	.	PUNCT
cana-6099	156	1	the	the	DET
cana-6099	156	2	graphs	graph	NOUN
cana-6099	156	3	have	have	AUX
cana-6099	156	4	been	be	AUX
cana-6099	156	5	plotted	plot	VERB
cana-6099	156	6	along	along	ADP
cana-6099	156	7	radial	radial	ADJ
cana-6099	156	8	direction	direction	NOUN
cana-6099	156	9	i.e.	i.e.	X
cana-6099	156	10	in	in	ADP
cana-6099	156	11	the	the	DET
cana-6099	156	12	middle	middle	ADJ
cana-6099	156	13	plane	plane	NOUN
cana-6099	156	14	when	when	SCONJ
cana-6099	156	15	z	z	NOUN
cana-6099	156	16	=	=	NOUN
cana-6099	156	17	0	0	NUM
cana-6099	156	18	.	.	PUNCT
cana-6099	157	1	the	the	DET
cana-6099	157	2	changing	change	VERB
cana-6099	157	3	behaviour	behaviour	NOUN
cana-6099	157	4	of	of	ADP
cana-6099	157	5	field	field	NOUN
cana-6099	157	6	variables	variable	NOUN
cana-6099	157	7	have	have	AUX
cana-6099	157	8	been	be	AUX
cana-6099	157	9	studied	study	VERB
cana-6099	157	10	through	through	ADP
cana-6099	157	11	graphs	graph	NOUN
cana-6099	157	12	in	in	ADP
cana-6099	157	13	two	two	NUM
cana-6099	157	14	cases	case	NOUN
cana-6099	157	15	:	:	PUNCT
cana-6099	157	16	(	(	PUNCT
cana-6099	157	17	1	1	X
cana-6099	157	18	)	)	PUNCT
cana-6099	157	19	for	for	ADP
cana-6099	157	20	distinct	distinct	ADJ
cana-6099	157	21	values	value	NOUN
cana-6099	157	22	of	of	ADP
cana-6099	157	23	time	time	NOUN
cana-6099	157	24	t	t	PROPN
cana-6099	157	25	=	=	SYM
cana-6099	157	26	0.05s,0.065s,0.08s	0.05s,0.065s,0.08s	PROPN
cana-6099	157	27	when	when	SCONJ
cana-6099	157	28	α	α	NOUN
cana-6099	157	29	=	=	NOUN
cana-6099	157	30	0.25	0.25	NUM
cana-6099	157	31	,	,	PUNCT
cana-6099	157	32	shown	show	VERB
cana-6099	157	33	in	in	ADP
cana-6099	157	34	figures	figure	NOUN
cana-6099	157	35	2	2	NUM
cana-6099	157	36	,	,	PUNCT
cana-6099	157	37	4	4	NUM
cana-6099	157	38	,	,	PUNCT
cana-6099	157	39	6	6	NUM
cana-6099	157	40	,	,	PUNCT
cana-6099	157	41	8	8	NUM
cana-6099	157	42	,	,	PUNCT
cana-6099	157	43	10	10	NUM
cana-6099	157	44	,	,	PUNCT
cana-6099	157	45	12	12	NUM
cana-6099	157	46	and	and	CCONJ
cana-6099	157	47	(	(	PUNCT
cana-6099	157	48	2	2	NUM
cana-6099	157	49	)	)	PUNCT
cana-6099	157	50	for	for	ADP
cana-6099	157	51	distinct	distinct	ADJ
cana-6099	157	52	values	value	NOUN
cana-6099	157	53	of	of	ADP
cana-6099	157	54	fractional	fractional	ADJ
cana-6099	157	55	order	order	NOUN
cana-6099	157	56	parameter	parameter	NOUN
cana-6099	157	57	α	α	NOUN
cana-6099	157	58	=	=	NOUN
cana-6099	157	59	0.25	0.25	NUM
cana-6099	157	60	,	,	PUNCT
cana-6099	157	61	0.50	0.50	NUM
cana-6099	157	62	,	,	PUNCT
cana-6099	157	63	0.75	0.75	NUM
cana-6099	157	64	when	when	SCONJ
cana-6099	157	65	t	t	PROPN
cana-6099	157	66	=	=	SYM
cana-6099	157	67	0.05s	0.05s	PROPN
cana-6099	157	68	,	,	PUNCT
cana-6099	157	69	as	as	ADP
cana-6099	157	70	in	in	ADP
cana-6099	157	71	figures	figure	NOUN
cana-6099	157	72	3	3	NUM
cana-6099	157	73	,	,	PUNCT
cana-6099	157	74	5	5	NUM
cana-6099	157	75	,	,	PUNCT
cana-6099	157	76	7	7	NUM
cana-6099	157	77	,	,	PUNCT
cana-6099	157	78	9	9	NUM
cana-6099	157	79	,	,	PUNCT
cana-6099	157	80	11	11	NUM
cana-6099	157	81	,	,	PUNCT
cana-6099	157	82	13	13	NUM
cana-6099	157	83	.	.	PUNCT
cana-6099	158	1	communications	communication	NOUN
cana-6099	158	2	on	on	ADP
cana-6099	158	3	applied	apply	VERB
cana-6099	158	4	nonlinear	nonlinear	ADJ
cana-6099	158	5	analysis	analysis	NOUN
cana-6099	158	6	issn	issn	NOUN
cana-6099	158	7	:	:	PUNCT
cana-6099	158	8	1074	1074	NUM
cana-6099	158	9	-	-	PUNCT
cana-6099	158	10	133x	133x	NUM
cana-6099	158	11	vol	vol	VERB
cana-6099	158	12	32	32	NUM
cana-6099	158	13	no	no	NOUN
cana-6099	158	14	.	.	PUNCT
cana-6099	159	1	10s	10	NOUN
cana-6099	159	2	(	(	PUNCT
cana-6099	159	3	2025	2025	NUM
cana-6099	159	4	)	)	PUNCT
cana-6099	159	5	3363	3363	NUM
cana-6099	159	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	159	7	figure	figure	NOUN
cana-6099	159	8	2	2	NUM
cana-6099	159	9	.	.	PUNCT
cana-6099	159	10	concentration	concentration	NOUN
cana-6099	159	11	c	c	NOUN
cana-6099	159	12	distribution	distribution	NOUN
cana-6099	159	13	for	for	ADP
cana-6099	159	14	distinct	distinct	ADJ
cana-6099	159	15	values	value	NOUN
cana-6099	159	16	of	of	ADP
cana-6099	159	17	time	time	NOUN
cana-6099	159	18	t(s	t(s	PROPN
cana-6099	159	19	)	)	PUNCT
cana-6099	159	20	figures	figure	NOUN
cana-6099	159	21	2	2	NUM
cana-6099	159	22	,	,	PUNCT
cana-6099	159	23	4	4	NUM
cana-6099	159	24	,	,	PUNCT
cana-6099	159	25	6	6	NUM
cana-6099	159	26	,	,	PUNCT
cana-6099	159	27	8	8	NUM
cana-6099	159	28	,	,	PUNCT
cana-6099	159	29	10	10	NUM
cana-6099	159	30	,	,	PUNCT
cana-6099	159	31	12	12	NUM
cana-6099	159	32	shows	show	VERB
cana-6099	159	33	concentration	concentration	NOUN
cana-6099	159	34	,	,	PUNCT
cana-6099	159	35	temperature	temperature	NOUN
cana-6099	159	36	,	,	PUNCT
cana-6099	159	37	chemical	chemical	NOUN
cana-6099	159	38	potential	potential	NOUN
cana-6099	159	39	,	,	PUNCT
cana-6099	159	40	displacement	displacement	NOUN
cana-6099	159	41	,	,	PUNCT
cana-6099	159	42	radial	radial	ADJ
cana-6099	159	43	stress	stress	NOUN
cana-6099	159	44	,	,	PUNCT
cana-6099	159	45	and	and	CCONJ
cana-6099	159	46	axial	axial	ADJ
cana-6099	159	47	stress	stress	NOUN
cana-6099	159	48	in	in	ADP
cana-6099	159	49	the	the	DET
cana-6099	159	50	radial	radial	ADJ
cana-6099	159	51	direction	direction	NOUN
cana-6099	159	52	for	for	ADP
cana-6099	159	53	α	α	NOUN
cana-6099	159	54	=	=	NOUN
cana-6099	159	55	0.25	0.25	NUM
cana-6099	159	56	order	order	NOUN
cana-6099	159	57	derivative	derivative	NOUN
cana-6099	159	58	and	and	CCONJ
cana-6099	159	59	t	t	NOUN
cana-6099	159	60	=	=	SYM
cana-6099	159	61	0.05s	0.05s	PROPN
cana-6099	159	62	,	,	PUNCT
cana-6099	159	63	0.065s	0.065s	NUM
cana-6099	159	64	,	,	PUNCT
cana-6099	159	65	0.08s	0.08s	NUM
cana-6099	159	66	in	in	ADP
cana-6099	159	67	context	context	NOUN
cana-6099	159	68	of	of	ADP
cana-6099	159	69	both	both	CCONJ
cana-6099	159	70	ls	ls	ADJ
cana-6099	159	71	and	and	CCONJ
cana-6099	159	72	cte	cte	PROPN
cana-6099	159	73	model	model	NOUN
cana-6099	159	74	.	.	PUNCT
cana-6099	160	1	figure	figure	VERB
cana-6099	160	2	3	3	NUM
cana-6099	160	3	.	.	PUNCT
cana-6099	160	4	concentration	concentration	NOUN
cana-6099	160	5	c	c	NOUN
cana-6099	160	6	distribution	distribution	NOUN
cana-6099	160	7	for	for	ADP
cana-6099	160	8	distinct	distinct	ADJ
cana-6099	160	9	values	value	NOUN
cana-6099	160	10	of	of	ADP
cana-6099	160	11	α	α	NOUN
cana-6099	160	12	communications	communication	NOUN
cana-6099	160	13	on	on	ADP
cana-6099	160	14	applied	apply	VERB
cana-6099	160	15	nonlinear	nonlinear	ADJ
cana-6099	160	16	analysis	analysis	NOUN
cana-6099	160	17	issn	issn	NOUN
cana-6099	160	18	:	:	PUNCT
cana-6099	160	19	1074	1074	NUM
cana-6099	160	20	-	-	PUNCT
cana-6099	160	21	133x	133x	NUM
cana-6099	160	22	vol	vol	VERB
cana-6099	160	23	32	32	NUM
cana-6099	160	24	no	no	NOUN
cana-6099	160	25	.	.	PUNCT
cana-6099	161	1	10s	10	NOUN
cana-6099	161	2	(	(	PUNCT
cana-6099	161	3	2025	2025	NUM
cana-6099	161	4	)	)	PUNCT
cana-6099	161	5	3364	3364	NUM
cana-6099	162	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	162	2	figure	figure	NOUN
cana-6099	162	3	4	4	NUM
cana-6099	162	4	.	.	PUNCT
cana-6099	162	5	temperature	temperature	NOUN
cana-6099	162	6	θ	θ	NOUN
cana-6099	162	7	distribution	distribution	NOUN
cana-6099	162	8	for	for	ADP
cana-6099	162	9	distinct	distinct	ADJ
cana-6099	162	10	values	value	NOUN
cana-6099	162	11	of	of	ADP
cana-6099	162	12	t(s	t(s	PROPN
cana-6099	162	13	)	)	PUNCT
cana-6099	162	14	figures	figure	NOUN
cana-6099	162	15	3	3	NUM
cana-6099	162	16	,	,	PUNCT
cana-6099	162	17	5	5	NUM
cana-6099	162	18	,	,	PUNCT
cana-6099	162	19	7	7	NUM
cana-6099	162	20	,	,	PUNCT
cana-6099	162	21	9	9	NUM
cana-6099	162	22	,	,	PUNCT
cana-6099	162	23	11	11	NUM
cana-6099	162	24	,	,	PUNCT
cana-6099	162	25	13	13	NUM
cana-6099	162	26	shows	show	VERB
cana-6099	162	27	concentration	concentration	NOUN
cana-6099	162	28	,	,	PUNCT
cana-6099	162	29	temperature	temperature	NOUN
cana-6099	162	30	,	,	PUNCT
cana-6099	162	31	chemical	chemical	NOUN
cana-6099	162	32	potential	potential	NOUN
cana-6099	162	33	,	,	PUNCT
cana-6099	162	34	displacement	displacement	NOUN
cana-6099	162	35	,	,	PUNCT
cana-6099	162	36	radial	radial	ADJ
cana-6099	162	37	stress	stress	NOUN
cana-6099	162	38	,	,	PUNCT
cana-6099	162	39	and	and	CCONJ
cana-6099	162	40	axial	axial	ADJ
cana-6099	162	41	stress	stress	NOUN
cana-6099	162	42	in	in	ADP
cana-6099	162	43	the	the	DET
cana-6099	162	44	radial	radial	ADJ
cana-6099	162	45	direction	direction	NOUN
cana-6099	162	46	for	for	ADP
cana-6099	162	47	fixed	fix	VERB
cana-6099	162	48	time	time	NOUN
cana-6099	162	49	t	t	PROPN
cana-6099	162	50	=	=	SYM
cana-6099	162	51	0.05s	0.05s	PROPN
cana-6099	162	52	and	and	CCONJ
cana-6099	162	53	distinct	distinct	ADJ
cana-6099	162	54	values	value	NOUN
cana-6099	162	55	of	of	ADP
cana-6099	162	56	fractional	fractional	ADJ
cana-6099	162	57	order	order	NOUN
cana-6099	162	58	parameter	parameter	NOUN
cana-6099	162	59	α	α	NOUN
cana-6099	162	60	=	=	SYM
cana-6099	162	61	0.05,0.065,0.08	0.05,0.065,0.08	PROPN
cana-6099	162	62	.	.	PUNCT
cana-6099	163	1	figures	figure	NOUN
cana-6099	163	2	2	2	NUM
cana-6099	163	3	,	,	PUNCT
cana-6099	163	4	6	6	NUM
cana-6099	163	5	shows	show	VERB
cana-6099	163	6	concentration	concentration	NOUN
cana-6099	163	7	and	and	CCONJ
cana-6099	163	8	chemical	chemical	NOUN
cana-6099	163	9	potential	potential	ADJ
cana-6099	163	10	distribution	distribution	NOUN
cana-6099	163	11	in	in	ADP
cana-6099	163	12	the	the	DET
cana-6099	163	13	middle	middle	ADJ
cana-6099	163	14	plane	plane	NOUN
cana-6099	163	15	z	z	NOUN
cana-6099	164	1	=	=	NOUN
cana-6099	165	1	0	0	X
cana-6099	165	2	.	.	PUNCT
cana-6099	166	1	these	these	DET
cana-6099	166	2	figures	figure	NOUN
cana-6099	166	3	display	display	VERB
cana-6099	166	4	second	second	ADJ
cana-6099	166	5	sound	sound	ADJ
cana-6099	166	6	effect	effect	NOUN
cana-6099	166	7	.	.	PUNCT
cana-6099	167	1	here	here	ADV
cana-6099	167	2	as	as	ADP
cana-6099	167	3	time	time	NOUN
cana-6099	167	4	increases	increase	NOUN
cana-6099	167	5	,	,	PUNCT
cana-6099	167	6	concentration	concentration	NOUN
cana-6099	167	7	decreases	decrease	VERB
cana-6099	167	8	for	for	ADP
cana-6099	167	9	0	0	NUM
cana-6099	167	10	≤	≤	NUM
cana-6099	167	11	r	r	NOUN
cana-6099	167	12	≤	≤	NUM
cana-6099	167	13	1.3	1.3	NUM
cana-6099	167	14	then	then	ADV
cana-6099	167	15	vanishes	vanish	VERB
cana-6099	167	16	at	at	ADP
cana-6099	167	17	r	r	PROPN
cana-6099	167	18	≈	≈	PROPN
cana-6099	167	19	1.3	1.3	NUM
cana-6099	167	20	and	and	CCONJ
cana-6099	167	21	for	for	ADP
cana-6099	167	22	1.3	1.3	NUM
cana-6099	167	23	≤	≤	NOUN
cana-6099	167	24	r	r	NOUN
cana-6099	167	25	≤	≤	NUM
cana-6099	167	26	2.4	2.4	NUM
cana-6099	167	27	,	,	PUNCT
cana-6099	167	28	it	it	PRON
cana-6099	167	29	increases	increase	VERB
cana-6099	167	30	with	with	ADP
cana-6099	167	31	time	time	NOUN
cana-6099	167	32	.	.	PUNCT
cana-6099	168	1	figure	figure	NOUN
cana-6099	168	2	4	4	NUM
cana-6099	168	3	represents	represent	VERB
cana-6099	168	4	temperature	temperature	NOUN
cana-6099	168	5	distribution	distribution	NOUN
cana-6099	168	6	along	along	ADP
cana-6099	168	7	radial	radial	ADJ
cana-6099	168	8	direction	direction	NOUN
cana-6099	168	9	.	.	PUNCT
cana-6099	169	1	it	it	PRON
cana-6099	169	2	also	also	ADV
cana-6099	169	3	exhibits	exhibit	VERB
cana-6099	169	4	second	second	ADJ
cana-6099	169	5	sound	sound	ADJ
cana-6099	169	6	effect	effect	NOUN
cana-6099	169	7	.	.	PUNCT
cana-6099	170	1	the	the	DET
cana-6099	170	2	graph	graph	NOUN
cana-6099	170	3	shows	show	VERB
cana-6099	170	4	a	a	DET
cana-6099	170	5	single	single	ADJ
cana-6099	170	6	curve	curve	NOUN
cana-6099	170	7	for	for	ADP
cana-6099	170	8	distinct	distinct	ADJ
cana-6099	170	9	values	value	NOUN
cana-6099	170	10	of	of	ADP
cana-6099	170	11	time	time	NOUN
cana-6099	170	12	t	t	PROPN
cana-6099	170	13	=	=	SYM
cana-6099	170	14	0.05s,0.065s,0.08s	0.05s,0.065s,0.08s	PROPN
cana-6099	170	15	.	.	PUNCT
cana-6099	171	1	thus	thus	ADV
cana-6099	171	2	θ	θ	PROPN
cana-6099	171	3	gives	give	VERB
cana-6099	171	4	same	same	ADJ
cana-6099	171	5	value	value	NOUN
cana-6099	171	6	as	as	ADP
cana-6099	171	7	time	time	NOUN
cana-6099	171	8	varies	vary	VERB
cana-6099	171	9	.	.	PUNCT
cana-6099	172	1	here	here	ADV
cana-6099	172	2	θ	θ	PROPN
cana-6099	172	3	decreases	decrease	VERB
cana-6099	172	4	for	for	ADP
cana-6099	172	5	0	0	NUM
cana-6099	172	6	≤	≤	NUM
cana-6099	172	7	r	r	NOUN
cana-6099	172	8	≤	≤	NUM
cana-6099	172	9	1.3	1.3	NUM
cana-6099	172	10	then	then	ADV
cana-6099	172	11	vanish	vanish	VERB
cana-6099	172	12	at	at	ADP
cana-6099	172	13	r	r	PROPN
cana-6099	172	14	≈	≈	PROPN
cana-6099	172	15	1.3	1.3	NUM
cana-6099	172	16	and	and	CCONJ
cana-6099	172	17	increases	increase	NOUN
cana-6099	172	18	for	for	ADP
cana-6099	172	19	1.3	1.3	NUM
cana-6099	172	20	≤	≤	NOUN
cana-6099	172	21	r	r	NOUN
cana-6099	172	22	≤	≤	NUM
cana-6099	172	23	2.4	2.4	NUM
cana-6099	172	24	.	.	PUNCT
cana-6099	173	1	figure	figure	NOUN
cana-6099	173	2	5	5	NUM
cana-6099	173	3	represents	represent	VERB
cana-6099	173	4	temperature	temperature	NOUN
cana-6099	173	5	along	along	ADP
cana-6099	173	6	radial	radial	ADJ
cana-6099	173	7	direction	direction	NOUN
cana-6099	173	8	for	for	ADP
cana-6099	173	9	α	α	NOUN
cana-6099	173	10	=	=	SYM
cana-6099	173	11	0.25,0.50,0.75	0.25,0.50,0.75	NOUN
cana-6099	173	12	.	.	PUNCT
cana-6099	174	1	the	the	DET
cana-6099	174	2	graph	graph	NOUN
cana-6099	174	3	shows	show	VERB
cana-6099	174	4	a	a	DET
cana-6099	174	5	single	single	ADJ
cana-6099	174	6	curve	curve	NOUN
cana-6099	174	7	for	for	ADP
cana-6099	174	8	distinct	distinct	ADJ
cana-6099	174	9	values	value	NOUN
cana-6099	174	10	of	of	ADP
cana-6099	174	11	fractional	fractional	ADJ
cana-6099	174	12	order	order	NOUN
cana-6099	174	13	parameter	parameter	NOUN
cana-6099	174	14	α	α	NOUN
cana-6099	174	15	=	=	NOUN
cana-6099	174	16	0.25,0.50,0.75	0.25,0.50,0.75	NOUN
cana-6099	174	17	for	for	ADP
cana-6099	174	18	both	both	CCONJ
cana-6099	174	19	ls	ls	ADJ
cana-6099	174	20	and	and	CCONJ
cana-6099	174	21	cte	cte	PROPN
cana-6099	174	22	model	model	NOUN
cana-6099	174	23	.	.	PUNCT
cana-6099	175	1	here	here	ADV
cana-6099	175	2	θ	θ	PROPN
cana-6099	175	3	decreases	decrease	VERB
cana-6099	175	4	for	for	ADP
cana-6099	175	5	0	0	NUM
cana-6099	175	6	≤	≤	NUM
cana-6099	175	7	r	r	NOUN
cana-6099	175	8	≤	≤	NUM
cana-6099	175	9	1.3	1.3	NUM
cana-6099	175	10	then	then	ADV
cana-6099	175	11	vanish	vanish	VERB
cana-6099	175	12	at	at	ADP
cana-6099	175	13	r	r	PROPN
cana-6099	175	14	≈	≈	PROPN
cana-6099	175	15	1.3	1.3	NUM
cana-6099	175	16	and	and	CCONJ
cana-6099	175	17	increases	increase	NOUN
cana-6099	175	18	for	for	ADP
cana-6099	175	19	1.3	1.3	NUM
cana-6099	175	20	≤	≤	NOUN
cana-6099	175	21	r	r	NOUN
cana-6099	175	22	≤	≤	NUM
cana-6099	175	23	2.4	2.4	NUM
cana-6099	175	24	.	.	PUNCT
cana-6099	176	1	figure	figure	NOUN
cana-6099	176	2	3	3	NUM
cana-6099	176	3	,	,	PUNCT
cana-6099	176	4	7	7	NUM
cana-6099	176	5	shows	show	VERB
cana-6099	176	6	concentration	concentration	NOUN
cana-6099	176	7	and	and	CCONJ
cana-6099	176	8	chemical	chemical	NOUN
cana-6099	176	9	potential	potential	ADJ
cana-6099	176	10	distribution	distribution	NOUN
cana-6099	176	11	in	in	ADP
cana-6099	176	12	the	the	DET
cana-6099	176	13	middle	middle	ADJ
cana-6099	176	14	plane	plane	NOUN
cana-6099	176	15	z	z	NOUN
cana-6099	176	16	=	=	SYM
cana-6099	176	17	0	0	NUM
cana-6099	176	18	for	for	ADP
cana-6099	176	19	distinct	distinct	ADJ
cana-6099	176	20	α	α	NOUN
cana-6099	176	21	in	in	ADP
cana-6099	176	22	context	context	NOUN
cana-6099	176	23	of	of	ADP
cana-6099	176	24	ls	ls	PROPN
cana-6099	176	25	and	and	CCONJ
cana-6099	176	26	cte	cte	PROPN
cana-6099	176	27	model	model	NOUN
cana-6099	176	28	.	.	PUNCT
cana-6099	177	1	communications	communication	NOUN
cana-6099	177	2	on	on	ADP
cana-6099	177	3	applied	apply	VERB
cana-6099	177	4	nonlinear	nonlinear	ADJ
cana-6099	177	5	analysis	analysis	NOUN
cana-6099	177	6	issn	issn	NOUN
cana-6099	177	7	:	:	PUNCT
cana-6099	177	8	1074	1074	NUM
cana-6099	177	9	-	-	PUNCT
cana-6099	177	10	133x	133x	NUM
cana-6099	177	11	vol	vol	VERB
cana-6099	177	12	32	32	NUM
cana-6099	177	13	no	no	NOUN
cana-6099	177	14	.	.	PUNCT
cana-6099	178	1	10s	10	NOUN
cana-6099	178	2	(	(	PUNCT
cana-6099	178	3	2025	2025	NUM
cana-6099	178	4	)	)	PUNCT
cana-6099	178	5	3365	3365	NUM
cana-6099	178	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	178	7	figure	figure	NOUN
cana-6099	178	8	8	8	NUM
cana-6099	178	9	shows	show	VERB
cana-6099	178	10	displacement	displacement	ADJ
cana-6099	178	11	component	component	NOUN
cana-6099	178	12	along	along	ADP
cana-6099	178	13	radial	radial	ADJ
cana-6099	178	14	direction	direction	NOUN
cana-6099	178	15	for	for	ADP
cana-6099	178	16	distinct	distinct	ADJ
cana-6099	178	17	values	value	NOUN
cana-6099	178	18	of	of	ADP
cana-6099	178	19	time	time	NOUN
cana-6099	178	20	,	,	PUNCT
cana-6099	178	21	where	where	SCONJ
cana-6099	178	22	the	the	DET
cana-6099	178	23	displacement	displacement	ADJ
cana-6099	178	24	component	component	NOUN
cana-6099	178	25	u	u	NOUN
cana-6099	178	26	decreases	decrease	VERB
cana-6099	178	27	gradually	gradually	ADV
cana-6099	178	28	,	,	PUNCT
cana-6099	178	29	takes	take	VERB
cana-6099	178	30	maximum	maximum	ADJ
cana-6099	178	31	value	value	NOUN
cana-6099	178	32	at	at	ADP
cana-6099	178	33	r	r	NOUN
cana-6099	178	34	≈	≈	PROPN
cana-6099	178	35	0.8	0.8	NUM
cana-6099	178	36	and	and	CCONJ
cana-6099	178	37	then	then	ADV
cana-6099	178	38	slowly	slowly	ADV
cana-6099	178	39	increases	increase	VERB
cana-6099	178	40	and	and	CCONJ
cana-6099	178	41	vanish	vanish	VERB
cana-6099	178	42	at	at	ADP
cana-6099	178	43	r	r	PROPN
cana-6099	178	44	≈	≈	PROPN
cana-6099	178	45	1.7	1.7	NUM
cana-6099	178	46	.	.	PUNCT
cana-6099	179	1	figure	figure	NOUN
cana-6099	179	2	5	5	NUM
cana-6099	179	3	.	.	PUNCT
cana-6099	179	4	temperature	temperature	NOUN
cana-6099	179	5	θ	θ	NOUN
cana-6099	179	6	distribution	distribution	NOUN
cana-6099	179	7	for	for	ADP
cana-6099	179	8	distinct	distinct	ADJ
cana-6099	179	9	values	value	NOUN
cana-6099	179	10	of	of	ADP
cana-6099	179	11	α	α	PRON
cana-6099	179	12	figure	figure	NOUN
cana-6099	179	13	6	6	NUM
cana-6099	179	14	.	.	PUNCT
cana-6099	179	15	chemical	chemical	NOUN
cana-6099	179	16	p	p	NOUN
cana-6099	179	17	potential	potential	NOUN
cana-6099	179	18	for	for	ADP
cana-6099	179	19	distinct	distinct	ADJ
cana-6099	179	20	values	value	NOUN
cana-6099	179	21	of	of	ADP
cana-6099	179	22	t(s	t(s	PROPN
cana-6099	179	23	)	)	PUNCT
cana-6099	179	24	communications	communication	NOUN
cana-6099	179	25	on	on	ADP
cana-6099	179	26	applied	apply	VERB
cana-6099	179	27	nonlinear	nonlinear	ADJ
cana-6099	179	28	analysis	analysis	NOUN
cana-6099	179	29	issn	issn	NOUN
cana-6099	179	30	:	:	PUNCT
cana-6099	179	31	1074	1074	NUM
cana-6099	179	32	-	-	PUNCT
cana-6099	179	33	133x	133x	NUM
cana-6099	179	34	vol	vol	VERB
cana-6099	179	35	32	32	NUM
cana-6099	179	36	no	no	NOUN
cana-6099	179	37	.	.	PUNCT
cana-6099	180	1	10s	10	NOUN
cana-6099	180	2	(	(	PUNCT
cana-6099	180	3	2025	2025	NUM
cana-6099	180	4	)	)	PUNCT
cana-6099	180	5	3366	3366	NUM
cana-6099	180	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	180	7	figure	figure	NOUN
cana-6099	180	8	9	9	NUM
cana-6099	180	9	shows	show	VERB
cana-6099	180	10	displacement	displacement	ADJ
cana-6099	180	11	component	component	NOUN
cana-6099	180	12	along	along	ADP
cana-6099	180	13	radial	radial	ADJ
cana-6099	180	14	direction	direction	NOUN
cana-6099	180	15	for	for	ADP
cana-6099	180	16	distinct	distinct	ADJ
cana-6099	180	17	values	value	NOUN
cana-6099	180	18	of	of	ADP
cana-6099	180	19	fractional	fractional	ADJ
cana-6099	180	20	order	order	NOUN
cana-6099	180	21	parameter	parameter	NOUN
cana-6099	180	22	α	α	NOUN
cana-6099	180	23	.	.	PUNCT
cana-6099	181	1	in	in	ADP
cana-6099	181	2	both	both	CCONJ
cana-6099	181	3	the	the	DET
cana-6099	181	4	cases	case	NOUN
cana-6099	181	5	of	of	ADP
cana-6099	181	6	ls	ls	ADJ
cana-6099	181	7	and	and	CCONJ
cana-6099	181	8	cte	cte	PROPN
cana-6099	181	9	model	model	NOUN
cana-6099	181	10	the	the	DET
cana-6099	181	11	displacement	displacement	ADJ
cana-6099	181	12	component	component	NOUN
cana-6099	181	13	u	u	NOUN
cana-6099	181	14	decreases	decrease	VERB
cana-6099	181	15	gradually	gradually	ADV
cana-6099	181	16	for	for	ADP
cana-6099	181	17	small	small	ADJ
cana-6099	181	18	values	value	NOUN
cana-6099	181	19	α	α	X
cana-6099	181	20	=	=	SYM
cana-6099	181	21	0.25,0.50	0.25,0.50	NOUN
cana-6099	181	22	,	,	PUNCT
cana-6099	181	23	figure	figure	VERB
cana-6099	181	24	7	7	NUM
cana-6099	181	25	.	.	PUNCT
cana-6099	181	26	chemical	chemical	NOUN
cana-6099	181	27	p	p	PROPN
cana-6099	181	28	potential	potential	NOUN
cana-6099	181	29	for	for	ADP
cana-6099	181	30	distinct	distinct	ADJ
cana-6099	181	31	values	value	NOUN
cana-6099	181	32	of	of	ADP
cana-6099	181	33	α	α	PRON
cana-6099	181	34	figure	figure	NOUN
cana-6099	181	35	8	8	NUM
cana-6099	181	36	.	.	PUNCT
cana-6099	182	1	displacement	displacement	ADJ
cana-6099	182	2	component	component	NOUN
cana-6099	182	3	u	u	NOUN
cana-6099	182	4	for	for	ADP
cana-6099	182	5	distinct	distinct	ADJ
cana-6099	182	6	values	value	NOUN
cana-6099	182	7	of	of	ADP
cana-6099	182	8	t(s	t(s	PROPN
cana-6099	182	9	)	)	PUNCT
cana-6099	182	10	communications	communication	NOUN
cana-6099	182	11	on	on	ADP
cana-6099	182	12	applied	apply	VERB
cana-6099	182	13	nonlinear	nonlinear	ADJ
cana-6099	182	14	analysis	analysis	NOUN
cana-6099	182	15	issn	issn	NOUN
cana-6099	182	16	:	:	PUNCT
cana-6099	182	17	1074	1074	NUM
cana-6099	182	18	-	-	PUNCT
cana-6099	182	19	133x	133x	NUM
cana-6099	182	20	vol	vol	VERB
cana-6099	182	21	32	32	NUM
cana-6099	182	22	no	no	NOUN
cana-6099	182	23	.	.	PUNCT
cana-6099	183	1	10s	10	NOUN
cana-6099	183	2	(	(	PUNCT
cana-6099	183	3	2025	2025	NUM
cana-6099	183	4	)	)	PUNCT
cana-6099	183	5	3367	3367	NUM
cana-6099	184	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	184	2	takes	take	VERB
cana-6099	184	3	maximum	maximum	ADJ
cana-6099	184	4	value	value	NOUN
cana-6099	184	5	at	at	ADP
cana-6099	184	6	r	r	NOUN
cana-6099	184	7	≈	≈	PROPN
cana-6099	184	8	0.8	0.8	NUM
cana-6099	184	9	and	and	CCONJ
cana-6099	184	10	then	then	ADV
cana-6099	184	11	slowly	slowly	ADV
cana-6099	184	12	increases	increase	VERB
cana-6099	184	13	and	and	CCONJ
cana-6099	184	14	vanish	vanish	VERB
cana-6099	184	15	at	at	ADP
cana-6099	184	16	r	r	NOUN
cana-6099	184	17	≈	≈	PROPN
cana-6099	184	18	1.7	1.7	NUM
cana-6099	184	19	.	.	PUNCT
cana-6099	185	1	but	but	CCONJ
cana-6099	185	2	in	in	ADP
cana-6099	185	3	cte	cte	PROPN
cana-6099	185	4	model	model	NOUN
cana-6099	185	5	for	for	ADP
cana-6099	185	6	large	large	ADJ
cana-6099	185	7	value	value	NOUN
cana-6099	185	8	α	α	NOUN
cana-6099	185	9	=	=	NOUN
cana-6099	185	10	0.75	0.75	NUM
cana-6099	185	11	,	,	PUNCT
cana-6099	185	12	displacement	displacement	NOUN
cana-6099	185	13	u	u	NOUN
cana-6099	185	14	increases	increase	VERB
cana-6099	185	15	gradually	gradually	ADV
cana-6099	185	16	takes	take	VERB
cana-6099	185	17	maximum	maximum	NOUN
cana-6099	185	18	at	at	ADP
cana-6099	185	19	r	r	NOUN
cana-6099	185	20	≈	≈	PROPN
cana-6099	185	21	0.8	0.8	NUM
cana-6099	185	22	and	and	CCONJ
cana-6099	185	23	then	then	ADV
cana-6099	185	24	slowly	slowly	ADV
cana-6099	185	25	decreases	decrease	VERB
cana-6099	185	26	and	and	CCONJ
cana-6099	185	27	vanish	vanish	VERB
cana-6099	185	28	at	at	ADP
cana-6099	185	29	r	r	PROPN
cana-6099	185	30	≈	≈	PROPN
cana-6099	185	31	1.7	1.7	NUM
cana-6099	185	32	.	.	PUNCT
cana-6099	186	1	figure	figure	NOUN
cana-6099	186	2	9	9	NUM
cana-6099	186	3	.	.	PUNCT
cana-6099	187	1	displacement	displacement	ADJ
cana-6099	187	2	component	component	NOUN
cana-6099	187	3	u	u	NOUN
cana-6099	187	4	for	for	ADP
cana-6099	187	5	distinct	distinct	ADJ
cana-6099	187	6	values	value	NOUN
cana-6099	187	7	of	of	ADP
cana-6099	187	8	α	α	PRON
cana-6099	187	9	figure	figure	NOUN
cana-6099	187	10	10	10	NUM
cana-6099	187	11	.	.	PUNCT
cana-6099	188	1	radial	radial	ADJ
cana-6099	188	2	stress	stress	NOUN
cana-6099	188	3	σrr	σrr	PROPN
cana-6099	188	4	component	component	NOUN
cana-6099	188	5	for	for	ADP
cana-6099	188	6	distinct	distinct	ADJ
cana-6099	188	7	values	value	NOUN
cana-6099	188	8	of	of	ADP
cana-6099	188	9	t(s	t(s	PROPN
cana-6099	188	10	)	)	PUNCT
cana-6099	188	11	communications	communication	NOUN
cana-6099	188	12	on	on	ADP
cana-6099	188	13	applied	apply	VERB
cana-6099	188	14	nonlinear	nonlinear	ADJ
cana-6099	188	15	analysis	analysis	NOUN
cana-6099	188	16	issn	issn	NOUN
cana-6099	188	17	:	:	PUNCT
cana-6099	188	18	1074	1074	NUM
cana-6099	188	19	-	-	PUNCT
cana-6099	188	20	133x	133x	NUM
cana-6099	188	21	vol	vol	VERB
cana-6099	188	22	32	32	NUM
cana-6099	188	23	no	no	NOUN
cana-6099	188	24	.	.	PUNCT
cana-6099	189	1	10s	10	NOUN
cana-6099	189	2	(	(	PUNCT
cana-6099	189	3	2025	2025	NUM
cana-6099	189	4	)	)	PUNCT
cana-6099	189	5	3368	3368	NUM
cana-6099	190	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	190	2	figure	figure	NOUN
cana-6099	190	3	10	10	NUM
cana-6099	190	4	shows	show	VERB
cana-6099	190	5	the	the	DET
cana-6099	190	6	oscillatory	oscillatory	ADJ
cana-6099	190	7	nature	nature	NOUN
cana-6099	190	8	of	of	ADP
cana-6099	190	9	radial	radial	ADJ
cana-6099	190	10	stress	stress	NOUN
cana-6099	190	11	σrr	σrr	PROPN
cana-6099	190	12	.	.	PUNCT
cana-6099	191	1	the	the	DET
cana-6099	191	2	nature	nature	NOUN
cana-6099	191	3	of	of	ADP
cana-6099	191	4	radial	radial	ADJ
cana-6099	191	5	stress	stress	NOUN
cana-6099	191	6	σrr	σrr	NOUN
cana-6099	191	7	is	be	AUX
cana-6099	191	8	oscillating	oscillate	VERB
cana-6099	191	9	as	as	SCONJ
cana-6099	191	10	shown	show	VERB
cana-6099	191	11	in	in	ADP
cana-6099	191	12	figure	figure	NOUN
cana-6099	191	13	11	11	NUM
cana-6099	191	14	.	.	PUNCT
cana-6099	192	1	while	while	SCONJ
cana-6099	192	2	the	the	DET
cana-6099	192	3	axial	axial	ADJ
cana-6099	192	4	stress	stress	NOUN
cana-6099	192	5	is	be	AUX
cana-6099	192	6	increases	increase	NOUN
cana-6099	192	7	with	with	ADP
cana-6099	192	8	increase	increase	NOUN
cana-6099	192	9	in	in	ADP
cana-6099	192	10	value	value	NOUN
cana-6099	192	11	of	of	ADP
cana-6099	192	12	α	α	NOUN
cana-6099	192	13	and	and	CCONJ
cana-6099	192	14	figure	figure	VERB
cana-6099	192	15	11	11	NUM
cana-6099	192	16	.	.	PUNCT
cana-6099	193	1	radial	radial	ADJ
cana-6099	193	2	stress	stress	NOUN
cana-6099	193	3	σrr	σrr	PROPN
cana-6099	193	4	component	component	NOUN
cana-6099	193	5	for	for	ADP
cana-6099	193	6	distinct	distinct	ADJ
cana-6099	193	7	values	value	NOUN
cana-6099	193	8	of	of	ADP
cana-6099	193	9	α	α	NOUN
cana-6099	193	10	becomes	become	VERB
cana-6099	193	11	zero	zero	NUM
cana-6099	193	12	at	at	ADP
cana-6099	193	13	r	r	NOUN
cana-6099	193	14	=	=	NOUN
cana-6099	193	15	1	1	NUM
cana-6099	193	16	then	then	ADV
cana-6099	193	17	after	after	ADP
cana-6099	193	18	decreases	decrease	NOUN
cana-6099	193	19	as	as	ADP
cana-6099	193	20	α	α	PRON
cana-6099	193	21	increases	increase	NOUN
cana-6099	193	22	.	.	PUNCT
cana-6099	194	1	in	in	ADP
cana-6099	194	2	figure	figure	NOUN
cana-6099	194	3	12	12	NUM
cana-6099	194	4	axial	axial	ADJ
cana-6099	194	5	stress	stress	NOUN
cana-6099	194	6	σzz	σzz	PROPN
cana-6099	194	7	is	be	AUX
cana-6099	194	8	compressive	compressive	ADJ
cana-6099	194	9	for	for	ADP
cana-6099	194	10	0	0	NUM
cana-6099	194	11	≤	≤	NUM
cana-6099	194	12	r	r	NOUN
cana-6099	194	13	≤	≤	NUM
cana-6099	194	14	1	1	NUM
cana-6099	194	15	then	then	ADV
cana-6099	194	16	after	after	SCONJ
cana-6099	194	17	it	it	PRON
cana-6099	194	18	is	be	AUX
cana-6099	194	19	tensile	tensile	NOUN
cana-6099	194	20	for	for	ADP
cana-6099	194	21	1	1	NUM
cana-6099	194	22	≤	≤	NOUN
cana-6099	194	23	r	r	NOUN
cana-6099	194	24	≤	≤	NUM
cana-6099	194	25	2.4	2.4	NUM
cana-6099	194	26	.	.	PUNCT
cana-6099	195	1	figure	figure	NOUN
cana-6099	195	2	10	10	NUM
cana-6099	195	3	,	,	PUNCT
cana-6099	195	4	12	12	NUM
cana-6099	195	5	represents	represent	VERB
cana-6099	195	6	the	the	DET
cana-6099	195	7	radial	radial	ADJ
cana-6099	195	8	stress	stress	NOUN
cana-6099	195	9	σrr	σrr	NOUN
cana-6099	195	10	and	and	CCONJ
cana-6099	195	11	the	the	DET
cana-6099	195	12	axial	axial	ADJ
cana-6099	195	13	stress	stress	NOUN
cana-6099	195	14	σzz	σzz	NOUN
cana-6099	195	15	in	in	ADP
cana-6099	195	16	the	the	DET
cana-6099	195	17	middle	middle	ADJ
cana-6099	195	18	plane	plane	NOUN
cana-6099	195	19	z	z	NOUN
cana-6099	196	1	=	=	NOUN
cana-6099	197	1	0	0	PROPN
cana-6099	197	2	.	.	PUNCT
cana-6099	198	1	the	the	DET
cana-6099	198	2	nature	nature	NOUN
cana-6099	198	3	of	of	ADP
cana-6099	198	4	stresses	stress	NOUN
cana-6099	198	5	differ	differ	VERB
cana-6099	198	6	.	.	PUNCT
cana-6099	199	1	theses	theses	PROPN
cana-6099	199	2	stresses	stress	NOUN
cana-6099	199	3	shows	show	VERB
cana-6099	199	4	continuity	continuity	NOUN
cana-6099	199	5	near	near	ADP
cana-6099	199	6	the	the	DET
cana-6099	199	7	centre	centre	NOUN
cana-6099	199	8	of	of	ADP
cana-6099	199	9	the	the	DET
cana-6099	199	10	thick	thick	ADJ
cana-6099	199	11	circular	circular	ADJ
cana-6099	199	12	plate	plate	NOUN
cana-6099	199	13	.	.	PUNCT
cana-6099	200	1	both	both	PRON
cana-6099	200	2	radial	radial	ADJ
cana-6099	200	3	σrr	σrr	NOUN
cana-6099	200	4	and	and	CCONJ
cana-6099	200	5	axial	axial	ADJ
cana-6099	200	6	σzz	σzz	NOUN
cana-6099	200	7	stresses	stress	NOUN
cana-6099	200	8	becomes	become	VERB
cana-6099	200	9	zero	zero	NUM
cana-6099	200	10	at	at	ADP
cana-6099	200	11	r	r	NOUN
cana-6099	200	12	=	=	SYM
cana-6099	200	13	1	1	NUM
cana-6099	200	14	.	.	NUM
cana-6099	200	15	figures	figure	NOUN
cana-6099	200	16	11	11	NUM
cana-6099	200	17	,	,	PUNCT
cana-6099	200	18	13	13	NUM
cana-6099	200	19	displays	display	VERB
cana-6099	200	20	the	the	DET
cana-6099	200	21	radial	radial	ADJ
cana-6099	200	22	and	and	CCONJ
cana-6099	200	23	axial	axial	ADJ
cana-6099	200	24	stresses	stress	NOUN
cana-6099	200	25	for	for	ADP
cana-6099	200	26	distinct	distinct	ADJ
cana-6099	200	27	values	value	NOUN
cana-6099	200	28	of	of	ADP
cana-6099	200	29	α	α	NOUN
cana-6099	200	30	in	in	ADP
cana-6099	200	31	axial	axial	ADJ
cana-6099	200	32	direction	direction	NOUN
cana-6099	200	33	.	.	PUNCT
cana-6099	201	1	the	the	DET
cana-6099	201	2	nature	nature	NOUN
cana-6099	201	3	of	of	ADP
cana-6099	201	4	graphs	graph	NOUN
cana-6099	201	5	in	in	ADP
cana-6099	201	6	each	each	DET
cana-6099	201	7	case	case	NOUN
cana-6099	201	8	is	be	AUX
cana-6099	201	9	similar	similar	ADJ
cana-6099	201	10	for	for	ADP
cana-6099	201	11	ls	ls	ADJ
cana-6099	201	12	and	and	CCONJ
cana-6099	201	13	cte	cte	NOUN
cana-6099	201	14	model	model	NOUN
cana-6099	201	15	as	as	SCONJ
cana-6099	201	16	shown	show	VERB
cana-6099	201	17	in	in	ADP
cana-6099	201	18	figures	figure	NOUN
cana-6099	201	19	2	2	NUM
cana-6099	201	20	,	,	PUNCT
cana-6099	201	21	4	4	NUM
cana-6099	201	22	,	,	PUNCT
cana-6099	201	23	6	6	NUM
cana-6099	201	24	,	,	PUNCT
cana-6099	201	25	8	8	NUM
cana-6099	201	26	,	,	PUNCT
cana-6099	201	27	10	10	NUM
cana-6099	201	28	,	,	PUNCT
cana-6099	201	29	12	12	NUM
cana-6099	201	30	.	.	PUNCT
cana-6099	202	1	also	also	ADV
cana-6099	202	2	it	it	PRON
cana-6099	202	3	is	be	AUX
cana-6099	202	4	clearly	clearly	ADV
cana-6099	202	5	seen	see	VERB
cana-6099	202	6	that	that	SCONJ
cana-6099	202	7	the	the	DET
cana-6099	202	8	solutions	solution	NOUN
cana-6099	202	9	of	of	ADP
cana-6099	202	10	ls	ls	PROPN
cana-6099	202	11	and	and	CCONJ
cana-6099	202	12	cte	cte	PROPN
cana-6099	202	13	theory	theory	NOUN
cana-6099	202	14	differs	differ	VERB
cana-6099	202	15	for	for	ADP
cana-6099	202	16	t	t	PROPN
cana-6099	202	17	=	=	SYM
cana-6099	202	18	0.05s,0.065s,0.08s	0.05s,0.065s,0.08s	PROPN
cana-6099	202	19	.	.	PUNCT
cana-6099	203	1	for	for	ADP
cana-6099	203	2	large	large	ADJ
cana-6099	203	3	times	time	NOUN
cana-6099	203	4	the	the	DET
cana-6099	203	5	results	result	NOUN
cana-6099	203	6	are	be	AUX
cana-6099	203	7	similar	similar	ADJ
cana-6099	203	8	for	for	ADP
cana-6099	203	9	ls	ls	PROPN
cana-6099	203	10	and	and	CCONJ
cana-6099	203	11	cte	cte	PROPN
cana-6099	203	12	theory	theory	NOUN
cana-6099	203	13	,	,	PUNCT
cana-6099	203	14	since	since	SCONJ
cana-6099	203	15	the	the	DET
cana-6099	203	16	thermal	thermal	ADJ
cana-6099	203	17	disturbances	disturbance	NOUN
cana-6099	203	18	reach	reach	VERB
cana-6099	203	19	all	all	DET
cana-6099	203	20	parts	part	NOUN
cana-6099	203	21	of	of	ADP
cana-6099	203	22	the	the	DET
cana-6099	203	23	medium	medium	NOUN
cana-6099	203	24	along	along	ADV
cana-6099	203	25	with	with	ADP
cana-6099	203	26	finite	finite	ADJ
cana-6099	203	27	speed	speed	NOUN
cana-6099	203	28	of	of	ADP
cana-6099	203	29	propagation	propagation	NOUN
cana-6099	203	30	.	.	PUNCT
cana-6099	204	1	for	for	ADP
cana-6099	204	2	ls	ls	PROPN
cana-6099	204	3	model	model	NOUN
cana-6099	204	4	the	the	DET
cana-6099	204	5	variations	variation	NOUN
cana-6099	204	6	in	in	ADP
cana-6099	204	7	the	the	DET
cana-6099	204	8	value	value	NOUN
cana-6099	204	9	of	of	ADP
cana-6099	204	10	fractional	fractional	ADJ
cana-6099	204	11	order	order	NOUN
cana-6099	204	12	parameter	parameter	NOUN
cana-6099	204	13	α	α	PROPN
cana-6099	204	14	does	do	AUX
cana-6099	204	15	n’t	not	PART
cana-6099	204	16	affect	affect	VERB
cana-6099	204	17	concentration	concentration	NOUN
cana-6099	204	18	,	,	PUNCT
cana-6099	204	19	temperature	temperature	NOUN
cana-6099	204	20	,	,	PUNCT
cana-6099	204	21	chemical	chemical	NOUN
cana-6099	204	22	potential	potential	NOUN
cana-6099	204	23	,	,	PUNCT
cana-6099	204	24	displacement	displacement	NOUN
cana-6099	204	25	,	,	PUNCT
cana-6099	204	26	radial	radial	ADJ
cana-6099	204	27	stress	stress	NOUN
cana-6099	204	28	,	,	PUNCT
cana-6099	204	29	and	and	CCONJ
cana-6099	204	30	axial	axial	ADJ
cana-6099	204	31	stress	stress	NOUN
cana-6099	204	32	as	as	ADP
cana-6099	204	33	displays	display	NOUN
cana-6099	204	34	in	in	ADP
cana-6099	204	35	figures	figure	NOUN
cana-6099	204	36	3	3	NUM
cana-6099	204	37	,	,	PUNCT
cana-6099	204	38	5	5	NUM
cana-6099	204	39	,	,	PUNCT
cana-6099	204	40	7	7	NUM
cana-6099	204	41	,	,	PUNCT
cana-6099	204	42	9	9	NUM
cana-6099	204	43	,	,	PUNCT
cana-6099	204	44	11	11	NUM
cana-6099	204	45	,	,	PUNCT
cana-6099	204	46	13	13	NUM
cana-6099	204	47	.	.	PUNCT
cana-6099	205	1	thus	thus	ADV
cana-6099	205	2	it	it	PRON
cana-6099	205	3	gives	give	VERB
cana-6099	205	4	a	a	DET
cana-6099	205	5	single	single	ADJ
cana-6099	205	6	curve	curve	NOUN
cana-6099	205	7	for	for	ADP
cana-6099	205	8	α	α	NOUN
cana-6099	205	9	=	=	SYM
cana-6099	205	10	0.25,0.50,0.75	0.25,0.50,0.75	NOUN
cana-6099	205	11	in	in	ADP
cana-6099	205	12	each	each	DET
cana-6099	205	13	case	case	NOUN
cana-6099	205	14	.	.	PUNCT
cana-6099	206	1	for	for	SCONJ
cana-6099	206	2	cte	cte	PROPN
cana-6099	206	3	model	model	NOUN
cana-6099	206	4	as	as	ADP
cana-6099	206	5	value	value	NOUN
cana-6099	206	6	of	of	ADP
cana-6099	206	7	fractional	fractional	ADJ
cana-6099	206	8	order	order	NOUN
cana-6099	206	9	parameter	parameter	NOUN
cana-6099	206	10	α	α	PROPN
cana-6099	206	11	increases	increase	VERB
cana-6099	206	12	the	the	DET
cana-6099	206	13	value	value	NOUN
cana-6099	206	14	of	of	ADP
cana-6099	206	15	communications	communication	NOUN
cana-6099	206	16	on	on	ADP
cana-6099	206	17	applied	apply	VERB
cana-6099	206	18	nonlinear	nonlinear	ADJ
cana-6099	206	19	analysis	analysis	NOUN
cana-6099	206	20	issn	issn	NOUN
cana-6099	206	21	:	:	PUNCT
cana-6099	206	22	1074	1074	NUM
cana-6099	206	23	-	-	PUNCT
cana-6099	206	24	133x	133x	NUM
cana-6099	206	25	vol	vol	VERB
cana-6099	206	26	32	32	NUM
cana-6099	206	27	no	no	NOUN
cana-6099	206	28	.	.	PUNCT
cana-6099	207	1	10s	10	NOUN
cana-6099	207	2	(	(	PUNCT
cana-6099	207	3	2025	2025	NUM
cana-6099	207	4	)	)	PUNCT
cana-6099	207	5	3369	3369	NUM
cana-6099	207	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	207	7	concentration	concentration	NOUN
cana-6099	207	8	distribution	distribution	NOUN
cana-6099	207	9	c	c	NOUN
cana-6099	207	10	decreases	decrease	VERB
cana-6099	207	11	for	for	ADP
cana-6099	207	12	0	0	NUM
cana-6099	207	13	≤	≤	NUM
cana-6099	207	14	r	r	NOUN
cana-6099	207	15	≤	≤	NUM
cana-6099	207	16	1.3	1.3	NUM
cana-6099	207	17	,	,	PUNCT
cana-6099	207	18	becomes	become	VERB
cana-6099	207	19	zero	zero	NUM
cana-6099	207	20	at	at	ADP
cana-6099	207	21	r	r	PROPN
cana-6099	207	22	≈	≈	PROPN
cana-6099	207	23	1.3	1.3	NUM
cana-6099	207	24	and	and	CCONJ
cana-6099	207	25	then	then	ADV
cana-6099	207	26	increases	increase	VERB
cana-6099	207	27	with	with	ADP
cana-6099	207	28	α	α	PROPN
cana-6099	207	29	.	.	PUNCT
cana-6099	207	30	figure	figure	NOUN
cana-6099	207	31	12	12	NUM
cana-6099	207	32	.	.	PUNCT
cana-6099	208	1	axial	axial	ADJ
cana-6099	208	2	stress	stress	NOUN
cana-6099	208	3	σzz	σzz	PROPN
cana-6099	208	4	component	component	NOUN
cana-6099	208	5	for	for	ADP
cana-6099	208	6	distinct	distinct	ADJ
cana-6099	208	7	values	value	NOUN
cana-6099	208	8	of	of	ADP
cana-6099	208	9	t(s	t(s	PROPN
cana-6099	208	10	)	)	PUNCT
cana-6099	208	11	figure	figure	NOUN
cana-6099	208	12	13	13	NUM
cana-6099	208	13	.	.	PUNCT
cana-6099	209	1	axial	axial	ADJ
cana-6099	209	2	stress	stress	NOUN
cana-6099	209	3	σzz	σzz	PROPN
cana-6099	209	4	component	component	NOUN
cana-6099	209	5	for	for	ADP
cana-6099	209	6	distinct	distinct	ADJ
cana-6099	209	7	values	value	NOUN
cana-6099	209	8	of	of	ADP
cana-6099	209	9	α	α	NOUN
cana-6099	209	10	communications	communication	NOUN
cana-6099	209	11	on	on	ADP
cana-6099	209	12	applied	apply	VERB
cana-6099	209	13	nonlinear	nonlinear	ADJ
cana-6099	209	14	analysis	analysis	NOUN
cana-6099	209	15	issn	issn	NOUN
cana-6099	209	16	:	:	PUNCT
cana-6099	209	17	1074	1074	NUM
cana-6099	209	18	-	-	PUNCT
cana-6099	209	19	133x	133x	NUM
cana-6099	209	20	vol	vol	VERB
cana-6099	209	21	32	32	NUM
cana-6099	209	22	no	no	NOUN
cana-6099	209	23	.	.	PUNCT
cana-6099	210	1	10s	10	NOUN
cana-6099	210	2	(	(	PUNCT
cana-6099	210	3	2025	2025	NUM
cana-6099	210	4	)	)	PUNCT
cana-6099	210	5	3370	3370	NUM
cana-6099	211	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	211	2	conclusion	conclusion	NOUN
cana-6099	211	3	in	in	ADP
cana-6099	211	4	this	this	DET
cana-6099	211	5	chapter	chapter	NOUN
cana-6099	211	6	,	,	PUNCT
cana-6099	211	7	we	we	PRON
cana-6099	211	8	analytically	analytically	ADV
cana-6099	211	9	solved	solve	VERB
cana-6099	211	10	the	the	DET
cana-6099	211	11	generalized	generalize	VERB
cana-6099	211	12	fractional	fractional	ADJ
cana-6099	211	13	order	order	NOUN
cana-6099	211	14	thermoelastic	thermoelastic	ADJ
cana-6099	211	15	problem	problem	NOUN
cana-6099	211	16	for	for	ADP
cana-6099	211	17	a	a	DET
cana-6099	211	18	thick	thick	ADJ
cana-6099	211	19	circular	circular	ADJ
cana-6099	211	20	plate	plate	NOUN
cana-6099	211	21	using	use	VERB
cana-6099	211	22	a	a	DET
cana-6099	211	23	direct	direct	ADJ
cana-6099	211	24	approach	approach	NOUN
cana-6099	211	25	and	and	CCONJ
cana-6099	211	26	integral	integral	ADJ
cana-6099	211	27	transform	transform	NOUN
cana-6099	211	28	techniques	technique	NOUN
cana-6099	211	29	.	.	PUNCT
cana-6099	212	1	the	the	DET
cana-6099	212	2	important	important	ADJ
cana-6099	212	3	findings	finding	NOUN
cana-6099	212	4	of	of	ADP
cana-6099	212	5	this	this	DET
cana-6099	212	6	chapter	chapter	NOUN
cana-6099	212	7	are	be	AUX
cana-6099	212	8	as	as	SCONJ
cana-6099	212	9	follows	follow	VERB
cana-6099	212	10	:	:	PUNCT
cana-6099	212	11	•	•	SCONJ
cana-6099	212	12	the	the	DET
cana-6099	212	13	used	used	ADJ
cana-6099	212	14	approach	approach	NOUN
cana-6099	212	15	avoids	avoid	VERB
cana-6099	212	16	the	the	DET
cana-6099	212	17	use	use	NOUN
cana-6099	212	18	of	of	ADP
cana-6099	212	19	potential	potential	ADJ
cana-6099	212	20	function	function	NOUN
cana-6099	212	21	,	,	PUNCT
cana-6099	212	22	offering	offer	VERB
cana-6099	212	23	a	a	DET
cana-6099	212	24	simplified	simplified	ADJ
cana-6099	212	25	and	and	CCONJ
cana-6099	212	26	efficient	efficient	ADJ
cana-6099	212	27	route	route	NOUN
cana-6099	212	28	to	to	PART
cana-6099	212	29	obtain	obtain	VERB
cana-6099	212	30	exact	exact	ADJ
cana-6099	212	31	solution	solution	NOUN
cana-6099	212	32	in	in	ADP
cana-6099	212	33	the	the	DET
cana-6099	212	34	laplace	laplace	NOUN
cana-6099	212	35	domain	domain	NOUN
cana-6099	212	36	.	.	PUNCT
cana-6099	213	1	•	•	NUM
cana-6099	213	2	graphical	graphical	ADJ
cana-6099	213	3	results	result	NOUN
cana-6099	213	4	demonstrate	demonstrate	VERB
cana-6099	213	5	how	how	SCONJ
cana-6099	213	6	temperature	temperature	NOUN
cana-6099	213	7	,	,	PUNCT
cana-6099	213	8	displacement	displacement	NOUN
cana-6099	213	9	,	,	PUNCT
cana-6099	213	10	stresses	stress	NOUN
cana-6099	213	11	,	,	PUNCT
cana-6099	213	12	concentration	concentration	NOUN
cana-6099	213	13	,	,	PUNCT
cana-6099	213	14	and	and	CCONJ
cana-6099	213	15	chemical	chemical	NOUN
cana-6099	213	16	potential	potential	NOUN
cana-6099	213	17	behave	behave	VERB
cana-6099	213	18	under	under	ADP
cana-6099	213	19	various	various	ADJ
cana-6099	213	20	time	time	NOUN
cana-6099	213	21	intervals	interval	NOUN
cana-6099	213	22	and	and	CCONJ
cana-6099	213	23	fractional	fractional	ADJ
cana-6099	213	24	order	order	NOUN
cana-6099	213	25	parameters	parameter	NOUN
cana-6099	213	26	.	.	PUNCT
cana-6099	214	1	•	•	NUM
cana-6099	214	2	a	a	DET
cana-6099	214	3	key	key	ADJ
cana-6099	214	4	observation	observation	NOUN
cana-6099	214	5	is	be	AUX
cana-6099	214	6	that	that	SCONJ
cana-6099	214	7	the	the	DET
cana-6099	214	8	fractional	fractional	ADJ
cana-6099	214	9	order	order	NOUN
cana-6099	214	10	parameter	parameter	NOUN
cana-6099	214	11	has	have	VERB
cana-6099	214	12	no	no	DET
cana-6099	214	13	significant	significant	ADJ
cana-6099	214	14	effect	effect	NOUN
cana-6099	214	15	in	in	ADP
cana-6099	214	16	the	the	DET
cana-6099	214	17	ls	ls	ADJ
cana-6099	214	18	model	model	NOUN
cana-6099	214	19	,	,	PUNCT
cana-6099	214	20	while	while	SCONJ
cana-6099	214	21	it	it	PRON
cana-6099	214	22	shows	show	VERB
cana-6099	214	23	noticeable	noticeable	ADJ
cana-6099	214	24	influence	influence	NOUN
cana-6099	214	25	in	in	ADP
cana-6099	214	26	the	the	DET
cana-6099	214	27	cte	cte	PROPN
cana-6099	214	28	model	model	NOUN
cana-6099	214	29	.	.	PUNCT
cana-6099	215	1	moreover	moreover	ADV
cana-6099	215	2	,	,	PUNCT
cana-6099	215	3	both	both	DET
cana-6099	215	4	models	model	NOUN
cana-6099	215	5	yield	yield	VERB
cana-6099	215	6	similar	similar	ADJ
cana-6099	215	7	outcomes	outcome	NOUN
cana-6099	215	8	at	at	ADP
cana-6099	215	9	higher	high	ADJ
cana-6099	215	10	time	time	NOUN
cana-6099	215	11	values	value	NOUN
cana-6099	215	12	,	,	PUNCT
cana-6099	215	13	indicating	indicate	VERB
cana-6099	215	14	convergence	convergence	NOUN
cana-6099	215	15	due	due	ADP
cana-6099	215	16	to	to	ADP
cana-6099	215	17	the	the	DET
cana-6099	215	18	finite	finite	ADJ
cana-6099	215	19	speed	speed	NOUN
cana-6099	215	20	of	of	ADP
cana-6099	215	21	thermal	thermal	ADJ
cana-6099	215	22	wave	wave	NOUN
cana-6099	215	23	propagation	propagation	NOUN
cana-6099	215	24	.	.	PUNCT
cana-6099	216	1	•	•	NOUN
cana-6099	216	2	the	the	DET
cana-6099	216	3	findings	finding	NOUN
cana-6099	216	4	have	have	VERB
cana-6099	216	5	significant	significant	ADJ
cana-6099	216	6	implications	implication	NOUN
cana-6099	216	7	for	for	ADP
cana-6099	216	8	researchers	researcher	NOUN
cana-6099	216	9	exploring	explore	VERB
cana-6099	216	10	fractional	fractional	ADJ
cana-6099	216	11	thermoelasticity	thermoelasticity	NOUN
cana-6099	216	12	,	,	PUNCT
cana-6099	216	13	particularly	particularly	ADV
cana-6099	216	14	in	in	ADP
cana-6099	216	15	the	the	DET
cana-6099	216	16	design	design	NOUN
cana-6099	216	17	of	of	ADP
cana-6099	216	18	advanced	advanced	ADJ
cana-6099	216	19	materials	material	NOUN
cana-6099	216	20	and	and	CCONJ
cana-6099	216	21	systems	system	NOUN
cana-6099	216	22	subjected	subject	VERB
cana-6099	216	23	to	to	ADP
cana-6099	216	24	thermal	thermal	ADJ
cana-6099	216	25	and	and	CCONJ
cana-6099	216	26	diffusion	diffusion	NOUN
cana-6099	216	27	effects	effect	NOUN
cana-6099	216	28	.	.	PUNCT
cana-6099	217	1	•	•	NUM
cana-6099	217	2	future	future	ADJ
cana-6099	217	3	studies	study	NOUN
cana-6099	217	4	may	may	AUX
cana-6099	217	5	extend	extend	VERB
cana-6099	217	6	this	this	DET
cana-6099	217	7	analysis	analysis	NOUN
cana-6099	217	8	along	along	ADP
cana-6099	217	9	the	the	DET
cana-6099	217	10	axial	axial	ADJ
cana-6099	217	11	direction	direction	NOUN
cana-6099	217	12	,	,	PUNCT
cana-6099	217	13	potentially	potentially	ADV
cana-6099	217	14	revealing	reveal	VERB
cana-6099	217	15	further	further	ADJ
cana-6099	217	16	insights	insight	NOUN
cana-6099	217	17	into	into	ADP
cana-6099	217	18	the	the	DET
cana-6099	217	19	behaviour	behaviour	NOUN
cana-6099	217	20	of	of	ADP
cana-6099	217	21	such	such	ADJ
cana-6099	217	22	materials	material	NOUN
cana-6099	217	23	.	.	PUNCT
cana-6099	218	1	author	author	NOUN
cana-6099	218	2	contributions	contribution	NOUN
cana-6099	218	3	all	all	DET
cana-6099	218	4	authors	author	NOUN
cana-6099	218	5	reviewed	review	VERB
cana-6099	218	6	the	the	DET
cana-6099	218	7	manuscript	manuscript	NOUN
cana-6099	218	8	.	.	PUNCT
cana-6099	219	1	data	datum	NOUN
cana-6099	219	2	availability	availability	NOUN
cana-6099	219	3	no	no	DET
cana-6099	219	4	datasets	dataset	NOUN
cana-6099	219	5	were	be	AUX
cana-6099	219	6	generated	generate	VERB
cana-6099	219	7	or	or	CCONJ
cana-6099	219	8	analysed	analyse	VERB
cana-6099	219	9	during	during	ADP
cana-6099	219	10	the	the	DET
cana-6099	219	11	current	current	ADJ
cana-6099	219	12	study	study	NOUN
cana-6099	219	13	.	.	PUNCT
cana-6099	220	1	declarations	declaration	NOUN
cana-6099	220	2	competing	compete	VERB
cana-6099	220	3	interests	interest	NOUN
cana-6099	220	4	the	the	DET
cana-6099	220	5	authors	author	NOUN
cana-6099	220	6	have	have	AUX
cana-6099	220	7	disclosed	disclose	VERB
cana-6099	220	8	that	that	SCONJ
cana-6099	220	9	they	they	PRON
cana-6099	220	10	have	have	VERB
cana-6099	220	11	no	no	DET
cana-6099	220	12	potential	potential	ADJ
cana-6099	220	13	conflicts	conflict	NOUN
cana-6099	220	14	of	of	ADP
cana-6099	220	15	interest	interest	NOUN
cana-6099	220	16	and	and	CCONJ
cana-6099	220	17	were	be	AUX
cana-6099	220	18	not	not	PART
cana-6099	220	19	aided	aid	VERB
cana-6099	220	20	by	by	ADP
cana-6099	220	21	any	any	DET
cana-6099	220	22	funding	funding	NOUN
cana-6099	220	23	in	in	ADP
cana-6099	220	24	the	the	DET
cana-6099	220	25	preparation	preparation	NOUN
cana-6099	220	26	of	of	ADP
cana-6099	220	27	this	this	DET
cana-6099	220	28	manuscript	manuscript	NOUN
cana-6099	220	29	.	.	PUNCT
cana-6099	221	1	references	reference	NOUN
cana-6099	221	2	1	1	NUM
cana-6099	221	3	.	.	PUNCT
cana-6099	222	1	y.	y.	PROPN
cana-6099	222	2	z.	z.	PROPN
cana-6099	222	3	povstenko	povstenko	PROPN
cana-6099	222	4	,	,	PUNCT
cana-6099	222	5	“	"	PUNCT
cana-6099	222	6	fractional	fractional	ADJ
cana-6099	222	7	heat	heat	NOUN
cana-6099	222	8	conduction	conduction	NOUN
cana-6099	222	9	equation	equation	NOUN
cana-6099	222	10	and	and	CCONJ
cana-6099	222	11	associated	associate	VERB
cana-6099	222	12	thermal	thermal	ADJ
cana-6099	222	13	stresses	stress	NOUN
cana-6099	222	14	”	"	PUNCT
cana-6099	222	15	,	,	PUNCT
cana-6099	222	16	journal	journal	NOUN
cana-6099	222	17	of	of	ADP
cana-6099	222	18	thermal	thermal	ADJ
cana-6099	222	19	stresses	stress	NOUN
cana-6099	222	20	,	,	PUNCT
cana-6099	222	21	28	28	NUM
cana-6099	222	22	,	,	PUNCT
cana-6099	222	23	83–102	83–102	NUM
cana-6099	222	24	,	,	PUNCT
cana-6099	222	25	2005	2005	NUM
cana-6099	222	26	.	.	PUNCT
cana-6099	223	1	2	2	NUM
cana-6099	223	2	.	.	PUNCT
cana-6099	223	3	s.	s.	PROPN
cana-6099	223	4	mukhopadhay	mukhopadhay	PROPN
cana-6099	223	5	,	,	PUNCT
cana-6099	223	6	r.	r.	PROPN
cana-6099	223	7	kumar	kumar	PROPN
cana-6099	223	8	,	,	PUNCT
cana-6099	223	9	“	"	PUNCT
cana-6099	223	10	a	a	DET
cana-6099	223	11	study	study	NOUN
cana-6099	223	12	of	of	ADP
cana-6099	223	13	generalized	generalized	ADJ
cana-6099	223	14	thermoelastic	thermoelastic	ADJ
cana-6099	223	15	interactions	interaction	NOUN
cana-6099	223	16	in	in	ADP
cana-6099	223	17	an	an	DET
cana-6099	223	18	unbounded	unbounded	ADJ
cana-6099	223	19	medium	medium	NOUN
cana-6099	223	20	with	with	ADP
cana-6099	223	21	a	a	DET
cana-6099	223	22	spherical	spherical	ADJ
cana-6099	223	23	cavity	cavity	NOUN
cana-6099	223	24	,	,	PUNCT
cana-6099	223	25	computers	computer	NOUN
cana-6099	223	26	and	and	CCONJ
cana-6099	223	27	mathematics	mathematic	NOUN
cana-6099	223	28	with	with	ADP
cana-6099	223	29	applications	application	NOUN
cana-6099	223	30	,	,	PUNCT
cana-6099	223	31	56,2329—2339	56,2329—2339	NUM
cana-6099	223	32	,	,	PUNCT
cana-6099	223	33	2008	2008	NUM
cana-6099	223	34	.	.	PUNCT
cana-6099	224	1	3	3	X
cana-6099	224	2	.	.	X
cana-6099	224	3	y.	y.	PROPN
cana-6099	224	4	z.	z.	PROPN
cana-6099	224	5	povstenko	povstenko	PROPN
cana-6099	224	6	,	,	PUNCT
cana-6099	224	7	“	"	PUNCT
cana-6099	224	8	thermoelasticity	thermoelasticity	NOUN
cana-6099	224	9	that	that	PRON
cana-6099	224	10	uses	use	VERB
cana-6099	224	11	fractional	fractional	ADJ
cana-6099	224	12	heat	heat	NOUN
cana-6099	224	13	conduction	conduction	NOUN
cana-6099	224	14	equation	equation	NOUN
cana-6099	224	15	”	"	PUNCT
cana-6099	224	16	,	,	PUNCT
cana-6099	224	17	j.	j.	PROPN
cana-6099	224	18	math	math	PROPN
cana-6099	224	19	.	.	PUNCT
cana-6099	225	1	science	science	NOUN
cana-6099	225	2	,	,	PUNCT
cana-6099	225	3	162	162	NUM
cana-6099	225	4	,	,	PUNCT
cana-6099	225	5	296–305	296–305	NUM
cana-6099	225	6	,	,	PUNCT
cana-6099	225	7	2009	2009	NUM
cana-6099	225	8	.	.	PUNCT
cana-6099	226	1	4	4	NUM
cana-6099	226	2	.	.	X
cana-6099	226	3	a.	a.	NOUN
cana-6099	226	4	kar	kar	PROPN
cana-6099	226	5	and	and	CCONJ
cana-6099	226	6	m.	m.	PROPN
cana-6099	226	7	kanoria	kanoria	PROPN
cana-6099	226	8	,	,	PUNCT
cana-6099	226	9	“	"	PUNCT
cana-6099	226	10	generalized	generalized	ADJ
cana-6099	226	11	thermoelasticity	thermoelasticity	NOUN
cana-6099	226	12	problem	problem	NOUN
cana-6099	226	13	of	of	ADP
cana-6099	226	14	a	a	DET
cana-6099	226	15	hollow	hollow	ADJ
cana-6099	226	16	sphere	sphere	NOUN
cana-6099	226	17	under	under	ADP
cana-6099	226	18	thermal	thermal	ADJ
cana-6099	226	19	shock	shock	NOUN
cana-6099	226	20	”	"	PUNCT
cana-6099	226	21	,	,	PUNCT
cana-6099	226	22	european	european	PROPN
cana-6099	226	23	journal	journal	PROPN
cana-6099	226	24	of	of	ADP
cana-6099	226	25	pure	pure	ADJ
cana-6099	226	26	and	and	CCONJ
cana-6099	226	27	applied	applied	ADJ
cana-6099	226	28	mathematics	mathematic	NOUN
cana-6099	226	29	,	,	PUNCT
cana-6099	226	30	2	2	NUM
cana-6099	226	31	,	,	PUNCT
cana-6099	226	32	125—146	125—146	NUM
cana-6099	226	33	,	,	PUNCT
cana-6099	226	34	2009	2009	NUM
cana-6099	226	35	.	.	PUNCT
cana-6099	227	1	5	5	NUM
cana-6099	227	2	.	.	PUNCT
cana-6099	227	3	h.	h.	PROPN
cana-6099	227	4	h.	h.	PROPN
cana-6099	227	5	sherief	sherief	PROPN
cana-6099	227	6	,	,	PUNCT
cana-6099	227	7	a.	a.	PROPN
cana-6099	227	8	el	el	PROPN
cana-6099	227	9	-	-	PUNCT
cana-6099	227	10	said	say	VERB
cana-6099	227	11	,	,	PUNCT
cana-6099	227	12	a.	a.	PROPN
cana-6099	227	13	abd	abd	PROPN
cana-6099	227	14	el	el	PROPN
cana-6099	227	15	-	-	PUNCT
cana-6099	227	16	latief	latief	NOUN
cana-6099	227	17	,	,	PUNCT
cana-6099	227	18	“	"	PUNCT
cana-6099	227	19	fractional	fractional	ADJ
cana-6099	227	20	order	order	NOUN
cana-6099	227	21	theory	theory	NOUN
cana-6099	227	22	of	of	ADP
cana-6099	227	23	thermoelasticity	thermoelasticity	NOUN
cana-6099	227	24	”	"	PUNCT
cana-6099	227	25	,	,	PUNCT
cana-6099	227	26	international	international	ADJ
cana-6099	227	27	journal	journal	NOUN
cana-6099	227	28	of	of	ADP
cana-6099	227	29	solids	solid	NOUN
cana-6099	227	30	and	and	CCONJ
cana-6099	227	31	structures	structure	NOUN
cana-6099	227	32	,	,	PUNCT
cana-6099	227	33	47	47	NUM
cana-6099	227	34	,	,	PUNCT
cana-6099	227	35	269–275	269–275	NUM
cana-6099	227	36	,	,	PUNCT
cana-6099	227	37	2010	2010	NUM
cana-6099	227	38	.	.	PUNCT
cana-6099	228	1	6	6	NUM
cana-6099	228	2	.	.	PUNCT
cana-6099	228	3	a.	a.	PROPN
cana-6099	228	4	sur	sur	PROPN
cana-6099	228	5	,	,	PUNCT
cana-6099	228	6	m.	m.	NOUN
cana-6099	228	7	kanoria	kanoria	PROPN
cana-6099	228	8	,	,	PUNCT
cana-6099	228	9	“	"	PUNCT
cana-6099	228	10	fractional	fractional	ADJ
cana-6099	228	11	order	order	NOUN
cana-6099	228	12	two	two	NUM
cana-6099	228	13	-	-	PUNCT
cana-6099	228	14	temperature	temperature	NOUN
cana-6099	228	15	thermoelasticity	thermoelasticity	NOUN
cana-6099	228	16	with	with	ADP
cana-6099	228	17	wave	wave	NOUN
cana-6099	228	18	speed	speed	NOUN
cana-6099	228	19	”	"	PUNCT
cana-6099	228	20	,	,	PUNCT
cana-6099	228	21	acta	acta	PROPN
cana-6099	228	22	mechanica	mechanica	PROPN
cana-6099	228	23	,	,	PUNCT
cana-6099	228	24	223	223	NUM
cana-6099	228	25	,	,	PUNCT
cana-6099	228	26	2685–2701	2685–2701	NUM
cana-6099	228	27	,	,	PUNCT
cana-6099	228	28	2012	2012	NUM
cana-6099	228	29	.	.	PUNCT
cana-6099	229	1	communications	communication	NOUN
cana-6099	229	2	on	on	ADP
cana-6099	229	3	applied	apply	VERB
cana-6099	229	4	nonlinear	nonlinear	ADJ
cana-6099	229	5	analysis	analysis	NOUN
cana-6099	229	6	issn	issn	NOUN
cana-6099	229	7	:	:	PUNCT
cana-6099	229	8	1074	1074	NUM
cana-6099	229	9	-	-	PUNCT
cana-6099	229	10	133x	133x	NUM
cana-6099	229	11	vol	vol	VERB
cana-6099	229	12	32	32	NUM
cana-6099	229	13	no	no	NOUN
cana-6099	229	14	.	.	PUNCT
cana-6099	230	1	10s	10	NOUN
cana-6099	230	2	(	(	PUNCT
cana-6099	230	3	2025	2025	NUM
cana-6099	230	4	)	)	PUNCT
cana-6099	230	5	3371	3371	NUM
cana-6099	230	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	230	7	7	7	X
cana-6099	230	8	.	.	PUNCT
cana-6099	230	9	h.	h.	PROPN
cana-6099	230	10	m.	m.	PROPN
cana-6099	230	11	youssef	youssef	PROPN
cana-6099	230	12	,	,	PUNCT
cana-6099	230	13	“	"	PUNCT
cana-6099	230	14	two	two	NUM
cana-6099	230	15	-	-	PUNCT
cana-6099	230	16	dimensional	dimensional	ADJ
cana-6099	230	17	thermal	thermal	ADJ
cana-6099	230	18	shock	shock	NOUN
cana-6099	230	19	problem	problem	NOUN
cana-6099	230	20	of	of	ADP
cana-6099	230	21	fractional	fractional	ADJ
cana-6099	230	22	order	order	NOUN
cana-6099	230	23	generalized	generalized	ADJ
cana-6099	230	24	thermoelasticity	thermoelasticity	NOUN
cana-6099	230	25	”	"	PUNCT
cana-6099	230	26	,	,	PUNCT
cana-6099	230	27	acta	acta	PROPN
cana-6099	230	28	mech	mech	PROPN
cana-6099	230	29	,	,	PUNCT
cana-6099	230	30	223	223	NUM
cana-6099	230	31	,	,	PUNCT
cana-6099	230	32	1219–1231	1219–1231	NUM
cana-6099	230	33	,	,	PUNCT
cana-6099	230	34	2012	2012	NUM
cana-6099	230	35	.	.	PUNCT
cana-6099	231	1	8	8	NUM
cana-6099	231	2	.	.	PUNCT
cana-6099	231	3	k.	k.	PROPN
cana-6099	231	4	r.	r.	PROPN
cana-6099	231	5	gaikwad	gaikwad	PROPN
cana-6099	231	6	,	,	PUNCT
cana-6099	231	7	k.	k.	PROPN
cana-6099	232	1	p.	p.	PROPN
cana-6099	232	2	ghadle	ghadle	PROPN
cana-6099	232	3	,	,	PUNCT
cana-6099	232	4	“	"	PUNCT
cana-6099	232	5	on	on	ADP
cana-6099	232	6	a	a	DET
cana-6099	232	7	certain	certain	ADJ
cana-6099	232	8	thermoelastic	thermoelastic	ADJ
cana-6099	232	9	problem	problem	NOUN
cana-6099	232	10	of	of	ADP
cana-6099	232	11	temperature	temperature	NOUN
cana-6099	232	12	and	and	CCONJ
cana-6099	232	13	thermal	thermal	ADJ
cana-6099	232	14	stresses	stress	NOUN
cana-6099	232	15	in	in	ADP
cana-6099	232	16	a	a	DET
cana-6099	232	17	thick	thick	ADJ
cana-6099	232	18	circular	circular	ADJ
cana-6099	232	19	plate	plate	NOUN
cana-6099	232	20	”	"	PUNCT
cana-6099	232	21	,	,	PUNCT
cana-6099	232	22	australian	australian	ADJ
cana-6099	232	23	journal	journal	NOUN
cana-6099	232	24	of	of	ADP
cana-6099	232	25	basic	basic	ADJ
cana-6099	232	26	and	and	CCONJ
cana-6099	232	27	applied	applied	ADJ
cana-6099	232	28	sciences	science	NOUN
cana-6099	232	29	,	,	PUNCT
cana-6099	232	30	6	6	NUM
cana-6099	232	31	,	,	PUNCT
cana-6099	232	32	34–48	34–48	NUM
cana-6099	232	33	,	,	PUNCT
cana-6099	232	34	2012	2012	NUM
cana-6099	232	35	.	.	PUNCT
cana-6099	233	1	9	9	NUM
cana-6099	233	2	.	.	X
cana-6099	233	3	k.	k.	PROPN
cana-6099	233	4	r.	r.	PROPN
cana-6099	233	5	gaikwad	gaikwad	PROPN
cana-6099	233	6	,	,	PUNCT
cana-6099	233	7	k.	k.	PROPN
cana-6099	234	1	p.	p.	PROPN
cana-6099	234	2	ghadle	ghadle	PROPN
cana-6099	234	3	,	,	PUNCT
cana-6099	234	4	“	"	PUNCT
cana-6099	234	5	nonhomogeneous	nonhomogeneous	ADJ
cana-6099	234	6	heat	heat	NOUN
cana-6099	234	7	conduction	conduction	NOUN
cana-6099	234	8	problem	problem	NOUN
cana-6099	234	9	and	and	CCONJ
cana-6099	234	10	its	its	PRON
cana-6099	234	11	thermal	thermal	ADJ
cana-6099	234	12	deflection	deflection	NOUN
cana-6099	234	13	due	due	ADP
cana-6099	234	14	to	to	ADP
cana-6099	234	15	internal	internal	ADJ
cana-6099	234	16	heat	heat	NOUN
cana-6099	234	17	generation	generation	NOUN
cana-6099	234	18	in	in	ADP
cana-6099	234	19	a	a	DET
cana-6099	234	20	thin	thin	ADJ
cana-6099	234	21	hollow	hollow	ADJ
cana-6099	234	22	circular	circular	ADJ
cana-6099	234	23	disk	disk	NOUN
cana-6099	234	24	”	"	PUNCT
cana-6099	234	25	,	,	PUNCT
cana-6099	234	26	journal	journal	NOUN
cana-6099	234	27	of	of	ADP
cana-6099	234	28	thermal	thermal	ADJ
cana-6099	234	29	stresses	stress	NOUN
cana-6099	234	30	,	,	PUNCT
cana-6099	234	31	35	35	NUM
cana-6099	234	32	,	,	PUNCT
cana-6099	234	33	485–498	485–498	NUM
cana-6099	234	34	,	,	PUNCT
cana-6099	234	35	2012	2012	NUM
cana-6099	234	36	.	.	PUNCT
cana-6099	235	1	10	10	NUM
cana-6099	235	2	.	.	PUNCT
cana-6099	235	3	k.	k.	PROPN
cana-6099	235	4	r.	r.	PROPN
cana-6099	235	5	gaikwad	gaikwad	PROPN
cana-6099	235	6	,	,	PUNCT
cana-6099	235	7	“	"	PUNCT
cana-6099	235	8	analysis	analysis	NOUN
cana-6099	235	9	of	of	ADP
cana-6099	235	10	thermoelastic	thermoelastic	ADJ
cana-6099	235	11	deformation	deformation	NOUN
cana-6099	235	12	of	of	ADP
cana-6099	235	13	a	a	DET
cana-6099	235	14	thin	thin	ADJ
cana-6099	235	15	hollow	hollow	ADJ
cana-6099	235	16	circular	circular	ADJ
cana-6099	235	17	disk	disk	NOUN
cana-6099	235	18	due	due	ADP
cana-6099	235	19	to	to	PART
cana-6099	235	20	partially	partially	ADV
cana-6099	235	21	distributed	distribute	VERB
cana-6099	235	22	heat	heat	NOUN
cana-6099	235	23	supply	supply	NOUN
cana-6099	235	24	”	"	PUNCT
cana-6099	235	25	,	,	PUNCT
cana-6099	235	26	journal	journal	NOUN
cana-6099	235	27	of	of	ADP
cana-6099	235	28	thermal	thermal	ADJ
cana-6099	235	29	stresses	stress	NOUN
cana-6099	235	30	,	,	PUNCT
cana-6099	235	31	36	36	NUM
cana-6099	235	32	,	,	PUNCT
cana-6099	235	33	207–224	207–224	NUM
cana-6099	235	34	,	,	PUNCT
cana-6099	235	35	2013	2013	NUM
cana-6099	235	36	.	.	PUNCT
cana-6099	236	1	11	11	NUM
cana-6099	236	2	.	.	PUNCT
cana-6099	236	3	a.	a.	PROPN
cana-6099	236	4	sur	sur	PROPN
cana-6099	236	5	,	,	PUNCT
cana-6099	236	6	m.	m.	NOUN
cana-6099	236	7	kanoria	kanoria	PROPN
cana-6099	236	8	,	,	PUNCT
cana-6099	236	9	“	"	PUNCT
cana-6099	236	10	fractional	fractional	ADJ
cana-6099	236	11	order	order	NOUN
cana-6099	236	12	generalized	generalize	VERB
cana-6099	236	13	thermoelastic	thermoelastic	ADJ
cana-6099	236	14	functionally	functionally	ADV
cana-6099	236	15	graded	grade	VERB
cana-6099	236	16	solid	solid	ADJ
cana-6099	236	17	with	with	ADP
cana-6099	236	18	variable	variable	ADJ
cana-6099	236	19	material	material	NOUN
cana-6099	236	20	properties	property	NOUN
cana-6099	236	21	”	"	PUNCT
cana-6099	236	22	,	,	PUNCT
cana-6099	236	23	journal	journal	NOUN
cana-6099	236	24	of	of	ADP
cana-6099	236	25	solid	solid	ADJ
cana-6099	236	26	mechanics	mechanic	NOUN
cana-6099	236	27	,	,	PUNCT
cana-6099	236	28	6	6	NUM
cana-6099	236	29	,	,	PUNCT
cana-6099	236	30	54–69	54–69	NUM
cana-6099	236	31	,	,	PUNCT
cana-6099	236	32	2014	2014	NUM
cana-6099	236	33	.	.	PUNCT
cana-6099	237	1	12	12	NUM
cana-6099	237	2	.	.	PUNCT
cana-6099	238	1	e.	e.	PROPN
cana-6099	238	2	m.	m.	PROPN
cana-6099	238	3	hussain	hussain	PROPN
cana-6099	238	4	,	,	PUNCT
cana-6099	238	5	“	"	PUNCT
cana-6099	238	6	fractional	fractional	ADJ
cana-6099	238	7	order	order	NOUN
cana-6099	238	8	thermoelastic	thermoelastic	ADJ
cana-6099	238	9	problem	problem	NOUN
cana-6099	238	10	for	for	ADP
cana-6099	238	11	an	an	DET
cana-6099	238	12	infinitely	infinitely	ADV
cana-6099	238	13	long	long	ADJ
cana-6099	238	14	solid	solid	ADJ
cana-6099	238	15	circular	circular	ADJ
cana-6099	238	16	cylinder	cylinder	NOUN
cana-6099	238	17	”	"	PUNCT
cana-6099	238	18	,	,	PUNCT
cana-6099	238	19	journal	journal	NOUN
cana-6099	238	20	of	of	ADP
cana-6099	238	21	thermal	thermal	ADJ
cana-6099	238	22	stresses	stress	NOUN
cana-6099	238	23	,	,	PUNCT
cana-6099	238	24	38	38	NUM
cana-6099	238	25	,	,	PUNCT
cana-6099	238	26	133—145	133—145	NOUN
cana-6099	238	27	,	,	PUNCT
cana-6099	238	28	2014	2014	NUM
cana-6099	238	29	.	.	PUNCT
cana-6099	239	1	13	13	NUM
cana-6099	239	2	.	.	PUNCT
cana-6099	239	3	w.	w.	PROPN
cana-6099	239	4	raslan	raslan	PROPN
cana-6099	239	5	,	,	PUNCT
cana-6099	239	6	“	"	PUNCT
cana-6099	239	7	application	application	NOUN
cana-6099	239	8	of	of	ADP
cana-6099	239	9	fractional	fractional	ADJ
cana-6099	239	10	order	order	NOUN
cana-6099	239	11	theory	theory	NOUN
cana-6099	239	12	of	of	ADP
cana-6099	239	13	thermoelasticity	thermoelasticity	NOUN
cana-6099	239	14	to	to	ADP
cana-6099	239	15	a	a	DET
cana-6099	239	16	1d	1d	NUM
cana-6099	239	17	problem	problem	NOUN
cana-6099	239	18	for	for	ADP
cana-6099	239	19	a	a	DET
cana-6099	239	20	cylindrical	cylindrical	ADJ
cana-6099	239	21	cavity	cavity	NOUN
cana-6099	239	22	”	"	PUNCT
cana-6099	239	23	,	,	PUNCT
cana-6099	239	24	arch	arch	NOUN
cana-6099	239	25	.	.	PUNCT
cana-6099	240	1	mech	mech	PROPN
cana-6099	240	2	,	,	PUNCT
cana-6099	240	3	66	66	NUM
cana-6099	240	4	,	,	PUNCT
cana-6099	240	5	257–267	257–267	NUM
cana-6099	240	6	,	,	PUNCT
cana-6099	240	7	2014	2014	NUM
cana-6099	240	8	.	.	PUNCT
cana-6099	241	1	14	14	NUM
cana-6099	241	2	.	.	PUNCT
cana-6099	242	1	k.	k.	PROPN
cana-6099	242	2	r.	r.	PROPN
cana-6099	242	3	gaikwad	gaikwad	PROPN
cana-6099	242	4	,	,	PUNCT
cana-6099	242	5	“	"	PUNCT
cana-6099	242	6	mathematical	mathematical	ADJ
cana-6099	242	7	modelling	modelling	NOUN
cana-6099	242	8	of	of	ADP
cana-6099	242	9	thermoelastic	thermoelastic	ADJ
cana-6099	242	10	problem	problem	NOUN
cana-6099	242	11	in	in	ADP
cana-6099	242	12	a	a	DET
cana-6099	242	13	circular	circular	ADJ
cana-6099	242	14	sector	sector	NOUN
cana-6099	242	15	disk	disk	NOUN
cana-6099	242	16	subject	subject	NOUN
cana-6099	242	17	to	to	ADP
cana-6099	242	18	heat	heat	NOUN
cana-6099	242	19	generation	generation	NOUN
cana-6099	242	20	”	"	PUNCT
cana-6099	242	21	,	,	PUNCT
cana-6099	242	22	int	int	NOUN
cana-6099	242	23	.	.	PUNCT
cana-6099	243	1	j.	j.	PROPN
cana-6099	243	2	adv	adv	PROPN
cana-6099	243	3	.	.	PUNCT
cana-6099	243	4	appl	appl	PROPN
cana-6099	243	5	.	.	PROPN
cana-6099	243	6	math	math	PROPN
cana-6099	243	7	.	.	PUNCT
cana-6099	244	1	and	and	CCONJ
cana-6099	244	2	mech	mech	PROPN
cana-6099	244	3	.	.	PUNCT
cana-6099	244	4	,	,	PUNCT
cana-6099	244	5	2	2	NUM
cana-6099	244	6	,	,	PUNCT
cana-6099	244	7	183–195	183–195	NUM
cana-6099	244	8	,	,	PUNCT
cana-6099	244	9	2015	2015	NUM
cana-6099	244	10	.	.	PUNCT
cana-6099	245	1	15	15	NUM
cana-6099	245	2	.	.	PUNCT
cana-6099	245	3	a.	a.	NOUN
cana-6099	245	4	bayat	bayat	PROPN
cana-6099	245	5	,	,	PUNCT
cana-6099	245	6	h.	h.	PROPN
cana-6099	245	7	moosavi	moosavi	PROPN
cana-6099	245	8	,	,	PUNCT
cana-6099	245	9	y.	y.	PROPN
cana-6099	245	10	bayat	bayat	PROPN
cana-6099	245	11	,	,	PUNCT
cana-6099	245	12	“	"	PUNCT
cana-6099	245	13	thermo	thermo	NOUN
cana-6099	245	14	-	-	PUNCT
cana-6099	245	15	mechanical	mechanical	ADJ
cana-6099	245	16	analysis	analysis	NOUN
cana-6099	245	17	of	of	ADP
cana-6099	245	18	functionally	functionally	ADV
cana-6099	245	19	graded	grade	VERB
cana-6099	245	20	thick	thick	ADJ
cana-6099	245	21	spheres	sphere	NOUN
cana-6099	245	22	with	with	ADP
cana-6099	245	23	linearly	linearly	ADJ
cana-6099	245	24	time	time	NOUN
cana-6099	245	25	-	-	PUNCT
cana-6099	245	26	dependent	dependent	ADJ
cana-6099	245	27	temperature	temperature	NOUN
cana-6099	245	28	”	"	PUNCT
cana-6099	245	29	,	,	PUNCT
cana-6099	245	30	scientia	scientia	PROPN
cana-6099	245	31	iranica	iranica	PROPN
cana-6099	245	32	b.	b.	PROPN
cana-6099	245	33	,	,	PUNCT
cana-6099	245	34	22	22	NUM
cana-6099	245	35	,	,	PUNCT
cana-6099	245	36	1801	1801	NUM
cana-6099	245	37	—	—	PUNCT
cana-6099	245	38	1812	1812	NUM
cana-6099	245	39	,	,	PUNCT
cana-6099	245	40	2015	2015	NUM
cana-6099	245	41	.	.	PUNCT
cana-6099	246	1	16	16	NUM
cana-6099	246	2	.	.	PUNCT
cana-6099	247	1	w.	w.	PROPN
cana-6099	247	2	raslan	raslan	PROPN
cana-6099	247	3	,	,	PUNCT
cana-6099	247	4	“	"	PUNCT
cana-6099	247	5	application	application	NOUN
cana-6099	247	6	of	of	ADP
cana-6099	247	7	fractional	fractional	ADJ
cana-6099	247	8	order	order	NOUN
cana-6099	247	9	theory	theory	NOUN
cana-6099	247	10	of	of	ADP
cana-6099	247	11	thermoelasticity	thermoelasticity	NOUN
cana-6099	247	12	in	in	ADP
cana-6099	247	13	a	a	DET
cana-6099	247	14	thick	thick	ADJ
cana-6099	247	15	plate	plate	NOUN
cana-6099	247	16	under	under	ADP
cana-6099	247	17	axisymmetric	axisymmetric	ADJ
cana-6099	247	18	temperature	temperature	NOUN
cana-6099	247	19	distribution	distribution	NOUN
cana-6099	247	20	”	"	PUNCT
cana-6099	247	21	,	,	PUNCT
cana-6099	247	22	journal	journal	NOUN
cana-6099	247	23	of	of	ADP
cana-6099	247	24	thermal	thermal	ADJ
cana-6099	247	25	stresses	stress	NOUN
cana-6099	247	26	,	,	PUNCT
cana-6099	247	27	38	38	NUM
cana-6099	247	28	,	,	PUNCT
cana-6099	247	29	733–743	733–743	NUM
cana-6099	247	30	,	,	PUNCT
cana-6099	247	31	2015	2015	NUM
cana-6099	247	32	.	.	PUNCT
cana-6099	248	1	17	17	NUM
cana-6099	248	2	.	.	PUNCT
cana-6099	249	1	j.	j.	PROPN
cana-6099	249	2	j.	j.	PROPN
cana-6099	249	3	tripathi	tripathi	PROPN
cana-6099	249	4	,	,	PUNCT
cana-6099	249	5	g.	g.	PROPN
cana-6099	249	6	d.	d.	PROPN
cana-6099	249	7	kedar	kedar	PROPN
cana-6099	249	8	,	,	PUNCT
cana-6099	249	9	k.	k.	PROPN
cana-6099	249	10	c.	c.	PROPN
cana-6099	249	11	deshmukh	deshmukh	PROPN
cana-6099	249	12	,	,	PUNCT
cana-6099	249	13	“	"	PUNCT
cana-6099	249	14	generalized	generalize	VERB
cana-6099	249	15	thermoelastic	thermoelastic	ADJ
cana-6099	249	16	diffusion	diffusion	NOUN
cana-6099	249	17	problem	problem	NOUN
cana-6099	249	18	in	in	ADP
cana-6099	249	19	a	a	DET
cana-6099	249	20	thick	thick	ADJ
cana-6099	249	21	circular	circular	ADJ
cana-6099	249	22	plate	plate	NOUN
cana-6099	249	23	with	with	ADP
cana-6099	249	24	axisymmetric	axisymmetric	ADJ
cana-6099	249	25	heat	heat	NOUN
cana-6099	249	26	supply	supply	NOUN
cana-6099	249	27	”	"	PUNCT
cana-6099	249	28	,	,	PUNCT
cana-6099	249	29	acta	acta	PROPN
cana-6099	249	30	mechanica	mechanica	PROPN
cana-6099	249	31	,	,	PUNCT
cana-6099	249	32	226	226	NUM
cana-6099	249	33	,	,	PUNCT
cana-6099	249	34	2121–2134	2121–2134	NUM
cana-6099	249	35	,	,	PUNCT
cana-6099	249	36	2015	2015	NUM
cana-6099	249	37	.	.	PUNCT
cana-6099	250	1	18	18	NUM
cana-6099	250	2	.	.	PUNCT
cana-6099	250	3	m.	m.	NOUN
cana-6099	250	4	a.	a.	PROPN
cana-6099	250	5	ezzat	ezzat	PROPN
cana-6099	250	6	,	,	PUNCT
cana-6099	250	7	a.	a.	NOUN
cana-6099	250	8	karamany	karamany	PROPN
cana-6099	250	9	,	,	PUNCT
cana-6099	250	10	a.	a.	PROPN
cana-6099	250	11	a.	a.	PROPN
cana-6099	250	12	el	el	PROPN
cana-6099	250	13	-	-	PUNCT
cana-6099	250	14	bary	bary	NOUN
cana-6099	250	15	,	,	PUNCT
cana-6099	250	16	“	"	PUNCT
cana-6099	250	17	application	application	NOUN
cana-6099	250	18	of	of	ADP
cana-6099	250	19	fractional	fractional	ADJ
cana-6099	250	20	order	order	NOUN
cana-6099	250	21	theory	theory	NOUN
cana-6099	250	22	of	of	ADP
cana-6099	250	23	thermoelasticity	thermoelasticity	NOUN
cana-6099	250	24	to	to	ADP
cana-6099	250	25	3d	3d	NUM
cana-6099	250	26	timedependent	timedependent	NOUN
cana-6099	250	27	thermal	thermal	ADJ
cana-6099	250	28	shock	shock	NOUN
cana-6099	250	29	problem	problem	NOUN
cana-6099	250	30	for	for	ADP
cana-6099	250	31	a	a	DET
cana-6099	250	32	half	half	ADJ
cana-6099	250	33	-	-	PUNCT
cana-6099	250	34	space	space	NOUN
cana-6099	250	35	”	"	PUNCT
cana-6099	250	36	,	,	PUNCT
cana-6099	250	37	mechanics	mechanic	NOUN
cana-6099	250	38	of	of	ADP
cana-6099	250	39	advanced	advanced	ADJ
cana-6099	250	40	materials	material	NOUN
cana-6099	250	41	and	and	CCONJ
cana-6099	250	42	structures	structure	NOUN
cana-6099	250	43	,	,	PUNCT
cana-6099	250	44	226	226	NUM
cana-6099	250	45	,	,	PUNCT
cana-6099	250	46	27—35	27—35	NUM
cana-6099	250	47	,	,	PUNCT
cana-6099	250	48	2016	2016	NUM
cana-6099	250	49	.	.	PUNCT
cana-6099	251	1	19	19	NUM
cana-6099	251	2	.	.	PUNCT
cana-6099	251	3	k.	k.	PROPN
cana-6099	251	4	r.	r.	PROPN
cana-6099	251	5	gaikwad	gaikwad	PROPN
cana-6099	251	6	,	,	PUNCT
cana-6099	251	7	“	"	PUNCT
cana-6099	251	8	two	two	NUM
cana-6099	251	9	-	-	PUNCT
cana-6099	251	10	dimensional	dimensional	ADJ
cana-6099	251	11	steady	steady	ADJ
cana-6099	251	12	-	-	PUNCT
cana-6099	251	13	state	state	NOUN
cana-6099	251	14	temperature	temperature	NOUN
cana-6099	251	15	distribution	distribution	NOUN
cana-6099	251	16	of	of	ADP
cana-6099	251	17	a	a	DET
cana-6099	251	18	thin	thin	ADJ
cana-6099	251	19	circular	circular	ADJ
cana-6099	251	20	plate	plate	NOUN
cana-6099	251	21	due	due	ADP
cana-6099	251	22	to	to	ADP
cana-6099	251	23	uniform	uniform	ADJ
cana-6099	251	24	internal	internal	ADJ
cana-6099	251	25	energy	energy	NOUN
cana-6099	251	26	generation	generation	NOUN
cana-6099	251	27	”	"	PUNCT
cana-6099	251	28	,	,	PUNCT
cana-6099	251	29	cogent	cogent	NOUN
cana-6099	251	30	mathematics	mathematic	NOUN
cana-6099	251	31	,	,	PUNCT
cana-6099	251	32	3	3	NUM
cana-6099	251	33	,	,	PUNCT
cana-6099	251	34	1–10	1–10	NOUN
cana-6099	251	35	,	,	PUNCT
cana-6099	251	36	2016	2016	NUM
cana-6099	251	37	.	.	PUNCT
cana-6099	252	1	20	20	NUM
cana-6099	252	2	.	.	PUNCT
cana-6099	253	1	k.	k.	PROPN
cana-6099	253	2	r.	r.	PROPN
cana-6099	253	3	gaikwad	gaikwad	PROPN
cana-6099	253	4	,	,	PUNCT
cana-6099	253	5	s.	s.	PROPN
cana-6099	253	6	g.	g.	PROPN
cana-6099	253	7	khavale	khavale	PROPN
cana-6099	253	8	,	,	PUNCT
cana-6099	253	9	“	"	PUNCT
cana-6099	253	10	time	time	NOUN
cana-6099	253	11	fractional	fractional	ADJ
cana-6099	253	12	heat	heat	NOUN
cana-6099	253	13	conduction	conduction	NOUN
cana-6099	253	14	problem	problem	NOUN
cana-6099	253	15	in	in	ADP
cana-6099	253	16	a	a	DET
cana-6099	253	17	thin	thin	ADJ
cana-6099	253	18	hollow	hollow	ADJ
cana-6099	253	19	circular	circular	ADJ
cana-6099	253	20	disk	disk	NOUN
cana-6099	253	21	and	and	CCONJ
cana-6099	253	22	its	its	PRON
cana-6099	253	23	thermal	thermal	ADJ
cana-6099	253	24	deflection	deflection	NOUN
cana-6099	253	25	”	"	PUNCT
cana-6099	253	26	,	,	PUNCT
cana-6099	253	27	easy	easy	ADJ
cana-6099	253	28	chair	chair	NOUN
cana-6099	253	29	,	,	PUNCT
cana-6099	253	30	1672	1672	NUM
cana-6099	253	31	,	,	PUNCT
cana-6099	253	32	1–11	1–11	PROPN
cana-6099	253	33	,	,	PUNCT
cana-6099	253	34	2019	2019	NUM
cana-6099	253	35	.	.	PUNCT
cana-6099	254	1	21	21	NUM
cana-6099	254	2	.	.	PUNCT
cana-6099	254	3	s.	s.	PROPN
cana-6099	254	4	g.	g.	PROPN
cana-6099	254	5	khavale	khavale	PROPN
cana-6099	254	6	,	,	PUNCT
cana-6099	254	7	k.	k.	PROPN
cana-6099	254	8	r.	r.	PROPN
cana-6099	254	9	gaikwad	gaikwad	PROPN
cana-6099	254	10	,	,	PUNCT
cana-6099	254	11	“	"	PUNCT
cana-6099	254	12	generalized	generalized	ADJ
cana-6099	254	13	theory	theory	NOUN
cana-6099	254	14	of	of	ADP
cana-6099	254	15	magneto	magneto	NOUN
cana-6099	254	16	-	-	PUNCT
cana-6099	254	17	thermo	thermo	NOUN
cana-6099	254	18	-	-	PUNCT
cana-6099	254	19	viscoelastic	viscoelastic	ADJ
cana-6099	254	20	spherical	spherical	ADJ
cana-6099	254	21	cavity	cavity	NOUN
cana-6099	254	22	problem	problem	NOUN
cana-6099	254	23	under	under	ADP
cana-6099	254	24	fractional	fractional	ADJ
cana-6099	254	25	order	order	NOUN
cana-6099	254	26	derivative	derivative	NOUN
cana-6099	254	27	:	:	PUNCT
cana-6099	254	28	state	state	NOUN
cana-6099	254	29	space	space	NOUN
cana-6099	254	30	approach	approach	NOUN
cana-6099	254	31	”	"	PUNCT
cana-6099	254	32	,	,	PUNCT
cana-6099	254	33	advances	advance	NOUN
cana-6099	254	34	in	in	ADP
cana-6099	254	35	mathematics	mathematic	NOUN
cana-6099	254	36	:	:	PUNCT
cana-6099	254	37	scientific	scientific	ADJ
cana-6099	254	38	journal	journal	NOUN
cana-6099	254	39	,	,	PUNCT
cana-6099	254	40	9	9	NUM
cana-6099	254	41	,	,	PUNCT
cana-6099	254	42	9769–9780	9769–9780	NUM
cana-6099	254	43	,	,	PUNCT
cana-6099	254	44	2020	2020	NUM
cana-6099	254	45	.	.	PUNCT
cana-6099	255	1	communications	communication	NOUN
cana-6099	255	2	on	on	ADP
cana-6099	255	3	applied	apply	VERB
cana-6099	255	4	nonlinear	nonlinear	ADJ
cana-6099	255	5	analysis	analysis	NOUN
cana-6099	255	6	issn	issn	NOUN
cana-6099	255	7	:	:	PUNCT
cana-6099	255	8	1074	1074	NUM
cana-6099	255	9	-	-	PUNCT
cana-6099	255	10	133x	133x	NUM
cana-6099	255	11	vol	vol	VERB
cana-6099	255	12	32	32	NUM
cana-6099	255	13	no	no	NOUN
cana-6099	255	14	.	.	PUNCT
cana-6099	256	1	10s	10	NOUN
cana-6099	256	2	(	(	PUNCT
cana-6099	256	3	2025	2025	NUM
cana-6099	256	4	)	)	PUNCT
cana-6099	256	5	3372	3372	NUM
cana-6099	256	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	256	7	22	22	NUM
cana-6099	256	8	.	.	PUNCT
cana-6099	257	1	k.	k.	PROPN
cana-6099	257	2	r.	r.	PROPN
cana-6099	257	3	gaikwad	gaikwad	PROPN
cana-6099	257	4	,	,	PUNCT
cana-6099	257	5	s.	s.	PROPN
cana-6099	257	6	g.	g.	PROPN
cana-6099	257	7	khavale	khavale	PROPN
cana-6099	257	8	,	,	PUNCT
cana-6099	257	9	“	"	PUNCT
cana-6099	257	10	time	time	NOUN
cana-6099	257	11	fractional	fractional	ADJ
cana-6099	257	12	2d	2d	PROPN
cana-6099	257	13	thermoelastic	thermoelastic	ADJ
cana-6099	257	14	problem	problem	NOUN
cana-6099	257	15	of	of	ADP
cana-6099	257	16	thin	thin	ADJ
cana-6099	257	17	hollow	hollow	ADJ
cana-6099	257	18	circular	circular	ADJ
cana-6099	257	19	disk	disk	NOUN
cana-6099	257	20	and	and	CCONJ
cana-6099	257	21	its	its	PRON
cana-6099	257	22	associated	associated	ADJ
cana-6099	257	23	thermal	thermal	ADJ
cana-6099	257	24	stresses	stress	NOUN
cana-6099	257	25	”	"	PUNCT
cana-6099	257	26	,	,	PUNCT
cana-6099	257	27	bulletin	bulletin	NOUN
cana-6099	257	28	of	of	ADP
cana-6099	257	29	the	the	DET
cana-6099	257	30	marathwada	marathwada	PROPN
cana-6099	257	31	mathematical	mathematical	PROPN
cana-6099	257	32	society	society	NOUN
cana-6099	257	33	,	,	PUNCT
cana-6099	257	34	21(1	21(1	NUM
cana-6099	257	35	&	&	CCONJ
cana-6099	257	36	2	2	NUM
cana-6099	257	37	)	)	PUNCT
cana-6099	257	38	,	,	PUNCT
cana-6099	257	39	37-–47	37-–47	NUM
cana-6099	257	40	,	,	PUNCT
cana-6099	257	41	2020	2020	NUM
cana-6099	257	42	.	.	PUNCT
cana-6099	258	1	23	23	NUM
cana-6099	258	2	.	.	PUNCT
cana-6099	259	1	k.	k.	PROPN
cana-6099	259	2	r.	r.	PROPN
cana-6099	259	3	gaikwad	gaikwad	PROPN
cana-6099	259	4	,	,	PUNCT
cana-6099	259	5	y.	y.	PROPN
cana-6099	259	6	u.	u.	PROPN
cana-6099	259	7	naner	naner	NOUN
cana-6099	259	8	,	,	PUNCT
cana-6099	259	9	“	"	PUNCT
cana-6099	259	10	transient	transient	ADJ
cana-6099	259	11	thermoelastic	thermoelastic	ADJ
cana-6099	259	12	stress	stress	NOUN
cana-6099	259	13	analysis	analysis	NOUN
cana-6099	259	14	of	of	ADP
cana-6099	259	15	a	a	DET
cana-6099	259	16	thin	thin	ADJ
cana-6099	259	17	circular	circular	ADJ
cana-6099	259	18	plate	plate	NOUN
cana-6099	259	19	due	due	ADP
cana-6099	259	20	to	to	ADP
cana-6099	259	21	uniform	uniform	ADJ
cana-6099	259	22	internal	internal	ADJ
cana-6099	259	23	heat	heat	NOUN
cana-6099	259	24	generation	generation	NOUN
cana-6099	259	25	”	"	PUNCT
cana-6099	259	26	,	,	PUNCT
cana-6099	259	27	journal	journal	NOUN
cana-6099	259	28	of	of	ADP
cana-6099	259	29	the	the	DET
cana-6099	259	30	korean	korean	ADJ
cana-6099	259	31	society	society	NOUN
cana-6099	259	32	for	for	ADP
cana-6099	259	33	industrial	industrial	ADJ
cana-6099	259	34	and	and	CCONJ
cana-6099	259	35	applied	applied	ADJ
cana-6099	259	36	mathematics	mathematic	NOUN
cana-6099	259	37	,	,	PUNCT
cana-6099	259	38	24	24	NUM
cana-6099	259	39	,	,	PUNCT
cana-6099	259	40	293–303	293–303	NUM
cana-6099	259	41	,	,	PUNCT
cana-6099	259	42	2020	2020	NUM
cana-6099	259	43	.	.	PUNCT
cana-6099	260	1	24	24	NUM
cana-6099	260	2	.	.	PUNCT
cana-6099	260	3	k.	k.	PROPN
cana-6099	260	4	r.	r.	PROPN
cana-6099	260	5	gaikwad	gaikwad	PROPN
cana-6099	260	6	,	,	PUNCT
cana-6099	260	7	y.	y.	PROPN
cana-6099	260	8	u.	u.	PROPN
cana-6099	260	9	naner	naner	NOUN
cana-6099	260	10	,	,	PUNCT
cana-6099	260	11	“	"	PUNCT
cana-6099	260	12	analysis	analysis	NOUN
cana-6099	260	13	of	of	ADP
cana-6099	260	14	transient	transient	ADJ
cana-6099	260	15	thermoelastic	thermoelastic	ADJ
cana-6099	260	16	temperature	temperature	NOUN
cana-6099	260	17	distribution	distribution	NOUN
cana-6099	260	18	of	of	ADP
cana-6099	260	19	a	a	DET
cana-6099	260	20	thin	thin	ADJ
cana-6099	260	21	circular	circular	ADJ
cana-6099	260	22	plate	plate	NOUN
cana-6099	260	23	and	and	CCONJ
cana-6099	260	24	its	its	PRON
cana-6099	260	25	thermal	thermal	ADJ
cana-6099	260	26	deflection	deflection	NOUN
cana-6099	260	27	under	under	ADP
cana-6099	260	28	uniform	uniform	ADJ
cana-6099	260	29	heat	heat	NOUN
cana-6099	260	30	generation	generation	NOUN
cana-6099	260	31	”	"	PUNCT
cana-6099	260	32	,	,	PUNCT
cana-6099	260	33	journal	journal	NOUN
cana-6099	260	34	of	of	ADP
cana-6099	260	35	thermal	thermal	ADJ
cana-6099	260	36	stress	stress	NOUN
cana-6099	260	37	,	,	PUNCT
cana-6099	260	38	44(1	44(1	PROPN
cana-6099	260	39	)	)	PUNCT
cana-6099	260	40	,	,	PUNCT
cana-6099	260	41	75–85	75–85	NOUN
cana-6099	260	42	,	,	PUNCT
cana-6099	260	43	2021	2021	NUM
cana-6099	260	44	.	.	PUNCT
cana-6099	261	1	25	25	NUM
cana-6099	261	2	.	.	PUNCT
cana-6099	261	3	k.	k.	PROPN
cana-6099	261	4	r.	r.	PROPN
cana-6099	261	5	gaikwad	gaikwad	PROPN
cana-6099	261	6	,	,	PUNCT
cana-6099	261	7	y.	y.	PROPN
cana-6099	261	8	u.	u.	PROPN
cana-6099	261	9	naner	naner	NOUN
cana-6099	261	10	,	,	PUNCT
cana-6099	261	11	s.	s.	PROPN
cana-6099	261	12	g.	g.	PROPN
cana-6099	261	13	khavale	khavale	PROPN
cana-6099	261	14	,	,	PUNCT
cana-6099	261	15	“	"	PUNCT
cana-6099	261	16	time	time	NOUN
cana-6099	261	17	fractional	fractional	ADJ
cana-6099	261	18	thermoelastic	thermoelastic	ADJ
cana-6099	261	19	stress	stress	NOUN
cana-6099	261	20	analysis	analysis	NOUN
cana-6099	261	21	of	of	ADP
cana-6099	261	22	a	a	DET
cana-6099	261	23	thin	thin	ADJ
cana-6099	261	24	rectangular	rectangular	ADJ
cana-6099	261	25	plate	plate	NOUN
cana-6099	261	26	”	"	PUNCT
cana-6099	261	27	,	,	PUNCT
cana-6099	261	28	novyi	novyi	PROPN
cana-6099	261	29	mir	mir	PROPN
cana-6099	261	30	research	research	PROPN
cana-6099	261	31	journal	journal	PROPN
cana-6099	261	32	,	,	PUNCT
cana-6099	261	33	6(1	6(1	NUM
cana-6099	261	34	)	)	PUNCT
cana-6099	261	35	,	,	PUNCT
cana-6099	261	36	42–56	42–56	NUM
cana-6099	261	37	,	,	PUNCT
cana-6099	261	38	2021	2021	NUM
cana-6099	261	39	.	.	PUNCT
cana-6099	262	1	26	26	NUM
cana-6099	262	2	.	.	PUNCT
cana-6099	262	3	s.	s.	PROPN
cana-6099	262	4	g.	g.	PROPN
cana-6099	262	5	khavale	khavale	PROPN
cana-6099	262	6	,	,	PUNCT
cana-6099	262	7	k.	k.	PROPN
cana-6099	262	8	r.	r.	PROPN
cana-6099	262	9	gaikwad	gaikwad	PROPN
cana-6099	262	10	,	,	PUNCT
cana-6099	262	11	“	"	PUNCT
cana-6099	262	12	fractional	fractional	ADJ
cana-6099	262	13	order	order	NOUN
cana-6099	262	14	thermoelastic	thermoelastic	ADJ
cana-6099	262	15	problem	problem	NOUN
cana-6099	262	16	of	of	ADP
cana-6099	262	17	thin	thin	ADJ
cana-6099	262	18	hollow	hollow	ADJ
cana-6099	262	19	circular	circular	ADJ
cana-6099	262	20	disk	disk	NOUN
cana-6099	262	21	and	and	CCONJ
cana-6099	262	22	its	its	PRON
cana-6099	262	23	thermal	thermal	ADJ
cana-6099	262	24	stresses	stress	NOUN
cana-6099	262	25	under	under	ADP
cana-6099	262	26	axi	axi	NOUN
cana-6099	262	27	-	-	PUNCT
cana-6099	262	28	symmetric	symmetric	ADJ
cana-6099	262	29	heat	heat	NOUN
cana-6099	262	30	supply	supply	NOUN
cana-6099	262	31	”	"	PUNCT
cana-6099	262	32	,	,	PUNCT
cana-6099	262	33	design	design	NOUN
cana-6099	262	34	engineering	engineering	NOUN
cana-6099	262	35	,	,	PUNCT
cana-6099	262	36	2021(9	2021(9	NOUN
cana-6099	262	37	)	)	PUNCT
cana-6099	262	38	,	,	PUNCT
cana-6099	262	39	13851–13862	13851–13862	NUM
cana-6099	262	40	,	,	PUNCT
cana-6099	262	41	2021	2021	NUM
cana-6099	262	42	.	.	PUNCT
cana-6099	263	1	27	27	NUM
cana-6099	263	2	.	.	PUNCT
cana-6099	264	1	k.	k.	PROPN
cana-6099	264	2	r.	r.	PROPN
cana-6099	264	3	gaikwad	gaikwad	PROPN
cana-6099	264	4	,	,	PUNCT
cana-6099	264	5	v.	v.	PROPN
cana-6099	264	6	g.	g.	PROPN
cana-6099	264	7	bhandwalkar	bhandwalkar	PROPN
cana-6099	264	8	,	,	PUNCT
cana-6099	264	9	“	"	PUNCT
cana-6099	264	10	fractional	fractional	ADJ
cana-6099	264	11	order	order	NOUN
cana-6099	264	12	thermoelastic	thermoelastic	ADJ
cana-6099	264	13	problem	problem	NOUN
cana-6099	264	14	for	for	ADP
cana-6099	264	15	finite	finite	ADJ
cana-6099	264	16	piezoelectric	piezoelectric	NOUN
cana-6099	264	17	rod	rod	NOUN
cana-6099	264	18	subjected	subject	VERB
cana-6099	264	19	to	to	ADP
cana-6099	264	20	different	different	ADJ
cana-6099	264	21	types	type	NOUN
cana-6099	264	22	of	of	ADP
cana-6099	264	23	thermal	thermal	ADJ
cana-6099	264	24	loading	loading	NOUN
cana-6099	264	25	direct	direct	ADJ
cana-6099	264	26	approach	approach	NOUN
cana-6099	264	27	”	"	PUNCT
cana-6099	264	28	,	,	PUNCT
cana-6099	264	29	journal	journal	NOUN
cana-6099	264	30	of	of	ADP
cana-6099	264	31	the	the	DET
cana-6099	264	32	korean	korean	ADJ
cana-6099	264	33	society	society	NOUN
cana-6099	264	34	for	for	ADP
cana-6099	264	35	industrial	industrial	ADJ
cana-6099	264	36	and	and	CCONJ
cana-6099	264	37	applied	apply	VERB
cana-6099	264	38	mathematics	mathematic	NOUN
cana-6099	264	39	,	,	PUNCT
cana-6099	264	40	25(3	25(3	NUM
cana-6099	264	41	)	)	PUNCT
cana-6099	264	42	,	,	PUNCT
cana-6099	264	43	117-–131	117-–131	NUM
cana-6099	264	44	,	,	PUNCT
cana-6099	264	45	2021	2021	NUM
cana-6099	264	46	.	.	PUNCT
cana-6099	265	1	28	28	NUM
cana-6099	265	2	.	.	PUNCT
cana-6099	266	1	s.	s.	PROPN
cana-6099	266	2	g.	g.	PROPN
cana-6099	266	3	khavale	khavale	PROPN
cana-6099	266	4	,	,	PUNCT
cana-6099	266	5	k.	k.	PROPN
cana-6099	266	6	r.	r.	PROPN
cana-6099	266	7	gaikwad	gaikwad	PROPN
cana-6099	266	8	,	,	PUNCT
cana-6099	266	9	“	"	PUNCT
cana-6099	266	10	analysis	analysis	NOUN
cana-6099	266	11	of	of	ADP
cana-6099	266	12	non	non	ADJ
cana-6099	266	13	-	-	ADJ
cana-6099	266	14	integer	integer	ADJ
cana-6099	266	15	order	order	NOUN
cana-6099	266	16	thermoelastic	thermoelastic	ADJ
cana-6099	266	17	temperature	temperature	NOUN
cana-6099	266	18	distribution	distribution	NOUN
cana-6099	266	19	and	and	CCONJ
cana-6099	266	20	thermal	thermal	ADJ
cana-6099	266	21	deflection	deflection	NOUN
cana-6099	266	22	of	of	ADP
cana-6099	266	23	thin	thin	ADJ
cana-6099	266	24	hollow	hollow	ADJ
cana-6099	266	25	circular	circular	ADJ
cana-6099	266	26	disk	disk	NOUN
cana-6099	266	27	under	under	ADP
cana-6099	266	28	the	the	DET
cana-6099	266	29	axi	axi	NOUN
cana-6099	266	30	-	-	PUNCT
cana-6099	266	31	symmetric	symmetric	ADJ
cana-6099	266	32	heat	heat	NOUN
cana-6099	266	33	supply	supply	NOUN
cana-6099	266	34	”	"	PUNCT
cana-6099	266	35	,	,	PUNCT
cana-6099	266	36	journal	journal	NOUN
cana-6099	266	37	of	of	ADP
cana-6099	266	38	the	the	DET
cana-6099	266	39	korean	korean	ADJ
cana-6099	266	40	society	society	NOUN
cana-6099	266	41	for	for	ADP
cana-6099	266	42	industrial	industrial	ADJ
cana-6099	266	43	and	and	CCONJ
cana-6099	266	44	applied	applied	ADJ
cana-6099	266	45	mathematics	mathematic	NOUN
cana-6099	266	46	,	,	PUNCT
cana-6099	266	47	26(1	26(1	NUM
cana-6099	266	48	)	)	PUNCT
cana-6099	266	49	,	,	PUNCT
cana-6099	266	50	67-–75	67-–75	NUM
cana-6099	266	51	,	,	PUNCT
cana-6099	266	52	2022	2022	NUM
cana-6099	266	53	.	.	PUNCT
cana-6099	267	1	29	29	NUM
cana-6099	267	2	.	.	PUNCT
cana-6099	268	1	k.	k.	PROPN
cana-6099	268	2	r.	r.	PROPN
cana-6099	268	3	gaikwad	gaikwad	PROPN
cana-6099	268	4	,	,	PUNCT
cana-6099	268	5	s.	s.	PROPN
cana-6099	268	6	g.	g.	PROPN
cana-6099	268	7	khavale	khavale	PROPN
cana-6099	268	8	,	,	PUNCT
cana-6099	268	9	“	"	PUNCT
cana-6099	268	10	fractional	fractional	ADJ
cana-6099	268	11	order	order	NOUN
cana-6099	268	12	transient	transient	ADJ
cana-6099	268	13	thermoelastic	thermoelastic	ADJ
cana-6099	268	14	stress	stress	NOUN
cana-6099	268	15	analysis	analysis	NOUN
cana-6099	268	16	of	of	ADP
cana-6099	268	17	a	a	DET
cana-6099	268	18	thin	thin	ADJ
cana-6099	268	19	circular	circular	ADJ
cana-6099	268	20	sector	sector	NOUN
cana-6099	268	21	disk	disk	NOUN
cana-6099	268	22	”	"	PUNCT
cana-6099	268	23	,	,	PUNCT
cana-6099	268	24	international	international	ADJ
cana-6099	268	25	journal	journal	NOUN
cana-6099	268	26	of	of	ADP
cana-6099	268	27	thermodynamics	thermodynamic	NOUN
cana-6099	268	28	,	,	PUNCT
cana-6099	268	29	25(1	25(1	NUM
cana-6099	268	30	)	)	PUNCT
cana-6099	268	31	,	,	PUNCT
cana-6099	268	32	1-–8	1-–8	NUM
cana-6099	268	33	,	,	PUNCT
cana-6099	268	34	2022	2022	NUM
cana-6099	268	35	.	.	PUNCT
cana-6099	269	1	30	30	NUM
cana-6099	269	2	.	.	PUNCT
cana-6099	270	1	s.	s.	PROPN
cana-6099	270	2	g.	g.	PROPN
cana-6099	270	3	khavale	khavale	PROPN
cana-6099	270	4	,	,	PUNCT
cana-6099	270	5	k.	k.	PROPN
cana-6099	270	6	r.	r.	PROPN
cana-6099	270	7	gaikwad	gaikwad	PROPN
cana-6099	270	8	,	,	PUNCT
cana-6099	270	9	“	"	PUNCT
cana-6099	270	10	2d	2d	NUM
cana-6099	270	11	problem	problem	NOUN
cana-6099	270	12	for	for	ADP
cana-6099	270	13	a	a	DET
cana-6099	270	14	sphere	sphere	NOUN
cana-6099	270	15	in	in	ADP
cana-6099	270	16	the	the	DET
cana-6099	270	17	fractional	fractional	ADJ
cana-6099	270	18	order	order	NOUN
cana-6099	270	19	theory	theory	NOUN
cana-6099	270	20	thermoelasticity	thermoelasticity	NOUN
cana-6099	270	21	to	to	PART
cana-6099	270	22	axisymmetric	axisymmetric	VERB
cana-6099	270	23	temperature	temperature	NOUN
cana-6099	270	24	distribution	distribution	NOUN
cana-6099	270	25	”	"	PUNCT
cana-6099	270	26	,	,	PUNCT
cana-6099	270	27	advances	advance	NOUN
cana-6099	270	28	in	in	ADP
cana-6099	270	29	mathematics	mathematic	NOUN
cana-6099	270	30	:	:	PUNCT
cana-6099	270	31	scientific	scientific	ADJ
cana-6099	270	32	journal	journal	NOUN
cana-6099	270	33	,	,	PUNCT
cana-6099	270	34	11(1	11(1	NUM
cana-6099	270	35	)	)	PUNCT
cana-6099	270	36	,	,	PUNCT
cana-6099	270	37	1–15	1–15	NUM
cana-6099	270	38	,	,	PUNCT
cana-6099	270	39	2022	2022	NUM
cana-6099	270	40	.	.	PUNCT
cana-6099	271	1	31	31	NUM
cana-6099	271	2	.	.	PUNCT
cana-6099	272	1	s.	s.	PROPN
cana-6099	272	2	g.	g.	PROPN
cana-6099	272	3	khavale	khavale	PROPN
cana-6099	272	4	,	,	PUNCT
cana-6099	272	5	k.	k.	PROPN
cana-6099	272	6	r.	r.	PROPN
cana-6099	272	7	gaikwad	gaikwad	PROPN
cana-6099	272	8	,	,	PUNCT
cana-6099	272	9	“	"	PUNCT
cana-6099	272	10	two	two	NUM
cana-6099	272	11	-	-	PUNCT
cana-6099	272	12	dimensional	dimensional	ADJ
cana-6099	272	13	generalized	generalized	ADJ
cana-6099	272	14	magnetothermoviscoelasticity	magnetothermoviscoelasticity	NOUN
cana-6099	272	15	problem	problem	NOUN
cana-6099	272	16	for	for	ADP
cana-6099	272	17	a	a	DET
cana-6099	272	18	spherical	spherical	ADJ
cana-6099	272	19	cavity	cavity	NOUN
cana-6099	272	20	with	with	ADP
cana-6099	272	21	one	one	NUM
cana-6099	272	22	relaxation	relaxation	NOUN
cana-6099	272	23	time	time	NOUN
cana-6099	272	24	using	use	VERB
cana-6099	272	25	fractional	fractional	ADJ
cana-6099	272	26	derivative	derivative	NOUN
cana-6099	272	27	”	"	PUNCT
cana-6099	272	28	,	,	PUNCT
cana-6099	272	29	international	international	ADJ
cana-6099	272	30	journal	journal	NOUN
cana-6099	272	31	of	of	ADP
cana-6099	272	32	thermodynamics	thermodynamic	NOUN
cana-6099	272	33	,	,	PUNCT
cana-6099	272	34	25(2	25(2	NUM
cana-6099	272	35	)	)	PUNCT
cana-6099	272	36	,	,	PUNCT
cana-6099	272	37	89—97	89—97	NUM
cana-6099	272	38	,	,	PUNCT
cana-6099	272	39	2022	2022	NUM
cana-6099	272	40	.	.	PUNCT
cana-6099	273	1	32	32	NUM
cana-6099	273	2	.	.	PUNCT
cana-6099	274	1	k.	k.	PROPN
cana-6099	274	2	r.	r.	PROPN
cana-6099	274	3	gaikwad	gaikwad	PROPN
cana-6099	274	4	,	,	PUNCT
cana-6099	274	5	y.	y.	PROPN
cana-6099	274	6	u.	u.	PROPN
cana-6099	274	7	naner	naner	NOUN
cana-6099	274	8	,	,	PUNCT
cana-6099	274	9	s.	s.	PROPN
cana-6099	274	10	g.	g.	PROPN
cana-6099	274	11	khavale	khavale	PROPN
cana-6099	274	12	,	,	PUNCT
cana-6099	274	13	“	"	PUNCT
cana-6099	274	14	transient	transient	ADJ
cana-6099	274	15	thermoelastic	thermoelastic	ADJ
cana-6099	274	16	bending	bending	NOUN
cana-6099	274	17	analysis	analysis	NOUN
cana-6099	274	18	of	of	ADP
cana-6099	274	19	a	a	DET
cana-6099	274	20	rectangular	rectangular	ADJ
cana-6099	274	21	plate	plate	NOUN
cana-6099	274	22	with	with	ADP
cana-6099	274	23	a	a	DET
cana-6099	274	24	simply	simply	ADV
cana-6099	274	25	supported	support	VERB
cana-6099	274	26	edge	edge	NOUN
cana-6099	274	27	under	under	ADP
cana-6099	274	28	heat	heat	NOUN
cana-6099	274	29	source	source	NOUN
cana-6099	274	30	:	:	PUNCT
cana-6099	274	31	green	green	PROPN
cana-6099	274	32	’s	’s	PART
cana-6099	274	33	function	function	NOUN
cana-6099	274	34	approach	approach	NOUN
cana-6099	274	35	”	"	PUNCT
cana-6099	274	36	,	,	PUNCT
cana-6099	274	37	int	int	NOUN
cana-6099	274	38	.	.	PUNCT
cana-6099	275	1	j.	j.	PROPN
cana-6099	275	2	nonlinear	nonlinear	PROPN
cana-6099	275	3	anal	anal	PROPN
cana-6099	275	4	.	.	PUNCT
cana-6099	276	1	appl	appl	PROPN
cana-6099	276	2	.	.	PROPN
cana-6099	276	3	,	,	PUNCT
cana-6099	276	4	in	in	ADP
cana-6099	276	5	press	press	NOUN
cana-6099	276	6	,	,	PUNCT
cana-6099	276	7	1—15	1—15	NUM
cana-6099	276	8	,	,	PUNCT
cana-6099	276	9	2022	2022	NUM
cana-6099	276	10	.	.	PUNCT
cana-6099	277	1	33	33	NUM
cana-6099	277	2	.	.	PUNCT
cana-6099	278	1	s.	s.	PROPN
cana-6099	278	2	g.	g.	PROPN
cana-6099	278	3	khavale	khavale	PROPN
cana-6099	278	4	,	,	PUNCT
cana-6099	278	5	k.	k.	PROPN
cana-6099	278	6	r.	r.	PROPN
cana-6099	278	7	gaikwad	gaikwad	PROPN
cana-6099	278	8	,	,	PUNCT
cana-6099	278	9	“	"	PUNCT
cana-6099	278	10	fractional	fractional	ADJ
cana-6099	278	11	thermoelasticity	thermoelasticity	NOUN
cana-6099	278	12	:	:	PUNCT
cana-6099	278	13	a	a	DET
cana-6099	278	14	review	review	NOUN
cana-6099	278	15	”	"	PUNCT
cana-6099	278	16	,	,	PUNCT
cana-6099	278	17	easy	easy	ADJ
cana-6099	278	18	chair	chair	NOUN
cana-6099	278	19	,	,	PUNCT
cana-6099	278	20	9531	9531	NUM
cana-6099	278	21	,	,	PUNCT
cana-6099	278	22	1–9	1–9	NUM
cana-6099	278	23	,	,	PUNCT
cana-6099	278	24	2023	2023	NUM
cana-6099	278	25	.	.	PUNCT
cana-6099	279	1	34	34	NUM
cana-6099	279	2	.	.	PUNCT
cana-6099	280	1	v.	v.	PROPN
cana-6099	280	2	g.	g.	PROPN
cana-6099	280	3	bhandwalkar	bhandwalkar	PROPN
cana-6099	280	4	,	,	PUNCT
cana-6099	280	5	k.	k.	PROPN
cana-6099	280	6	r.	r.	PROPN
cana-6099	280	7	gaikwad	gaikwad	PROPN
cana-6099	280	8	,	,	PUNCT
cana-6099	280	9	s.	s.	PROPN
cana-6099	280	10	g.	g.	PROPN
cana-6099	280	11	khavale	khavale	PROPN
cana-6099	280	12	,	,	PUNCT
cana-6099	280	13	y.	y.	PROPN
cana-6099	280	14	u.	u.	PROPN
cana-6099	280	15	naner	naner	NOUN
cana-6099	280	16	,	,	PUNCT
cana-6099	280	17	“	"	PUNCT
cana-6099	280	18	a	a	DET
cana-6099	280	19	homotopy	homotopy	NOUN
cana-6099	280	20	analysis	analysis	NOUN
cana-6099	280	21	approach	approach	NOUN
cana-6099	280	22	to	to	ADP
cana-6099	280	23	a	a	DET
cana-6099	280	24	1d	1d	NUM
cana-6099	280	25	fractional	fractional	ADJ
cana-6099	280	26	order	order	NOUN
cana-6099	280	27	problem	problem	NOUN
cana-6099	280	28	with	with	ADP
cana-6099	280	29	lord	lord	PROPN
cana-6099	280	30	-	-	PUNCT
cana-6099	280	31	shulman	shulman	PROPN
cana-6099	280	32	and	and	CCONJ
cana-6099	280	33	dual	dual	ADJ
cana-6099	280	34	-	-	PUNCT
cana-6099	280	35	phase	phase	NOUN
cana-6099	280	36	-	-	PUNCT
cana-6099	280	37	lag	lag	NOUN
cana-6099	280	38	model	model	NOUN
cana-6099	280	39	”	"	PUNCT
cana-6099	280	40	,	,	PUNCT
cana-6099	280	41	nanotechnology	nanotechnology	NOUN
cana-6099	280	42	perceptions	perception	NOUN
cana-6099	280	43	,	,	PUNCT
cana-6099	280	44	20(s16	20(s16	NUM
cana-6099	280	45	)	)	PUNCT
cana-6099	280	46	,	,	PUNCT
cana-6099	280	47	2033–2052	2033–2052	NUM
cana-6099	280	48	,	,	PUNCT
cana-6099	280	49	2024	2024	NUM
cana-6099	280	50	.	.	PUNCT
cana-6099	281	1	communications	communication	NOUN
cana-6099	281	2	on	on	ADP
cana-6099	281	3	applied	apply	VERB
cana-6099	281	4	nonlinear	nonlinear	ADJ
cana-6099	281	5	analysis	analysis	NOUN
cana-6099	281	6	issn	issn	NOUN
cana-6099	281	7	:	:	PUNCT
cana-6099	281	8	1074	1074	NUM
cana-6099	281	9	-	-	PUNCT
cana-6099	281	10	133x	133x	NUM
cana-6099	281	11	vol	vol	VERB
cana-6099	281	12	32	32	NUM
cana-6099	281	13	no	no	NOUN
cana-6099	281	14	.	.	PUNCT
cana-6099	282	1	10s	10	NOUN
cana-6099	282	2	(	(	PUNCT
cana-6099	282	3	2025	2025	NUM
cana-6099	282	4	)	)	PUNCT
cana-6099	282	5	3373	3373	NUM
cana-6099	282	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6099	282	7	35	35	NUM
cana-6099	282	8	.	.	PUNCT
cana-6099	283	1	v.	v.	PROPN
cana-6099	283	2	g.	g.	PROPN
cana-6099	283	3	bhandwalkar	bhandwalkar	PROPN
cana-6099	283	4	,	,	PUNCT
cana-6099	283	5	k.	k.	PROPN
cana-6099	283	6	r.	r.	PROPN
cana-6099	283	7	gaikwad	gaikwad	PROPN
cana-6099	283	8	,	,	PUNCT
cana-6099	283	9	“	"	PUNCT
cana-6099	283	10	the	the	DET
cana-6099	283	11	effect	effect	NOUN
cana-6099	283	12	of	of	ADP
cana-6099	283	13	fractional	fractional	ADJ
cana-6099	283	14	order	order	NOUN
cana-6099	283	15	derivative	derivative	NOUN
cana-6099	283	16	on	on	ADP
cana-6099	283	17	human	human	ADJ
cana-6099	283	18	head	head	NOUN
cana-6099	283	19	skin	skin	NOUN
cana-6099	283	20	tissue	tissue	NOUN
cana-6099	283	21	in	in	ADP
cana-6099	283	22	response	response	NOUN
cana-6099	283	23	to	to	ADP
cana-6099	283	24	thermal	thermal	ADJ
cana-6099	283	25	diffusion	diffusion	NOUN
cana-6099	283	26	”	"	PUNCT
cana-6099	283	27	,	,	PUNCT
cana-6099	283	28	jp	jp	NOUN
cana-6099	283	29	journal	journal	PROPN
cana-6099	283	30	of	of	ADP
cana-6099	283	31	heat	heat	NOUN
cana-6099	283	32	and	and	CCONJ
cana-6099	283	33	mass	mass	NOUN
cana-6099	283	34	transfer	transfer	NOUN
cana-6099	283	35	,	,	PUNCT
cana-6099	283	36	pushpa	pushpa	VERB
cana-6099	283	37	pub	pub	NOUN
cana-6099	283	38	.	.	PUNCT
cana-6099	283	39	,	,	PUNCT
cana-6099	283	40	2025	2025	NUM
cana-6099	283	41	.	.	PUNCT
cana-6099	284	1	36	36	NUM
cana-6099	284	2	.	.	PUNCT
cana-6099	284	3	n.	n.	PROPN
cana-6099	284	4	m.	m.	PROPN
cana-6099	284	5	ozisik	ozisik	PROPN
cana-6099	284	6	,	,	PUNCT
cana-6099	284	7	boundary	boundary	ADJ
cana-6099	284	8	value	value	NOUN
cana-6099	284	9	problem	problem	NOUN
cana-6099	284	10	of	of	ADP
cana-6099	284	11	heat	heat	NOUN
cana-6099	284	12	conduction	conduction	NOUN
cana-6099	284	13	,	,	PUNCT
cana-6099	284	14	international	international	ADJ
cana-6099	284	15	textbook	textbook	NOUN
cana-6099	284	16	company	company	NOUN
cana-6099	284	17	,	,	PUNCT
cana-6099	284	18	scranton	scranton	PROPN
cana-6099	284	19	,	,	PUNCT
cana-6099	284	20	pennsylvania	pennsylvania	PROPN
cana-6099	284	21	,	,	PUNCT
cana-6099	284	22	1968	1968	NUM
cana-6099	284	23	.	.	PUNCT
cana-6099	285	1	37	37	NUM
cana-6099	285	2	.	.	PUNCT
cana-6099	285	3	i.	i.	PROPN
cana-6099	285	4	n.	n.	PROPN
cana-6099	285	5	sneddon	sneddon	PROPN
cana-6099	285	6	,	,	PUNCT
cana-6099	285	7	the	the	DET
cana-6099	285	8	use	use	NOUN
cana-6099	285	9	of	of	ADP
cana-6099	285	10	integral	integral	ADJ
cana-6099	285	11	transform	transform	NOUN
cana-6099	285	12	,	,	PUNCT
cana-6099	285	13	mcgraw	mcgraw	PROPN
cana-6099	285	14	hill	hill	PROPN
cana-6099	285	15	,	,	PUNCT
cana-6099	285	16	new	new	PROPN
cana-6099	285	17	york	york	PROPN
cana-6099	285	18	,	,	PUNCT
cana-6099	285	19	1972	1972	NUM
cana-6099	285	20	.	.	PUNCT
cana-6099	286	1	38	38	NUM
cana-6099	286	2	.	.	PUNCT
cana-6099	287	1	d.	d.	PROPN
cana-6099	287	2	tzou	tzou	PROPN
cana-6099	287	3	,	,	PUNCT
cana-6099	287	4	macro	macro	NOUN
cana-6099	287	5	-	-	PUNCT
cana-6099	287	6	to	to	ADP
cana-6099	287	7	-	-	PUNCT
cana-6099	287	8	micro	micro	NOUN
cana-6099	287	9	heat	heat	NOUN
cana-6099	287	10	transfer	transfer	NOUN
cana-6099	287	11	,	,	PUNCT
cana-6099	287	12	taylor	taylor	PROPN
cana-6099	287	13	and	and	CCONJ
cana-6099	287	14	francis	francis	PROPN
cana-6099	287	15	,	,	PUNCT
cana-6099	287	16	washington	washington	PROPN
cana-6099	287	17	dc	dc	PROPN
cana-6099	287	18	.	.	PROPN
cana-6099	287	19	,	,	PUNCT
cana-6099	287	20	1996	1996	NUM
cana-6099	287	21	.	.	PUNCT
cana-6099	288	1	39	39	NUM
cana-6099	288	2	.	.	PUNCT
cana-6099	288	3	i.	i.	NOUN
cana-6099	288	4	podlubny	podlubny	PROPN
cana-6099	288	5	,	,	PUNCT
cana-6099	288	6	fractional	fractional	ADJ
cana-6099	288	7	differential	differential	NOUN
cana-6099	288	8	equation	equation	NOUN
cana-6099	288	9	,	,	PUNCT
cana-6099	288	10	academic	academic	ADJ
cana-6099	288	11	press	press	NOUN
cana-6099	288	12	,	,	PUNCT
cana-6099	288	13	san	san	PROPN
cana-6099	288	14	diego	diego	PROPN
cana-6099	288	15	,	,	PUNCT
cana-6099	288	16	1999	1999	NUM
cana-6099	288	17	.	.	PUNCT
cana-6099	289	1	[	[	X
cana-6099	289	2	40	40	NUM
cana-6099	289	3	]	]	X
cana-6099	289	4	y.	y.	PROPN
cana-6099	289	5	z.	z.	PROPN
cana-6099	289	6	povstenko	povstenko	PROPN
cana-6099	289	7	,	,	PUNCT
cana-6099	289	8	fractional	fractional	ADJ
cana-6099	289	9	thermoelasticity	thermoelasticity	NOUN
cana-6099	289	10	,	,	PUNCT
cana-6099	289	11	new	new	PROPN
cana-6099	289	12	york	york	PROPN
cana-6099	289	13	:	:	PUNCT
cana-6099	289	14	springer	springer	NOUN
cana-6099	289	15	,	,	PUNCT
cana-6099	289	16	2015	2015	NUM
cana-6099	289	17	.	.	PUNCT