id	sid	tid	token	lemma	pos
ejpam-7119	1	1	european	european	PROPN
ejpam-7119	1	2	journal	journal	PROPN
ejpam-7119	1	3	of	of	ADP
ejpam-7119	1	4	pure	pure	ADJ
ejpam-7119	1	5	and	and	CCONJ
ejpam-7119	1	6	applied	applied	ADJ
ejpam-7119	1	7	mathematics	mathematic	NOUN
ejpam-7119	1	8	2025	2025	NUM
ejpam-7119	1	9	,	,	PUNCT
ejpam-7119	1	10	vol	vol	NOUN
ejpam-7119	1	11	.	.	PROPN
ejpam-7119	1	12	18	18	NUM
ejpam-7119	1	13	,	,	PUNCT
ejpam-7119	1	14	issue	issue	NOUN
ejpam-7119	1	15	4	4	NUM
ejpam-7119	1	16	,	,	PUNCT
ejpam-7119	1	17	article	article	NOUN
ejpam-7119	1	18	number	number	NOUN
ejpam-7119	1	19	7119	7119	NUM
ejpam-7119	1	20	issn	issn	PROPN
ejpam-7119	1	21	1307	1307	NUM
ejpam-7119	1	22	-	-	SYM
ejpam-7119	1	23	5543	5543	NUM
ejpam-7119	1	24	–	–	PUNCT
ejpam-7119	1	25	ejpam.com	ejpam.com	X
ejpam-7119	1	26	published	publish	VERB
ejpam-7119	1	27	by	by	ADP
ejpam-7119	1	28	new	new	PROPN
ejpam-7119	1	29	york	york	PROPN
ejpam-7119	1	30	business	business	PROPN
ejpam-7119	1	31	global	global	ADJ
ejpam-7119	1	32	fractional	fractional	ADJ
ejpam-7119	1	33	-	-	PUNCT
ejpam-7119	1	34	order	order	NOUN
ejpam-7119	1	35	neutrosophic	neutrosophic	ADJ
ejpam-7119	1	36	mr	mr	PROPN
ejpam-7119	1	37	-	-	PUNCT
ejpam-7119	1	38	metric	metric	ADJ
ejpam-7119	1	39	spaces	space	NOUN
ejpam-7119	1	40	:	:	PUNCT
ejpam-7119	1	41	theory	theory	NOUN
ejpam-7119	1	42	,	,	PUNCT
ejpam-7119	1	43	fixed	fix	VERB
ejpam-7119	1	44	point	point	NOUN
ejpam-7119	1	45	theorems	theorem	NOUN
ejpam-7119	1	46	,	,	PUNCT
ejpam-7119	1	47	and	and	CCONJ
ejpam-7119	1	48	applications	application	NOUN
ejpam-7119	1	49	abed	abe	VERB
ejpam-7119	1	50	al	al	PROPN
ejpam-7119	1	51	-	-	PUNCT
ejpam-7119	1	52	rahman	rahman	PROPN
ejpam-7119	1	53	m.	m.	PROPN
ejpam-7119	1	54	malkawi1,∗and	malkawi1,∗and	PROPN
ejpam-7119	1	55	ayat	ayat	PROPN
ejpam-7119	1	56	m.	m.	NOUN
ejpam-7119	1	57	rabaiah1	rabaiah1	PROPN
ejpam-7119	1	58	1	1	NUM
ejpam-7119	1	59	department	department	NOUN
ejpam-7119	1	60	of	of	ADP
ejpam-7119	1	61	mathematics	mathematic	NOUN
ejpam-7119	1	62	,	,	PUNCT
ejpam-7119	1	63	faculty	faculty	NOUN
ejpam-7119	1	64	of	of	ADP
ejpam-7119	1	65	arts	art	NOUN
ejpam-7119	1	66	and	and	CCONJ
ejpam-7119	1	67	science	science	NOUN
ejpam-7119	1	68	,	,	PUNCT
ejpam-7119	1	69	amman	amman	PROPN
ejpam-7119	1	70	arab	arab	PROPN
ejpam-7119	1	71	university	university	PROPN
ejpam-7119	1	72	,	,	PUNCT
ejpam-7119	1	73	amman	amman	PROPN
ejpam-7119	1	74	11953	11953	NUM
ejpam-7119	1	75	,	,	PUNCT
ejpam-7119	1	76	jordan	jordan	PROPN
ejpam-7119	1	77	abstract	abstract	PROPN
ejpam-7119	1	78	.	.	PUNCT
ejpam-7119	2	1	this	this	DET
ejpam-7119	2	2	paper	paper	NOUN
ejpam-7119	2	3	introduces	introduce	VERB
ejpam-7119	2	4	the	the	DET
ejpam-7119	2	5	novel	novel	ADJ
ejpam-7119	2	6	concept	concept	NOUN
ejpam-7119	2	7	of	of	ADP
ejpam-7119	2	8	fractional	fractional	ADJ
ejpam-7119	2	9	-	-	PUNCT
ejpam-7119	2	10	order	order	NOUN
ejpam-7119	2	11	neutrosophic	neutrosophic	ADJ
ejpam-7119	2	12	mr	mr	PROPN
ejpam-7119	2	13	-	-	PUNCT
ejpam-7119	2	14	metric	metric	ADJ
ejpam-7119	2	15	spaces	space	NOUN
ejpam-7119	2	16	(	(	PUNCT
ejpam-7119	2	17	fonmr	fonmr	NOUN
ejpam-7119	2	18	-	-	PUNCT
ejpam-7119	2	19	ms	ms	NOUN
ejpam-7119	2	20	)	)	PUNCT
ejpam-7119	2	21	,	,	PUNCT
ejpam-7119	2	22	which	which	PRON
ejpam-7119	2	23	synergistically	synergistically	ADV
ejpam-7119	2	24	combines	combine	VERB
ejpam-7119	2	25	three	three	NUM
ejpam-7119	2	26	powerful	powerful	ADJ
ejpam-7119	2	27	mathematical	mathematical	ADJ
ejpam-7119	2	28	frameworks	framework	NOUN
ejpam-7119	2	29	:	:	PUNCT
ejpam-7119	2	30	mr	mr	ADJ
ejpam-7119	2	31	-	-	PUNCT
ejpam-7119	2	32	metric	metric	ADJ
ejpam-7119	2	33	spaces	space	NOUN
ejpam-7119	2	34	,	,	PUNCT
ejpam-7119	2	35	neutrosophic	neutrosophic	ADJ
ejpam-7119	2	36	logic	logic	NOUN
ejpam-7119	2	37	,	,	PUNCT
ejpam-7119	2	38	and	and	CCONJ
ejpam-7119	2	39	fractional	fractional	ADJ
ejpam-7119	2	40	calculus	calculus	NOUN
ejpam-7119	2	41	.	.	PUNCT
ejpam-7119	3	1	we	we	PRON
ejpam-7119	3	2	begin	begin	VERB
ejpam-7119	3	3	by	by	ADP
ejpam-7119	3	4	extending	extend	VERB
ejpam-7119	3	5	the	the	DET
ejpam-7119	3	6	classical	classical	ADJ
ejpam-7119	3	7	mr	mr	ADJ
ejpam-7119	3	8	-	-	PUNCT
ejpam-7119	3	9	metric	metric	ADJ
ejpam-7119	3	10	structure	structure	NOUN
ejpam-7119	3	11	through	through	ADP
ejpam-7119	3	12	the	the	DET
ejpam-7119	3	13	incorporation	incorporation	NOUN
ejpam-7119	3	14	of	of	ADP
ejpam-7119	3	15	fractional	fractional	ADJ
ejpam-7119	3	16	integrals	integral	NOUN
ejpam-7119	3	17	,	,	PUNCT
ejpam-7119	3	18	defining	define	VERB
ejpam-7119	3	19	a	a	DET
ejpam-7119	3	20	comprehensive	comprehensive	ADJ
ejpam-7119	3	21	fractional	fractional	ADJ
ejpam-7119	3	22	-	-	PUNCT
ejpam-7119	3	23	order	order	NOUN
ejpam-7119	3	24	metric	metric	NOUN
ejpam-7119	3	25	mα	mα	NOUN
ejpam-7119	3	26	and	and	CCONJ
ejpam-7119	3	27	corresponding	corresponding	ADJ
ejpam-7119	3	28	neutrosophic	neutrosophic	ADJ
ejpam-7119	3	29	functions	function	NOUN
ejpam-7119	3	30	tα	tα	PROPN
ejpam-7119	3	31	,	,	PUNCT
ejpam-7119	3	32	iα	iα	NOUN
ejpam-7119	3	33	,	,	PUNCT
ejpam-7119	3	34	fα	fα	NOUN
ejpam-7119	3	35	.	.	PUNCT
ejpam-7119	4	1	fundamental	fundamental	ADJ
ejpam-7119	4	2	properties	property	NOUN
ejpam-7119	4	3	including	include	VERB
ejpam-7119	4	4	non	non	ADJ
ejpam-7119	4	5	-	-	ADJ
ejpam-7119	4	6	negativity	negativity	ADJ
ejpam-7119	4	7	,	,	PUNCT
ejpam-7119	4	8	identity	identity	NOUN
ejpam-7119	4	9	,	,	PUNCT
ejpam-7119	4	10	symmetry	symmetry	NOUN
ejpam-7119	4	11	,	,	PUNCT
ejpam-7119	4	12	and	and	CCONJ
ejpam-7119	4	13	a	a	DET
ejpam-7119	4	14	generalized	generalize	VERB
ejpam-7119	4	15	fractional	fractional	ADJ
ejpam-7119	4	16	triangle	triangle	NOUN
ejpam-7119	4	17	inequality	inequality	NOUN
ejpam-7119	4	18	are	be	AUX
ejpam-7119	4	19	rigorously	rigorously	ADV
ejpam-7119	4	20	established	establish	VERB
ejpam-7119	4	21	.	.	PUNCT
ejpam-7119	5	1	the	the	DET
ejpam-7119	5	2	core	core	ADJ
ejpam-7119	5	3	theoretical	theoretical	ADJ
ejpam-7119	5	4	contribution	contribution	NOUN
ejpam-7119	5	5	is	be	AUX
ejpam-7119	5	6	a	a	DET
ejpam-7119	5	7	comprehensive	comprehensive	ADJ
ejpam-7119	5	8	fixed	fix	VERB
ejpam-7119	5	9	point	point	NOUN
ejpam-7119	5	10	theorem	theorem	NOUN
ejpam-7119	5	11	for	for	ADP
ejpam-7119	5	12	contraction	contraction	NOUN
ejpam-7119	5	13	mappings	mapping	NOUN
ejpam-7119	5	14	in	in	ADP
ejpam-7119	5	15	complete	complete	ADJ
ejpam-7119	5	16	fonmr	fonmr	ADJ
ejpam-7119	5	17	-	-	PUNCT
ejpam-7119	5	18	ms	ms	NOUN
ejpam-7119	5	19	,	,	PUNCT
ejpam-7119	5	20	accompanied	accompany	VERB
ejpam-7119	5	21	by	by	ADP
ejpam-7119	5	22	detailed	detailed	ADJ
ejpam-7119	5	23	convergence	convergence	NOUN
ejpam-7119	5	24	analysis	analysis	NOUN
ejpam-7119	5	25	and	and	CCONJ
ejpam-7119	5	26	neutrosophic	neutrosophic	ADJ
ejpam-7119	5	27	consistency	consistency	NOUN
ejpam-7119	5	28	conditions	condition	NOUN
ejpam-7119	5	29	.	.	PUNCT
ejpam-7119	6	1	we	we	PRON
ejpam-7119	6	2	further	far	ADV
ejpam-7119	6	3	provide	provide	VERB
ejpam-7119	6	4	extensive	extensive	ADJ
ejpam-7119	6	5	examples	example	NOUN
ejpam-7119	6	6	and	and	CCONJ
ejpam-7119	6	7	applications	application	NOUN
ejpam-7119	6	8	demonstrating	demonstrate	VERB
ejpam-7119	6	9	the	the	DET
ejpam-7119	6	10	utility	utility	NOUN
ejpam-7119	6	11	of	of	ADP
ejpam-7119	6	12	our	our	PRON
ejpam-7119	6	13	framework	framework	NOUN
ejpam-7119	6	14	in	in	ADP
ejpam-7119	6	15	modeling	model	VERB
ejpam-7119	6	16	anomalous	anomalous	ADJ
ejpam-7119	6	17	diffusion	diffusion	NOUN
ejpam-7119	6	18	processes	process	NOUN
ejpam-7119	6	19	,	,	PUNCT
ejpam-7119	6	20	image	image	NOUN
ejpam-7119	6	21	denoising	denoising	NOUN
ejpam-7119	6	22	,	,	PUNCT
ejpam-7119	6	23	and	and	CCONJ
ejpam-7119	6	24	machine	machine	NOUN
ejpam-7119	6	25	learning	learn	VERB
ejpam-7119	6	26	under	under	ADP
ejpam-7119	6	27	uncertainty	uncertainty	NOUN
ejpam-7119	6	28	.	.	PUNCT
ejpam-7119	7	1	this	this	DET
ejpam-7119	7	2	work	work	NOUN
ejpam-7119	7	3	significantly	significantly	ADV
ejpam-7119	7	4	generalizes	generalize	VERB
ejpam-7119	7	5	existing	exist	VERB
ejpam-7119	7	6	results	result	NOUN
ejpam-7119	7	7	in	in	ADP
ejpam-7119	7	8	fixed	fix	VERB
ejpam-7119	7	9	point	point	NOUN
ejpam-7119	7	10	theory	theory	NOUN
ejpam-7119	7	11	and	and	CCONJ
ejpam-7119	7	12	offers	offer	VERB
ejpam-7119	7	13	a	a	DET
ejpam-7119	7	14	robust	robust	ADJ
ejpam-7119	7	15	mathematical	mathematical	ADJ
ejpam-7119	7	16	foundation	foundation	NOUN
ejpam-7119	7	17	for	for	ADP
ejpam-7119	7	18	handling	handle	VERB
ejpam-7119	7	19	complex	complex	ADJ
ejpam-7119	7	20	systems	system	NOUN
ejpam-7119	7	21	characterized	characterize	VERB
ejpam-7119	7	22	by	by	ADP
ejpam-7119	7	23	fractional	fractional	ADJ
ejpam-7119	7	24	dynamics	dynamic	NOUN
ejpam-7119	7	25	and	and	CCONJ
ejpam-7119	7	26	neutrosophic	neutrosophic	ADJ
ejpam-7119	7	27	uncertainty	uncertainty	NOUN
ejpam-7119	7	28	.	.	PUNCT
ejpam-7119	8	1	2020	2020	NUM
ejpam-7119	8	2	mathematics	mathematic	NOUN
ejpam-7119	8	3	subject	subject	NOUN
ejpam-7119	8	4	classifications	classification	NOUN
ejpam-7119	8	5	:	:	PUNCT
ejpam-7119	8	6	47h10	47h10	NUM
ejpam-7119	8	7	,	,	PUNCT
ejpam-7119	8	8	54e35	54e35	NUM
ejpam-7119	8	9	,	,	PUNCT
ejpam-7119	8	10	26a33	26a33	NUM
ejpam-7119	8	11	,	,	PUNCT
ejpam-7119	8	12	03e72	03e72	X
ejpam-7119	8	13	key	key	ADJ
ejpam-7119	8	14	words	word	NOUN
ejpam-7119	8	15	and	and	CCONJ
ejpam-7119	8	16	phrases	phrase	NOUN
ejpam-7119	8	17	:	:	PUNCT
ejpam-7119	8	18	fractional	fractional	ADJ
ejpam-7119	8	19	-	-	PUNCT
ejpam-7119	8	20	order	order	NOUN
ejpam-7119	8	21	metric	metric	ADJ
ejpam-7119	8	22	spaces	space	NOUN
ejpam-7119	8	23	,	,	PUNCT
ejpam-7119	8	24	neutrosophic	neutrosophic	ADJ
ejpam-7119	8	25	logic	logic	NOUN
ejpam-7119	8	26	,	,	PUNCT
ejpam-7119	8	27	mr	mr	PROPN
ejpam-7119	8	28	-	-	PUNCT
ejpam-7119	8	29	metric	metric	ADJ
ejpam-7119	8	30	spaces	space	NOUN
ejpam-7119	8	31	,	,	PUNCT
ejpam-7119	8	32	fixed	fix	VERB
ejpam-7119	8	33	point	point	NOUN
ejpam-7119	8	34	theory	theory	NOUN
ejpam-7119	8	35	,	,	PUNCT
ejpam-7119	8	36	fractional	fractional	ADJ
ejpam-7119	8	37	calculus	calculus	NOUN
ejpam-7119	8	38	,	,	PUNCT
ejpam-7119	8	39	anomalous	anomalous	ADJ
ejpam-7119	8	40	diffusion	diffusion	NOUN
ejpam-7119	8	41	,	,	PUNCT
ejpam-7119	8	42	uncertainty	uncertainty	NOUN
ejpam-7119	8	43	modeling	model	VERB
ejpam-7119	8	44	1	1	NUM
ejpam-7119	8	45	.	.	PUNCT
ejpam-7119	9	1	introduction	introduction	NOUN
ejpam-7119	9	2	fixed	fix	VERB
ejpam-7119	9	3	point	point	NOUN
ejpam-7119	9	4	theory	theory	NOUN
ejpam-7119	9	5	represents	represent	VERB
ejpam-7119	9	6	one	one	NUM
ejpam-7119	9	7	of	of	ADP
ejpam-7119	9	8	the	the	DET
ejpam-7119	9	9	most	most	ADV
ejpam-7119	9	10	dynamic	dynamic	ADJ
ejpam-7119	9	11	and	and	CCONJ
ejpam-7119	9	12	applicable	applicable	ADJ
ejpam-7119	9	13	domains	domain	NOUN
ejpam-7119	9	14	in	in	ADP
ejpam-7119	9	15	mathematical	mathematical	ADJ
ejpam-7119	9	16	analysis	analysis	NOUN
ejpam-7119	9	17	,	,	PUNCT
ejpam-7119	9	18	with	with	ADP
ejpam-7119	9	19	profound	profound	ADJ
ejpam-7119	9	20	implications	implication	NOUN
ejpam-7119	9	21	across	across	ADP
ejpam-7119	9	22	differential	differential	ADJ
ejpam-7119	9	23	equations	equation	NOUN
ejpam-7119	9	24	,	,	PUNCT
ejpam-7119	9	25	optimization	optimization	NOUN
ejpam-7119	9	26	,	,	PUNCT
ejpam-7119	9	27	and	and	CCONJ
ejpam-7119	9	28	computational	computational	ADJ
ejpam-7119	9	29	mathematics	mathematic	NOUN
ejpam-7119	9	30	.	.	PUNCT
ejpam-7119	10	1	the	the	DET
ejpam-7119	10	2	evolution	evolution	NOUN
ejpam-7119	10	3	of	of	ADP
ejpam-7119	10	4	metric	metric	ADJ
ejpam-7119	10	5	spaces	space	NOUN
ejpam-7119	10	6	has	have	AUX
ejpam-7119	10	7	been	be	AUX
ejpam-7119	10	8	marked	mark	VERB
ejpam-7119	10	9	by	by	ADP
ejpam-7119	10	10	significant	significant	ADJ
ejpam-7119	10	11	generalizations	generalization	NOUN
ejpam-7119	10	12	to	to	PART
ejpam-7119	10	13	address	address	VERB
ejpam-7119	10	14	increasingly	increasingly	ADV
ejpam-7119	10	15	complex	complex	ADJ
ejpam-7119	10	16	mathematical	mathematical	ADJ
ejpam-7119	10	17	phenomena	phenomenon	NOUN
ejpam-7119	10	18	.	.	PUNCT
ejpam-7119	11	1	the	the	DET
ejpam-7119	11	2	inception	inception	NOUN
ejpam-7119	11	3	of	of	ADP
ejpam-7119	11	4	b	b	NOUN
ejpam-7119	11	5	-	-	PUNCT
ejpam-7119	11	6	metric	metric	ADJ
ejpam-7119	11	7	spaces	space	NOUN
ejpam-7119	11	8	by	by	ADP
ejpam-7119	11	9	bakhtin	bakhtin	NOUN
ejpam-7119	11	10	[	[	X
ejpam-7119	11	11	1	1	NUM
ejpam-7119	11	12	]	]	PUNCT
ejpam-7119	11	13	and	and	CCONJ
ejpam-7119	11	14	czerwik	czerwik	PROPN
ejpam-7119	12	1	[	[	X
ejpam-7119	12	2	2	2	NUM
ejpam-7119	12	3	]	]	PUNCT
ejpam-7119	12	4	relaxed	relax	VERB
ejpam-7119	12	5	the	the	DET
ejpam-7119	12	6	standard	standard	ADJ
ejpam-7119	12	7	triangle	triangle	NOUN
ejpam-7119	12	8	inequality	inequality	NOUN
ejpam-7119	12	9	,	,	PUNCT
ejpam-7119	12	10	paving	pave	VERB
ejpam-7119	12	11	the	the	DET
ejpam-7119	12	12	way	way	NOUN
ejpam-7119	12	13	for	for	ADP
ejpam-7119	12	14	more	more	ADV
ejpam-7119	12	15	flexible	flexible	ADJ
ejpam-7119	12	16	geometric	geometric	ADJ
ejpam-7119	12	17	structures	structure	NOUN
ejpam-7119	12	18	.	.	PUNCT
ejpam-7119	13	1	this	this	DET
ejpam-7119	13	2	trajectory	trajectory	NOUN
ejpam-7119	13	3	continued	continue	VERB
ejpam-7119	13	4	with	with	ADP
ejpam-7119	13	5	the	the	DET
ejpam-7119	13	6	development	development	NOUN
ejpam-7119	13	7	of	of	ADP
ejpam-7119	13	8	g	g	NOUN
ejpam-7119	13	9	-	-	PUNCT
ejpam-7119	13	10	metric	metric	ADJ
ejpam-7119	13	11	spaces	space	NOUN
ejpam-7119	13	12	and	and	CCONJ
ejpam-7119	13	13	their	their	PRON
ejpam-7119	13	14	variants	variant	NOUN
ejpam-7119	13	15	,	,	PUNCT
ejpam-7119	13	16	offering	offer	VERB
ejpam-7119	13	17	enhanced	enhance	VERB
ejpam-7119	13	18	frameworks	framework	NOUN
ejpam-7119	13	19	for	for	ADP
ejpam-7119	13	20	analyzing	analyze	VERB
ejpam-7119	13	21	triple	triple	ADJ
ejpam-7119	13	22	-	-	PUNCT
ejpam-7119	13	23	based	base	VERB
ejpam-7119	13	24	distance	distance	NOUN
ejpam-7119	13	25	functions	function	NOUN
ejpam-7119	13	26	.	.	PUNCT
ejpam-7119	14	1	the	the	DET
ejpam-7119	14	2	recent	recent	ADJ
ejpam-7119	14	3	introduction	introduction	NOUN
ejpam-7119	14	4	of	of	ADP
ejpam-7119	14	5	mr	mr	PROPN
ejpam-7119	14	6	-	-	PUNCT
ejpam-7119	14	7	metric	metric	ADJ
ejpam-7119	14	8	spaces	space	NOUN
ejpam-7119	14	9	by	by	ADP
ejpam-7119	14	10	malkawi	malkawi	PROPN
ejpam-7119	14	11	et	et	PROPN
ejpam-7119	14	12	al	al	PROPN
ejpam-7119	14	13	.	.	PUNCT
ejpam-7119	15	1	[	[	X
ejpam-7119	15	2	3	3	NUM
ejpam-7119	15	3	]	]	PUNCT
ejpam-7119	15	4	marked	mark	VERB
ejpam-7119	15	5	a	a	DET
ejpam-7119	15	6	substantial	substantial	ADJ
ejpam-7119	15	7	advancement	advancement	NOUN
ejpam-7119	15	8	,	,	PUNCT
ejpam-7119	15	9	providing	provide	VERB
ejpam-7119	15	10	a	a	DET
ejpam-7119	15	11	robust	robust	ADJ
ejpam-7119	15	12	structure	structure	NOUN
ejpam-7119	15	13	that	that	PRON
ejpam-7119	15	14	generalizes	generalize	VERB
ejpam-7119	15	15	several	several	ADJ
ejpam-7119	15	16	previous	previous	ADJ
ejpam-7119	15	17	metric	metric	ADJ
ejpam-7119	15	18	space	space	NOUN
ejpam-7119	15	19	extensions	extension	NOUN
ejpam-7119	15	20	while	while	SCONJ
ejpam-7119	15	21	maintaining	maintain	VERB
ejpam-7119	15	22	strong	strong	ADJ
ejpam-7119	15	23	theoretical	theoretical	ADJ
ejpam-7119	15	24	properties	property	NOUN
ejpam-7119	15	25	.	.	PUNCT
ejpam-7119	16	1	subsequent	subsequent	ADJ
ejpam-7119	16	2	research	research	NOUN
ejpam-7119	16	3	has	have	AUX
ejpam-7119	16	4	extensively	extensively	ADV
ejpam-7119	16	5	explored	explore	VERB
ejpam-7119	16	6	fixed	fix	VERB
ejpam-7119	16	7	point	point	NOUN
ejpam-7119	16	8	theorems	theorem	NOUN
ejpam-7119	16	9	within	within	ADP
ejpam-7119	16	10	this	this	DET
ejpam-7119	16	11	framework	framework	NOUN
ejpam-7119	16	12	[	[	X
ejpam-7119	16	13	1	1	NUM
ejpam-7119	16	14	,	,	PUNCT
ejpam-7119	16	15	2	2	NUM
ejpam-7119	16	16	,	,	PUNCT
ejpam-7119	16	17	4–13	4–13	PROPN
ejpam-7119	16	18	]	]	PUNCT
ejpam-7119	16	19	,	,	PUNCT
ejpam-7119	16	20	demonstrating	demonstrate	VERB
ejpam-7119	16	21	its	its	PRON
ejpam-7119	16	22	versatility	versatility	NOUN
ejpam-7119	16	23	in	in	ADP
ejpam-7119	16	24	handling	handle	VERB
ejpam-7119	16	25	various	various	ADJ
ejpam-7119	16	26	contraction	contraction	NOUN
ejpam-7119	16	27	types	type	NOUN
ejpam-7119	16	28	and	and	CCONJ
ejpam-7119	16	29	applications	application	NOUN
ejpam-7119	16	30	to	to	ADP
ejpam-7119	16	31	integral	integral	ADJ
ejpam-7119	16	32	equations	equation	NOUN
ejpam-7119	16	33	and	and	CCONJ
ejpam-7119	16	34	neutron	neutron	NOUN
ejpam-7119	16	35	transport	transport	NOUN
ejpam-7119	16	36	[	[	X
ejpam-7119	16	37	10	10	NUM
ejpam-7119	16	38	]	]	PUNCT
ejpam-7119	16	39	.	.	PUNCT
ejpam-7119	17	1	parallel	parallel	ADJ
ejpam-7119	17	2	to	to	ADP
ejpam-7119	17	3	these	these	DET
ejpam-7119	17	4	metric	metric	ADJ
ejpam-7119	17	5	space	space	NOUN
ejpam-7119	17	6	developments	development	NOUN
ejpam-7119	17	7	,	,	PUNCT
ejpam-7119	17	8	neutrosophic	neutrosophic	ADJ
ejpam-7119	17	9	logic	logic	NOUN
ejpam-7119	17	10	pioneered	pioneer	VERB
ejpam-7119	17	11	by	by	ADP
ejpam-7119	17	12	smarandache	smarandache	NOUN
ejpam-7119	17	13	has	have	AUX
ejpam-7119	17	14	emerged	emerge	VERB
ejpam-7119	17	15	as	as	ADP
ejpam-7119	17	16	a	a	DET
ejpam-7119	17	17	powerful	powerful	ADJ
ejpam-7119	17	18	paradigm	paradigm	NOUN
ejpam-7119	17	19	for	for	ADP
ejpam-7119	17	20	handling	handle	VERB
ejpam-7119	17	21	uncertainty	uncertainty	NOUN
ejpam-7119	17	22	,	,	PUNCT
ejpam-7119	17	23	indeterminacy	indeterminacy	NOUN
ejpam-7119	17	24	,	,	PUNCT
ejpam-7119	17	25	and	and	CCONJ
ejpam-7119	17	26	inconsistency	inconsistency	NOUN
ejpam-7119	17	27	∗corresponding	∗corresponde	VERB
ejpam-7119	17	28	author	author	NOUN
ejpam-7119	17	29	.	.	PUNCT
ejpam-7119	18	1	doi	doi	NOUN
ejpam-7119	18	2	:	:	PUNCT
ejpam-7119	18	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7119	https://doi.org/10.29020/nybg.ejpam.v18i4.7119	ADP
ejpam-7119	18	4	email	email	NOUN
ejpam-7119	18	5	addresses	address	NOUN
ejpam-7119	18	6	:	:	PUNCT
ejpam-7119	18	7	a.malkawi@aau.edu.jo	a.malkawi@aau.edu.jo	PROPN
ejpam-7119	18	8	and	and	CCONJ
ejpam-7119	18	9	math.malkawi@gmail.com	math.malkawi@gmail.com	X
ejpam-7119	18	10	(	(	PUNCT
ejpam-7119	18	11	a.	a.	NOUN
ejpam-7119	18	12	malkawi	malkawi	PROPN
ejpam-7119	18	13	)	)	PUNCT
ejpam-7119	18	14	,	,	PUNCT
ejpam-7119	18	15	a.rabaieha@aau.edu.jo	a.rabaieha@aau.edu.jo	PROPN
ejpam-7119	18	16	(	(	PUNCT
ejpam-7119	18	17	a.	a.	NOUN
ejpam-7119	18	18	rabaiah	rabaiah	PROPN
ejpam-7119	18	19	)	)	PUNCT
ejpam-7119	18	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7119	19	1	1	1	NUM
ejpam-7119	19	2	copyright	copyright	NOUN
ejpam-7119	19	3	:	:	PUNCT
ejpam-7119	19	4	©	©	PROPN
ejpam-7119	19	5	2025	2025	NUM
ejpam-7119	19	6	the	the	DET
ejpam-7119	19	7	author(s	author(s	NOUN
ejpam-7119	19	8	)	)	PUNCT
ejpam-7119	19	9	.	.	PUNCT
ejpam-7119	20	1	(	(	PUNCT
ejpam-7119	20	2	cc	cc	NOUN
ejpam-7119	20	3	by	by	ADP
ejpam-7119	20	4	-	-	PUNCT
ejpam-7119	20	5	nc	nc	PROPN
ejpam-7119	20	6	4.0	4.0	NUM
ejpam-7119	20	7	)	)	PUNCT
ejpam-7119	20	8	a.	a.	NOUN
ejpam-7119	20	9	malkawi	malkawi	PROPN
ejpam-7119	20	10	,	,	PUNCT
ejpam-7119	20	11	a.	a.	PROPN
ejpam-7119	20	12	rabaiah	rabaiah	PROPN
ejpam-7119	20	13	/	/	SYM
ejpam-7119	20	14	eur	eur	PROPN
ejpam-7119	20	15	.	.	PUNCT
ejpam-7119	21	1	j.	j.	PROPN
ejpam-7119	21	2	pure	pure	PROPN
ejpam-7119	21	3	appl	appl	PROPN
ejpam-7119	21	4	.	.	PROPN
ejpam-7119	21	5	math	math	PROPN
ejpam-7119	21	6	,	,	PUNCT
ejpam-7119	21	7	18	18	NUM
ejpam-7119	21	8	(	(	PUNCT
ejpam-7119	21	9	4	4	NUM
ejpam-7119	21	10	)	)	PUNCT
ejpam-7119	21	11	(	(	PUNCT
ejpam-7119	21	12	2025	2025	NUM
ejpam-7119	21	13	)	)	PUNCT
ejpam-7119	21	14	,	,	PUNCT
ejpam-7119	21	15	7119	7119	NUM
ejpam-7119	21	16	2	2	NUM
ejpam-7119	21	17	of	of	ADP
ejpam-7119	21	18	13	13	NUM
ejpam-7119	21	19	in	in	ADP
ejpam-7119	21	20	mathematical	mathematical	ADJ
ejpam-7119	21	21	systems	system	NOUN
ejpam-7119	21	22	.	.	PUNCT
ejpam-7119	22	1	the	the	DET
ejpam-7119	22	2	integration	integration	NOUN
ejpam-7119	22	3	of	of	ADP
ejpam-7119	22	4	neutrosophic	neutrosophic	ADJ
ejpam-7119	22	5	concepts	concept	NOUN
ejpam-7119	22	6	with	with	ADP
ejpam-7119	22	7	metric	metric	ADJ
ejpam-7119	22	8	spaces	space	NOUN
ejpam-7119	22	9	has	have	AUX
ejpam-7119	22	10	led	lead	VERB
ejpam-7119	22	11	to	to	ADP
ejpam-7119	22	12	the	the	DET
ejpam-7119	22	13	creation	creation	NOUN
ejpam-7119	22	14	of	of	ADP
ejpam-7119	22	15	neutrosophic	neutrosophic	ADJ
ejpam-7119	22	16	metric	metric	ADJ
ejpam-7119	22	17	spaces	space	NOUN
ejpam-7119	22	18	[	[	X
ejpam-7119	22	19	14	14	NUM
ejpam-7119	22	20	,	,	PUNCT
ejpam-7119	22	21	15	15	NUM
ejpam-7119	22	22	]	]	PUNCT
ejpam-7119	22	23	,	,	PUNCT
ejpam-7119	22	24	which	which	PRON
ejpam-7119	22	25	provide	provide	VERB
ejpam-7119	22	26	sophisticated	sophisticated	ADJ
ejpam-7119	22	27	tools	tool	NOUN
ejpam-7119	22	28	for	for	ADP
ejpam-7119	22	29	modeling	model	VERB
ejpam-7119	22	30	truth	truth	NOUN
ejpam-7119	22	31	,	,	PUNCT
ejpam-7119	22	32	falsity	falsity	NOUN
ejpam-7119	22	33	,	,	PUNCT
ejpam-7119	22	34	and	and	CCONJ
ejpam-7119	22	35	indeterminacy	indeterminacy	NOUN
ejpam-7119	22	36	degrees	degree	NOUN
ejpam-7119	22	37	in	in	ADP
ejpam-7119	22	38	distance	distance	NOUN
ejpam-7119	22	39	measurements	measurement	NOUN
ejpam-7119	22	40	.	.	PUNCT
ejpam-7119	23	1	recent	recent	ADJ
ejpam-7119	23	2	work	work	NOUN
ejpam-7119	23	3	by	by	ADP
ejpam-7119	23	4	hazaymeh	hazaymeh	NOUN
ejpam-7119	23	5	and	and	CCONJ
ejpam-7119	23	6	bataihah	bataihah	NOUN
ejpam-7119	23	7	[	[	X
ejpam-7119	23	8	14	14	NUM
ejpam-7119	23	9	]	]	PUNCT
ejpam-7119	23	10	and	and	CCONJ
ejpam-7119	23	11	bataihah	bataihah	ADJ
ejpam-7119	23	12	and	and	CCONJ
ejpam-7119	23	13	hazaymeh	hazaymeh	NOUN
ejpam-7119	23	14	[	[	X
ejpam-7119	23	15	15	15	NUM
ejpam-7119	23	16	]	]	PUNCT
ejpam-7119	23	17	has	have	AUX
ejpam-7119	23	18	established	establish	VERB
ejpam-7119	23	19	fundamental	fundamental	ADJ
ejpam-7119	23	20	results	result	NOUN
ejpam-7119	23	21	in	in	ADP
ejpam-7119	23	22	neutrosophic	neutrosophic	ADJ
ejpam-7119	23	23	fuzzy	fuzzy	ADJ
ejpam-7119	23	24	metric	metric	ADJ
ejpam-7119	23	25	spaces	space	NOUN
ejpam-7119	23	26	,	,	PUNCT
ejpam-7119	23	27	while	while	SCONJ
ejpam-7119	23	28	malkawi	malkawi	ADP
ejpam-7119	23	29	[	[	PUNCT
ejpam-7119	23	30	16	16	NUM
ejpam-7119	23	31	]	]	PUNCT
ejpam-7119	23	32	advanced	advance	VERB
ejpam-7119	23	33	this	this	PRON
ejpam-7119	23	34	further	far	ADV
ejpam-7119	23	35	through	through	ADP
ejpam-7119	23	36	neutrosophic	neutrosophic	ADJ
ejpam-7119	23	37	mr	mr	PROPN
ejpam-7119	23	38	-	-	PUNCT
ejpam-7119	23	39	metrics	metric	NOUN
ejpam-7119	23	40	with	with	ADP
ejpam-7119	23	41	fuzzy	fuzzy	ADJ
ejpam-7119	23	42	embedding	embed	VERB
ejpam-7119	23	43	principles	principle	NOUN
ejpam-7119	23	44	.	.	PUNCT
ejpam-7119	24	1	fractional	fractional	ADJ
ejpam-7119	24	2	calculus	calculus	NOUN
ejpam-7119	24	3	has	have	AUX
ejpam-7119	24	4	simultaneously	simultaneously	ADV
ejpam-7119	24	5	revolutionized	revolutionize	VERB
ejpam-7119	24	6	mathematical	mathematical	ADJ
ejpam-7119	24	7	modeling	modeling	NOUN
ejpam-7119	24	8	by	by	ADP
ejpam-7119	24	9	capturing	capture	VERB
ejpam-7119	24	10	non	non	ADJ
ejpam-7119	24	11	-	-	ADJ
ejpam-7119	24	12	local	local	ADJ
ejpam-7119	24	13	and	and	CCONJ
ejpam-7119	24	14	memory	memory	NOUN
ejpam-7119	24	15	-	-	PUNCT
ejpam-7119	24	16	dependent	dependent	ADJ
ejpam-7119	24	17	phenomena	phenomenon	NOUN
ejpam-7119	24	18	across	across	ADP
ejpam-7119	24	19	physics	physics	NOUN
ejpam-7119	24	20	,	,	PUNCT
ejpam-7119	24	21	engineering	engineering	NOUN
ejpam-7119	24	22	,	,	PUNCT
ejpam-7119	24	23	and	and	CCONJ
ejpam-7119	24	24	biological	biological	ADJ
ejpam-7119	24	25	systems	system	NOUN
ejpam-7119	24	26	.	.	PUNCT
ejpam-7119	25	1	the	the	DET
ejpam-7119	25	2	incorporation	incorporation	NOUN
ejpam-7119	25	3	of	of	ADP
ejpam-7119	25	4	fractional	fractional	ADJ
ejpam-7119	25	5	operators	operator	NOUN
ejpam-7119	25	6	into	into	ADP
ejpam-7119	25	7	metric	metric	ADJ
ejpam-7119	25	8	space	space	NOUN
ejpam-7119	25	9	theory	theory	NOUN
ejpam-7119	25	10	represents	represent	VERB
ejpam-7119	25	11	a	a	DET
ejpam-7119	25	12	natural	natural	ADJ
ejpam-7119	25	13	progression	progression	NOUN
ejpam-7119	25	14	,	,	PUNCT
ejpam-7119	25	15	with	with	ADP
ejpam-7119	25	16	recent	recent	ADJ
ejpam-7119	25	17	contributions	contribution	NOUN
ejpam-7119	25	18	by	by	ADP
ejpam-7119	25	19	al	al	PROPN
ejpam-7119	25	20	-	-	PUNCT
ejpam-7119	25	21	deiakeh	deiakeh	NOUN
ejpam-7119	25	22	et	et	PROPN
ejpam-7119	25	23	al	al	PROPN
ejpam-7119	25	24	.	.	PUNCT
ejpam-7119	26	1	[	[	X
ejpam-7119	26	2	17	17	NUM
ejpam-7119	26	3	]	]	PUNCT
ejpam-7119	26	4	in	in	ADP
ejpam-7119	26	5	fractional	fractional	ADJ
ejpam-7119	26	6	differential	differential	ADJ
ejpam-7119	26	7	equations	equation	NOUN
ejpam-7119	26	8	and	and	CCONJ
ejpam-7119	26	9	gharib	gharib	PROPN
ejpam-7119	26	10	et	et	PROPN
ejpam-7119	26	11	al	al	PROPN
ejpam-7119	26	12	.	.	PUNCT
ejpam-7119	27	1	[	[	X
ejpam-7119	27	2	18	18	NUM
ejpam-7119	27	3	]	]	PUNCT
ejpam-7119	27	4	in	in	ADP
ejpam-7119	27	5	fractional	fractional	ADJ
ejpam-7119	27	6	solution	solution	NOUN
ejpam-7119	27	7	methods	method	NOUN
ejpam-7119	27	8	highlighting	highlight	VERB
ejpam-7119	27	9	this	this	DET
ejpam-7119	27	10	trend	trend	NOUN
ejpam-7119	27	11	.	.	PUNCT
ejpam-7119	28	1	malkawi	malkawi	ADP
ejpam-7119	28	2	and	and	CCONJ
ejpam-7119	28	3	rabaiah	rabaiah	PROPN
ejpam-7119	29	1	[	[	X
ejpam-7119	29	2	19	19	NUM
ejpam-7119	29	3	,	,	PUNCT
ejpam-7119	29	4	20	20	NUM
ejpam-7119	29	5	]	]	PUNCT
ejpam-7119	29	6	have	have	AUX
ejpam-7119	29	7	recently	recently	ADV
ejpam-7119	29	8	explored	explore	VERB
ejpam-7119	29	9	the	the	DET
ejpam-7119	29	10	connections	connection	NOUN
ejpam-7119	29	11	between	between	ADP
ejpam-7119	29	12	mr	mr	PROPN
ejpam-7119	29	13	-	-	PUNCT
ejpam-7119	29	14	metric	metric	ADJ
ejpam-7119	29	15	spaces	space	NOUN
ejpam-7119	29	16	and	and	CCONJ
ejpam-7119	29	17	fractional	fractional	ADJ
ejpam-7119	29	18	calculus	calculus	NOUN
ejpam-7119	29	19	,	,	PUNCT
ejpam-7119	29	20	establishing	establish	VERB
ejpam-7119	29	21	important	important	ADJ
ejpam-7119	29	22	bridges	bridge	NOUN
ejpam-7119	29	23	between	between	ADP
ejpam-7119	29	24	these	these	DET
ejpam-7119	29	25	domains	domain	NOUN
ejpam-7119	29	26	.	.	PUNCT
ejpam-7119	30	1	the	the	DET
ejpam-7119	30	2	current	current	ADJ
ejpam-7119	30	3	literature	literature	NOUN
ejpam-7119	30	4	reveals	reveal	VERB
ejpam-7119	30	5	a	a	DET
ejpam-7119	30	6	significant	significant	ADJ
ejpam-7119	30	7	gap	gap	NOUN
ejpam-7119	30	8	:	:	PUNCT
ejpam-7119	30	9	no	no	DET
ejpam-7119	30	10	existing	exist	VERB
ejpam-7119	30	11	framework	framework	NOUN
ejpam-7119	30	12	simultaneously	simultaneously	ADV
ejpam-7119	30	13	incorporates	incorporate	VERB
ejpam-7119	30	14	fractional	fractional	ADJ
ejpam-7119	30	15	calculus	calculus	NOUN
ejpam-7119	30	16	,	,	PUNCT
ejpam-7119	30	17	neutrosophic	neutrosophic	ADJ
ejpam-7119	30	18	logic	logic	NOUN
ejpam-7119	30	19	,	,	PUNCT
ejpam-7119	30	20	and	and	CCONJ
ejpam-7119	30	21	mr	mr	PROPN
ejpam-7119	30	22	-	-	PUNCT
ejpam-7119	30	23	metric	metric	ADJ
ejpam-7119	30	24	structures	structure	NOUN
ejpam-7119	30	25	.	.	PUNCT
ejpam-7119	31	1	this	this	DET
ejpam-7119	31	2	research	research	NOUN
ejpam-7119	31	3	fills	fill	VERB
ejpam-7119	31	4	this	this	DET
ejpam-7119	31	5	void	void	NOUN
ejpam-7119	31	6	by	by	ADP
ejpam-7119	31	7	introducing	introduce	VERB
ejpam-7119	31	8	fractional	fractional	ADJ
ejpam-7119	31	9	-	-	PUNCT
ejpam-7119	31	10	order	order	NOUN
ejpam-7119	31	11	neutrosophic	neutrosophic	ADJ
ejpam-7119	31	12	mr	mr	PROPN
ejpam-7119	31	13	-	-	PUNCT
ejpam-7119	31	14	metric	metric	ADJ
ejpam-7119	31	15	spaces	space	NOUN
ejpam-7119	31	16	(	(	PUNCT
ejpam-7119	31	17	fonmr	fonmr	NOUN
ejpam-7119	31	18	-	-	PUNCT
ejpam-7119	31	19	ms	ms	NOUN
ejpam-7119	31	20	)	)	PUNCT
ejpam-7119	31	21	,	,	PUNCT
ejpam-7119	31	22	which	which	PRON
ejpam-7119	31	23	synergistically	synergistically	ADV
ejpam-7119	31	24	combine	combine	VERB
ejpam-7119	31	25	these	these	DET
ejpam-7119	31	26	three	three	NUM
ejpam-7119	31	27	powerful	powerful	ADJ
ejpam-7119	31	28	mathematical	mathematical	ADJ
ejpam-7119	31	29	paradigms	paradigm	NOUN
ejpam-7119	31	30	.	.	PUNCT
ejpam-7119	32	1	our	our	PRON
ejpam-7119	32	2	work	work	NOUN
ejpam-7119	32	3	draws	draw	VERB
ejpam-7119	32	4	inspiration	inspiration	NOUN
ejpam-7119	32	5	from	from	ADP
ejpam-7119	32	6	numerous	numerous	ADJ
ejpam-7119	32	7	contributions	contribution	NOUN
ejpam-7119	32	8	in	in	ADP
ejpam-7119	32	9	related	related	ADJ
ejpam-7119	32	10	areas	area	NOUN
ejpam-7119	32	11	,	,	PUNCT
ejpam-7119	32	12	including	include	VERB
ejpam-7119	32	13	the	the	DET
ejpam-7119	32	14	interpolative	interpolative	ADJ
ejpam-7119	32	15	contractions	contraction	NOUN
ejpam-7119	32	16	of	of	ADP
ejpam-7119	32	17	qawasmeh	qawasmeh	NOUN
ejpam-7119	32	18	[	[	X
ejpam-7119	32	19	21	21	NUM
ejpam-7119	32	20	]	]	PUNCT
ejpam-7119	32	21	,	,	PUNCT
ejpam-7119	32	22	simulation	simulation	NOUN
ejpam-7119	32	23	functions	function	NOUN
ejpam-7119	32	24	in	in	ADP
ejpam-7119	32	25	various	various	ADJ
ejpam-7119	32	26	metric	metric	ADJ
ejpam-7119	32	27	contexts	context	NOUN
ejpam-7119	33	1	[	[	X
ejpam-7119	33	2	22–24	22–24	NUM
ejpam-7119	33	3	]	]	PUNCT
ejpam-7119	33	4	,	,	PUNCT
ejpam-7119	33	5	cyclic	cyclic	ADJ
ejpam-7119	33	6	contractions	contraction	NOUN
ejpam-7119	34	1	[	[	X
ejpam-7119	34	2	25–28	25–28	NUM
ejpam-7119	34	3	]	]	PUNCT
ejpam-7119	34	4	,	,	PUNCT
ejpam-7119	34	5	and	and	CCONJ
ejpam-7119	34	6	ω	ω	VERB
ejpam-7119	34	7	-	-	PUNCT
ejpam-7119	34	8	distance	distance	NOUN
ejpam-7119	34	9	mappings	mapping	NOUN
ejpam-7119	35	1	[	[	X
ejpam-7119	35	2	24	24	NUM
ejpam-7119	35	3	,	,	PUNCT
ejpam-7119	35	4	27	27	NUM
ejpam-7119	35	5	,	,	PUNCT
ejpam-7119	35	6	29	29	NUM
ejpam-7119	35	7	]	]	PUNCT
ejpam-7119	35	8	.	.	PUNCT
ejpam-7119	36	1	this	this	DET
ejpam-7119	36	2	paper	paper	NOUN
ejpam-7119	36	3	is	be	AUX
ejpam-7119	36	4	organized	organize	VERB
ejpam-7119	36	5	as	as	SCONJ
ejpam-7119	36	6	follows	follow	VERB
ejpam-7119	36	7	:	:	PUNCT
ejpam-7119	36	8	section	section	NOUN
ejpam-7119	36	9	2	2	NUM
ejpam-7119	36	10	presents	present	VERB
ejpam-7119	36	11	our	our	PRON
ejpam-7119	36	12	main	main	ADJ
ejpam-7119	36	13	theoretical	theoretical	ADJ
ejpam-7119	36	14	contributions	contribution	NOUN
ejpam-7119	36	15	,	,	PUNCT
ejpam-7119	36	16	including	include	VERB
ejpam-7119	36	17	the	the	DET
ejpam-7119	36	18	formal	formal	ADJ
ejpam-7119	36	19	definition	definition	NOUN
ejpam-7119	36	20	of	of	ADP
ejpam-7119	36	21	fonmr	fonmr	ADJ
ejpam-7119	36	22	-	-	PUNCT
ejpam-7119	36	23	ms	ms	ADJ
ejpam-7119	36	24	,	,	PUNCT
ejpam-7119	36	25	fundamental	fundamental	ADJ
ejpam-7119	36	26	properties	property	NOUN
ejpam-7119	36	27	,	,	PUNCT
ejpam-7119	36	28	and	and	CCONJ
ejpam-7119	36	29	a	a	DET
ejpam-7119	36	30	comprehensive	comprehensive	ADJ
ejpam-7119	36	31	fixed	fix	VERB
ejpam-7119	36	32	point	point	NOUN
ejpam-7119	36	33	theorem	theorem	VERB
ejpam-7119	36	34	with	with	ADP
ejpam-7119	36	35	detailed	detailed	ADJ
ejpam-7119	36	36	convergence	convergence	NOUN
ejpam-7119	36	37	analysis	analysis	NOUN
ejpam-7119	36	38	.	.	PUNCT
ejpam-7119	37	1	section	section	NOUN
ejpam-7119	37	2	3	3	NUM
ejpam-7119	37	3	provides	provide	VERB
ejpam-7119	37	4	extensive	extensive	ADJ
ejpam-7119	37	5	examples	example	NOUN
ejpam-7119	37	6	and	and	CCONJ
ejpam-7119	37	7	applications	application	NOUN
ejpam-7119	37	8	demonstrating	demonstrate	VERB
ejpam-7119	37	9	the	the	DET
ejpam-7119	37	10	practical	practical	ADJ
ejpam-7119	37	11	utility	utility	NOUN
ejpam-7119	37	12	of	of	ADP
ejpam-7119	37	13	our	our	PRON
ejpam-7119	37	14	framework	framework	NOUN
ejpam-7119	37	15	.	.	PUNCT
ejpam-7119	38	1	our	our	PRON
ejpam-7119	38	2	results	result	NOUN
ejpam-7119	38	3	significantly	significantly	ADV
ejpam-7119	38	4	generalize	generalize	VERB
ejpam-7119	38	5	previous	previous	ADJ
ejpam-7119	38	6	work	work	NOUN
ejpam-7119	38	7	in	in	ADP
ejpam-7119	38	8	fixed	fix	VERB
ejpam-7119	38	9	point	point	NOUN
ejpam-7119	38	10	theory	theory	NOUN
ejpam-7119	38	11	[	[	X
ejpam-7119	38	12	7	7	NUM
ejpam-7119	38	13	,	,	PUNCT
ejpam-7119	38	14	9	9	NUM
ejpam-7119	38	15	,	,	PUNCT
ejpam-7119	38	16	10	10	NUM
ejpam-7119	38	17	,	,	PUNCT
ejpam-7119	38	18	30–32	30–32	NUM
ejpam-7119	38	19	]	]	PUNCT
ejpam-7119	38	20	,	,	PUNCT
ejpam-7119	38	21	metric	metric	ADJ
ejpam-7119	38	22	space	space	NOUN
ejpam-7119	38	23	theory	theory	NOUN
ejpam-7119	38	24	[	[	X
ejpam-7119	38	25	33–40	33–40	NUM
ejpam-7119	38	26	]	]	PUNCT
ejpam-7119	38	27	,	,	PUNCT
ejpam-7119	38	28	and	and	CCONJ
ejpam-7119	38	29	neutrosophic	neutrosophic	ADJ
ejpam-7119	38	30	analysis	analysis	NOUN
ejpam-7119	38	31	[	[	X
ejpam-7119	38	32	14	14	NUM
ejpam-7119	38	33	,	,	PUNCT
ejpam-7119	38	34	15	15	NUM
ejpam-7119	38	35	,	,	PUNCT
ejpam-7119	38	36	41–49	41–49	NUM
ejpam-7119	38	37	]	]	PUNCT
ejpam-7119	38	38	,	,	PUNCT
ejpam-7119	38	39	while	while	SCONJ
ejpam-7119	38	40	opening	open	VERB
ejpam-7119	38	41	new	new	ADJ
ejpam-7119	38	42	avenues	avenue	NOUN
ejpam-7119	38	43	for	for	ADP
ejpam-7119	38	44	modeling	model	VERB
ejpam-7119	38	45	complex	complex	ADJ
ejpam-7119	38	46	systems	system	NOUN
ejpam-7119	38	47	with	with	ADP
ejpam-7119	38	48	fractional	fractional	ADJ
ejpam-7119	38	49	dynamics	dynamic	NOUN
ejpam-7119	38	50	and	and	CCONJ
ejpam-7119	38	51	neutrosophic	neutrosophic	ADJ
ejpam-7119	38	52	uncertainty	uncertainty	NOUN
ejpam-7119	38	53	.	.	PUNCT
ejpam-7119	39	1	definition	definition	NOUN
ejpam-7119	39	2	1	1	NUM
ejpam-7119	39	3	.	.	PUNCT
ejpam-7119	40	1	[	[	X
ejpam-7119	40	2	3	3	X
ejpam-7119	40	3	]	]	PUNCT
ejpam-7119	40	4	consider	consider	VERB
ejpam-7119	40	5	a	a	DET
ejpam-7119	40	6	non	non	ADJ
ejpam-7119	40	7	-	-	ADJ
ejpam-7119	40	8	empty	empty	ADJ
ejpam-7119	40	9	set	set	NOUN
ejpam-7119	40	10	x	x	PUNCT
ejpam-7119	40	11	̸=	̸=	PROPN
ejpam-7119	40	12	∅	∅	NOUN
ejpam-7119	40	13	and	and	CCONJ
ejpam-7119	40	14	a	a	DET
ejpam-7119	40	15	real	real	ADJ
ejpam-7119	40	16	number	number	NOUN
ejpam-7119	40	17	r	r	NOUN
ejpam-7119	40	18	>	>	X
ejpam-7119	40	19	1	1	NUM
ejpam-7119	40	20	.	.	PUNCT
ejpam-7119	41	1	a	a	DET
ejpam-7119	41	2	function	function	NOUN
ejpam-7119	41	3	m	m	VERB
ejpam-7119	41	4	:	:	PUNCT
ejpam-7119	41	5	x×	x×	X
ejpam-7119	41	6	x×	x×	PUNCT
ejpam-7119	41	7	x	x	PUNCT
ejpam-7119	41	8	→	→	PUNCT
ejpam-7119	41	9	[	[	X
ejpam-7119	41	10	0,∞	0,∞	NOUN
ejpam-7119	41	11	)	)	PUNCT
ejpam-7119	41	12	is	be	AUX
ejpam-7119	41	13	termed	term	VERB
ejpam-7119	41	14	an	an	DET
ejpam-7119	41	15	mr	mr	PROPN
ejpam-7119	41	16	-	-	PUNCT
ejpam-7119	41	17	metric	metric	NOUN
ejpam-7119	41	18	if	if	SCONJ
ejpam-7119	41	19	it	it	PRON
ejpam-7119	41	20	satisfies	satisfy	VERB
ejpam-7119	41	21	the	the	DET
ejpam-7119	41	22	following	follow	VERB
ejpam-7119	41	23	conditions	condition	NOUN
ejpam-7119	41	24	for	for	ADP
ejpam-7119	41	25	all	all	PRON
ejpam-7119	41	26	v	v	NOUN
ejpam-7119	41	27	,	,	PUNCT
ejpam-7119	41	28	ξ	ξ	PROPN
ejpam-7119	41	29	,	,	PUNCT
ejpam-7119	41	30	s	s	PART
ejpam-7119	41	31	,	,	PUNCT
ejpam-7119	41	32	ℓ1	ℓ1	NOUN
ejpam-7119	41	33	∈	∈	NOUN
ejpam-7119	42	1	x	x	X
ejpam-7119	42	2	:	:	PUNCT
ejpam-7119	42	3	•	•	ADP
ejpam-7119	42	4	m(v	m(v	PROPN
ejpam-7119	42	5	,	,	PUNCT
ejpam-7119	42	6	ξ	ξ	PROPN
ejpam-7119	42	7	,	,	PUNCT
ejpam-7119	42	8	s	s	PART
ejpam-7119	42	9	)	)	PUNCT
ejpam-7119	42	10	≥	≥	NOUN
ejpam-7119	42	11	0	0	NUM
ejpam-7119	42	12	.	.	NOUN
ejpam-7119	42	13	•	•	NUM
ejpam-7119	42	14	m(v	m(v	PROPN
ejpam-7119	42	15	,	,	PUNCT
ejpam-7119	42	16	ξ	ξ	PROPN
ejpam-7119	42	17	,	,	PUNCT
ejpam-7119	42	18	s	s	PART
ejpam-7119	42	19	)	)	PUNCT
ejpam-7119	42	20	=	=	SYM
ejpam-7119	42	21	0	0	PUNCT
ejpam-7119	43	1	if	if	SCONJ
ejpam-7119	43	2	and	and	CCONJ
ejpam-7119	43	3	only	only	ADV
ejpam-7119	43	4	if	if	SCONJ
ejpam-7119	43	5	v	v	NOUN
ejpam-7119	43	6	=	=	SYM
ejpam-7119	43	7	ξ	ξ	PROPN
ejpam-7119	43	8	=	=	PUNCT
ejpam-7119	43	9	s.	s.	PROPN
ejpam-7119	43	10	•	•	ADP
ejpam-7119	43	11	m(v	m(v	PROPN
ejpam-7119	43	12	,	,	PUNCT
ejpam-7119	43	13	ξ	ξ	PROPN
ejpam-7119	43	14	,	,	PUNCT
ejpam-7119	43	15	s	s	PART
ejpam-7119	43	16	)	)	PUNCT
ejpam-7119	43	17	remains	remain	VERB
ejpam-7119	43	18	invariant	invariant	ADJ
ejpam-7119	43	19	under	under	ADP
ejpam-7119	43	20	any	any	DET
ejpam-7119	43	21	permutation	permutation	NOUN
ejpam-7119	43	22	p(v	p(v	NOUN
ejpam-7119	43	23	,	,	PUNCT
ejpam-7119	43	24	ξ	ξ	PROPN
ejpam-7119	43	25	,	,	PUNCT
ejpam-7119	43	26	s	s	PART
ejpam-7119	43	27	)	)	PUNCT
ejpam-7119	43	28	,	,	PUNCT
ejpam-7119	43	29	i.e.	i.e.	X
ejpam-7119	43	30	,	,	PUNCT
ejpam-7119	43	31	m(v	m(v	PROPN
ejpam-7119	43	32	,	,	PUNCT
ejpam-7119	43	33	ξ	ξ	PROPN
ejpam-7119	43	34	,	,	PUNCT
ejpam-7119	43	35	s	s	PART
ejpam-7119	43	36	)	)	PUNCT
ejpam-7119	43	37	=	=	SYM
ejpam-7119	43	38	m(p(v	m(p(v	NOUN
ejpam-7119	43	39	,	,	PUNCT
ejpam-7119	43	40	ξ	ξ	PROPN
ejpam-7119	43	41	,	,	PUNCT
ejpam-7119	43	42	s	s	NOUN
ejpam-7119	43	43	)	)	PUNCT
ejpam-7119	43	44	)	)	PUNCT
ejpam-7119	43	45	.	.	PUNCT
ejpam-7119	44	1	•	•	NUM
ejpam-7119	44	2	the	the	DET
ejpam-7119	44	3	following	follow	VERB
ejpam-7119	44	4	inequality	inequality	NOUN
ejpam-7119	44	5	holds	hold	VERB
ejpam-7119	44	6	:	:	PUNCT
ejpam-7119	44	7	m(v	m(v	NUM
ejpam-7119	44	8	,	,	PUNCT
ejpam-7119	44	9	ξ	ξ	PROPN
ejpam-7119	44	10	,	,	PUNCT
ejpam-7119	44	11	s	s	NOUN
ejpam-7119	44	12	)	)	PUNCT
ejpam-7119	44	13	≤	≤	NOUN
ejpam-7119	44	14	r	r	NOUN
ejpam-7119	45	1	[	[	X
ejpam-7119	45	2	m(v	m(v	X
ejpam-7119	45	3	,	,	PUNCT
ejpam-7119	45	4	ξ	ξ	X
ejpam-7119	45	5	,	,	PUNCT
ejpam-7119	45	6	ℓ1	ℓ1	NOUN
ejpam-7119	45	7	)	)	PUNCT
ejpam-7119	46	1	+	+	SYM
ejpam-7119	46	2	m(v	m(v	NOUN
ejpam-7119	46	3	,	,	PUNCT
ejpam-7119	46	4	ℓ1	ℓ1	NOUN
ejpam-7119	46	5	,	,	PUNCT
ejpam-7119	46	6	s	s	X
ejpam-7119	46	7	)	)	PUNCT
ejpam-7119	46	8	+	+	ADJ
ejpam-7119	46	9	m(ℓ1	m(ℓ1	NOUN
ejpam-7119	46	10	,	,	PUNCT
ejpam-7119	46	11	ξ	ξ	PROPN
ejpam-7119	46	12	,	,	PUNCT
ejpam-7119	46	13	s	s	PART
ejpam-7119	46	14	)	)	PUNCT
ejpam-7119	46	15	]	]	PUNCT
ejpam-7119	46	16	.	.	PUNCT
ejpam-7119	47	1	a	a	DET
ejpam-7119	47	2	structure	structure	NOUN
ejpam-7119	47	3	(	(	PUNCT
ejpam-7119	47	4	x	x	X
ejpam-7119	47	5	,	,	PUNCT
ejpam-7119	47	6	m	m	NOUN
ejpam-7119	47	7	)	)	PUNCT
ejpam-7119	47	8	that	that	PRON
ejpam-7119	47	9	adheres	adhere	VERB
ejpam-7119	47	10	to	to	ADP
ejpam-7119	47	11	these	these	DET
ejpam-7119	47	12	properties	property	NOUN
ejpam-7119	47	13	is	be	AUX
ejpam-7119	47	14	defined	define	VERB
ejpam-7119	47	15	as	as	ADP
ejpam-7119	47	16	an	an	DET
ejpam-7119	47	17	mr	mr	PROPN
ejpam-7119	47	18	-	-	PUNCT
ejpam-7119	47	19	metric	metric	ADJ
ejpam-7119	47	20	space	space	NOUN
ejpam-7119	47	21	.	.	PUNCT
ejpam-7119	48	1	definition	definition	NOUN
ejpam-7119	48	2	2	2	NUM
ejpam-7119	48	3	.	.	PUNCT
ejpam-7119	49	1	[	[	X
ejpam-7119	49	2	32][neutrosophic	32][neutrosophic	ADJ
ejpam-7119	49	3	mr	mr	ADJ
ejpam-7119	49	4	-	-	PUNCT
ejpam-7119	49	5	metric	metric	ADJ
ejpam-7119	49	6	space	space	NOUN
ejpam-7119	49	7	(	(	PUNCT
ejpam-7119	49	8	nmr	nmr	NOUN
ejpam-7119	49	9	-	-	PUNCT
ejpam-7119	49	10	ms	ms	NOUN
ejpam-7119	49	11	)	)	PUNCT
ejpam-7119	49	12	]	]	PUNCT
ejpam-7119	49	13	a	a	DET
ejpam-7119	49	14	9	9	NUM
ejpam-7119	49	15	-	-	PUNCT
ejpam-7119	49	16	tuple	tuple	NOUN
ejpam-7119	49	17	(	(	PUNCT
ejpam-7119	49	18	z	z	PROPN
ejpam-7119	49	19	,	,	PUNCT
ejpam-7119	49	20	m	m	PROPN
ejpam-7119	49	21	,	,	PUNCT
ejpam-7119	49	22	t	t	PROPN
ejpam-7119	49	23	,	,	PUNCT
ejpam-7119	49	24	f	f	PROPN
ejpam-7119	49	25	,	,	PUNCT
ejpam-7119	49	26	i	i	PRON
ejpam-7119	49	27	,	,	PUNCT
ejpam-7119	49	28	•	•	PROPN
ejpam-7119	49	29	,	,	PUNCT
ejpam-7119	49	30	⋄	⋄	PROPN
ejpam-7119	49	31	,	,	PUNCT
ejpam-7119	49	32	r	r	NOUN
ejpam-7119	49	33	,	,	PUNCT
ejpam-7119	49	34	⋆	⋆	CCONJ
ejpam-7119	49	35	)	)	PUNCT
ejpam-7119	49	36	is	be	AUX
ejpam-7119	49	37	called	call	VERB
ejpam-7119	49	38	a	a	DET
ejpam-7119	49	39	neutrosophic	neutrosophic	ADJ
ejpam-7119	49	40	mr	mr	ADJ
ejpam-7119	49	41	-	-	PUNCT
ejpam-7119	49	42	metric	metric	ADJ
ejpam-7119	49	43	space	space	NOUN
ejpam-7119	49	44	if	if	SCONJ
ejpam-7119	49	45	:	:	PUNCT
ejpam-7119	49	46	(	(	PUNCT
ejpam-7119	49	47	i	i	NOUN
ejpam-7119	49	48	)	)	PUNCT
ejpam-7119	49	49	z	z	PROPN
ejpam-7119	49	50	is	be	AUX
ejpam-7119	49	51	a	a	DET
ejpam-7119	49	52	non	non	ADJ
ejpam-7119	49	53	-	-	ADJ
ejpam-7119	49	54	empty	empty	ADJ
ejpam-7119	49	55	set	set	NOUN
ejpam-7119	49	56	.	.	PUNCT
ejpam-7119	50	1	(	(	PUNCT
ejpam-7119	50	2	ii	ii	NOUN
ejpam-7119	50	3	)	)	PUNCT
ejpam-7119	50	4	m	m	VERB
ejpam-7119	50	5	:	:	PUNCT
ejpam-7119	50	6	z	z	X
ejpam-7119	50	7	×	×	NOUN
ejpam-7119	50	8	z	z	NOUN
ejpam-7119	50	9	×z	×z	PROPN
ejpam-7119	50	10	→	→	SYM
ejpam-7119	50	11	[	[	X
ejpam-7119	50	12	0,∞	0,∞	NUM
ejpam-7119	50	13	)	)	PUNCT
ejpam-7119	50	14	is	be	AUX
ejpam-7119	50	15	an	an	DET
ejpam-7119	50	16	mr	mr	ADJ
ejpam-7119	50	17	-	-	PUNCT
ejpam-7119	50	18	metric	metric	ADJ
ejpam-7119	50	19	satisfying	satisfying	NOUN
ejpam-7119	50	20	:	:	PUNCT
ejpam-7119	50	21	(	(	PUNCT
ejpam-7119	50	22	m1	m1	NOUN
ejpam-7119	50	23	)	)	PUNCT
ejpam-7119	50	24	m(υ	m(υ	PROPN
ejpam-7119	50	25	,	,	PUNCT
ejpam-7119	50	26	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	50	27	)	)	PUNCT
ejpam-7119	50	28	≥	≥	NOUN
ejpam-7119	50	29	0	0	NUM
ejpam-7119	50	30	,	,	PUNCT
ejpam-7119	50	31	(	(	PUNCT
ejpam-7119	50	32	m2	m2	PROPN
ejpam-7119	50	33	)	)	PUNCT
ejpam-7119	50	34	m(υ	m(υ	PROPN
ejpam-7119	50	35	,	,	PUNCT
ejpam-7119	50	36	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	50	37	)	)	PUNCT
ejpam-7119	51	1	=	=	SYM
ejpam-7119	51	2	0	0	NUM
ejpam-7119	52	1	⇐	⇐	ADJ
ejpam-7119	52	2	⇒	⇒	NOUN
ejpam-7119	52	3	υ	υ	X
ejpam-7119	52	4	=	=	SYM
ejpam-7119	52	5	ξ	ξ	PROPN
ejpam-7119	52	6	=	=	SYM
ejpam-7119	52	7	ℑ	ℑ	PROPN
ejpam-7119	52	8	,	,	PUNCT
ejpam-7119	52	9	a.	a.	NOUN
ejpam-7119	52	10	malkawi	malkawi	PROPN
ejpam-7119	52	11	,	,	PUNCT
ejpam-7119	52	12	a.	a.	PROPN
ejpam-7119	52	13	rabaiah	rabaiah	PROPN
ejpam-7119	52	14	/	/	SYM
ejpam-7119	52	15	eur	eur	PROPN
ejpam-7119	52	16	.	.	PUNCT
ejpam-7119	53	1	j.	j.	PROPN
ejpam-7119	53	2	pure	pure	PROPN
ejpam-7119	53	3	appl	appl	PROPN
ejpam-7119	53	4	.	.	PROPN
ejpam-7119	53	5	math	math	PROPN
ejpam-7119	53	6	,	,	PUNCT
ejpam-7119	53	7	18	18	NUM
ejpam-7119	53	8	(	(	PUNCT
ejpam-7119	53	9	4	4	NUM
ejpam-7119	53	10	)	)	PUNCT
ejpam-7119	53	11	(	(	PUNCT
ejpam-7119	53	12	2025	2025	NUM
ejpam-7119	53	13	)	)	PUNCT
ejpam-7119	53	14	,	,	PUNCT
ejpam-7119	53	15	7119	7119	NUM
ejpam-7119	53	16	3	3	NUM
ejpam-7119	53	17	of	of	ADP
ejpam-7119	53	18	13	13	NUM
ejpam-7119	53	19	(	(	PUNCT
ejpam-7119	53	20	m3	m3	PROPN
ejpam-7119	53	21	)	)	PUNCT
ejpam-7119	53	22	symmetry	symmetry	NOUN
ejpam-7119	53	23	under	under	ADP
ejpam-7119	53	24	permutations	permutation	NOUN
ejpam-7119	53	25	,	,	PUNCT
ejpam-7119	53	26	(	(	PUNCT
ejpam-7119	53	27	m4	m4	PROPN
ejpam-7119	53	28	)	)	PUNCT
ejpam-7119	53	29	m(υ	m(υ	PROPN
ejpam-7119	53	30	,	,	PUNCT
ejpam-7119	53	31	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	53	32	)	)	PUNCT
ejpam-7119	53	33	≤	≤	NUM
ejpam-7119	54	1	r	r	NOUN
ejpam-7119	55	1	[	[	X
ejpam-7119	55	2	m(υ	m(υ	PROPN
ejpam-7119	55	3	,	,	PUNCT
ejpam-7119	55	4	ξ	ξ	PROPN
ejpam-7119	55	5	,	,	PUNCT
ejpam-7119	55	6	ℓ	ℓ	NUM
ejpam-7119	55	7	)	)	PUNCT
ejpam-7119	55	8	⋆	⋆	NOUN
ejpam-7119	56	1	m(υ	m(υ	PROPN
ejpam-7119	56	2	,	,	PUNCT
ejpam-7119	56	3	ℓ,ℑ	ℓ,ℑ	PROPN
ejpam-7119	56	4	)	)	PUNCT
ejpam-7119	56	5	⋆	⋆	NOUN
ejpam-7119	56	6	m(ℓ	m(ℓ	NOUN
ejpam-7119	56	7	,	,	PUNCT
ejpam-7119	56	8	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	56	9	)	)	PUNCT
ejpam-7119	56	10	]	]	PUNCT
ejpam-7119	56	11	,	,	PUNCT
ejpam-7119	56	12	r	r	NOUN
ejpam-7119	56	13	>	>	X
ejpam-7119	56	14	1	1	NUM
ejpam-7119	56	15	.	.	PUNCT
ejpam-7119	56	16	(	(	PUNCT
ejpam-7119	56	17	iii	iii	X
ejpam-7119	56	18	)	)	PUNCT
ejpam-7119	56	19	t	t	NOUN
ejpam-7119	56	20	,	,	PUNCT
ejpam-7119	56	21	f	f	PROPN
ejpam-7119	56	22	,	,	PUNCT
ejpam-7119	56	23	i	i	PRON
ejpam-7119	56	24	:	:	PUNCT
ejpam-7119	56	25	z	z	NOUN
ejpam-7119	56	26	×	×	PROPN
ejpam-7119	56	27	z	z	NOUN
ejpam-7119	56	28	×	×	NOUN
ejpam-7119	56	29	(	(	PUNCT
ejpam-7119	56	30	0,∞	0,∞	NOUN
ejpam-7119	56	31	)	)	PUNCT
ejpam-7119	57	1	→	→	PUNCT
ejpam-7119	57	2	[	[	X
ejpam-7119	57	3	0	0	NUM
ejpam-7119	57	4	,	,	PUNCT
ejpam-7119	57	5	1	1	NUM
ejpam-7119	57	6	]	]	PUNCT
ejpam-7119	57	7	are	be	AUX
ejpam-7119	57	8	neutrosophic	neutrosophic	ADJ
ejpam-7119	57	9	functions	function	NOUN
ejpam-7119	57	10	satisfying	satisfy	VERB
ejpam-7119	57	11	:	:	PUNCT
ejpam-7119	57	12	(	(	PUNCT
ejpam-7119	57	13	n1	n1	NOUN
ejpam-7119	57	14	)	)	PUNCT
ejpam-7119	57	15	t	t	NOUN
ejpam-7119	57	16	(	(	PUNCT
ejpam-7119	57	17	υ	υ	PROPN
ejpam-7119	57	18	,	,	PUNCT
ejpam-7119	57	19	ξ	ξ	PROPN
ejpam-7119	57	20	,	,	PUNCT
ejpam-7119	57	21	γ	γ	NOUN
ejpam-7119	57	22	)	)	PUNCT
ejpam-7119	57	23	=	=	SYM
ejpam-7119	57	24	1	1	NUM
ejpam-7119	57	25	⇐	⇐	ADJ
ejpam-7119	57	26	⇒	⇒	NOUN
ejpam-7119	57	27	υ	υ	X
ejpam-7119	57	28	=	=	SYM
ejpam-7119	57	29	ξ	ξ	PROPN
ejpam-7119	57	30	(	(	PUNCT
ejpam-7119	57	31	truth	truth	NOUN
ejpam-7119	57	32	-	-	PUNCT
ejpam-7119	57	33	identity	identity	NOUN
ejpam-7119	57	34	)	)	PUNCT
ejpam-7119	57	35	,	,	PUNCT
ejpam-7119	57	36	(	(	PUNCT
ejpam-7119	57	37	n2	n2	ADJ
ejpam-7119	57	38	)	)	PUNCT
ejpam-7119	57	39	t	t	NOUN
ejpam-7119	57	40	(	(	PUNCT
ejpam-7119	57	41	υ	υ	PROPN
ejpam-7119	57	42	,	,	PUNCT
ejpam-7119	57	43	ξ	ξ	PROPN
ejpam-7119	57	44	,	,	PUNCT
ejpam-7119	57	45	γ	γ	NOUN
ejpam-7119	57	46	)	)	PUNCT
ejpam-7119	57	47	=	=	SYM
ejpam-7119	57	48	t	t	PROPN
ejpam-7119	57	49	(	(	PUNCT
ejpam-7119	57	50	ξ	ξ	PROPN
ejpam-7119	57	51	,	,	PUNCT
ejpam-7119	57	52	υ	υ	PROPN
ejpam-7119	57	53	,	,	PUNCT
ejpam-7119	57	54	γ	γ	NOUN
ejpam-7119	57	55	)	)	PUNCT
ejpam-7119	57	56	(	(	PUNCT
ejpam-7119	57	57	symmetry	symmetry	NOUN
ejpam-7119	57	58	)	)	PUNCT
ejpam-7119	57	59	,	,	PUNCT
ejpam-7119	57	60	(	(	PUNCT
ejpam-7119	57	61	n3	n3	PROPN
ejpam-7119	57	62	)	)	PUNCT
ejpam-7119	57	63	t	t	PROPN
ejpam-7119	57	64	(	(	PUNCT
ejpam-7119	57	65	υ	υ	PROPN
ejpam-7119	57	66	,	,	PUNCT
ejpam-7119	57	67	ξ	ξ	PROPN
ejpam-7119	57	68	,	,	PUNCT
ejpam-7119	57	69	γ	γ	NOUN
ejpam-7119	57	70	)	)	PUNCT
ejpam-7119	57	71	•	•	NUM
ejpam-7119	57	72	t	t	PROPN
ejpam-7119	57	73	(	(	PUNCT
ejpam-7119	57	74	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	57	75	,	,	PUNCT
ejpam-7119	57	76	ρ	ρ	NOUN
ejpam-7119	57	77	)	)	PUNCT
ejpam-7119	57	78	≤	≤	NOUN
ejpam-7119	57	79	t	t	NOUN
ejpam-7119	57	80	(	(	PUNCT
ejpam-7119	57	81	υ,ℑ	υ,ℑ	PROPN
ejpam-7119	57	82	,	,	PUNCT
ejpam-7119	57	83	γ	γ	X
ejpam-7119	57	84	+	+	NOUN
ejpam-7119	57	85	ρ	ρ	PROPN
ejpam-7119	57	86	)	)	PUNCT
ejpam-7119	57	87	(	(	PUNCT
ejpam-7119	57	88	triangle	triangle	NOUN
ejpam-7119	57	89	inequality	inequality	NOUN
ejpam-7119	57	90	)	)	PUNCT
ejpam-7119	57	91	,	,	PUNCT
ejpam-7119	57	92	(	(	PUNCT
ejpam-7119	57	93	n4	n4	PROPN
ejpam-7119	57	94	)	)	PUNCT
ejpam-7119	57	95	limγ→∞	limγ→∞	PROPN
ejpam-7119	57	96	t	t	NOUN
ejpam-7119	57	97	(	(	PUNCT
ejpam-7119	57	98	υ	υ	PROPN
ejpam-7119	57	99	,	,	PUNCT
ejpam-7119	57	100	ξ	ξ	PROPN
ejpam-7119	57	101	,	,	PUNCT
ejpam-7119	57	102	γ	γ	NOUN
ejpam-7119	57	103	)	)	PUNCT
ejpam-7119	57	104	=	=	SYM
ejpam-7119	57	105	1	1	NUM
ejpam-7119	57	106	(	(	PUNCT
ejpam-7119	57	107	asymptotic	asymptotic	ADJ
ejpam-7119	57	108	behavior	behavior	NOUN
ejpam-7119	57	109	)	)	PUNCT
ejpam-7119	57	110	.	.	PUNCT
ejpam-7119	58	1	(	(	PUNCT
ejpam-7119	58	2	iv	iv	X
ejpam-7119	58	3	)	)	PUNCT
ejpam-7119	58	4	•	•	NOUN
ejpam-7119	58	5	(	(	PUNCT
ejpam-7119	58	6	t	t	NOUN
ejpam-7119	58	7	-	-	PUNCT
ejpam-7119	58	8	norm	norm	NOUN
ejpam-7119	58	9	)	)	PUNCT
ejpam-7119	58	10	and	and	CCONJ
ejpam-7119	58	11	⋄	⋄	PROPN
ejpam-7119	58	12	(	(	PUNCT
ejpam-7119	58	13	t	t	NOUN
ejpam-7119	58	14	-	-	PUNCT
ejpam-7119	58	15	conorm	conorm	NOUN
ejpam-7119	58	16	)	)	PUNCT
ejpam-7119	58	17	are	be	AUX
ejpam-7119	58	18	continuous	continuous	ADJ
ejpam-7119	58	19	operators	operator	NOUN
ejpam-7119	58	20	generalizing	generalize	VERB
ejpam-7119	58	21	fuzzy	fuzzy	ADJ
ejpam-7119	58	22	logic	logic	NOUN
ejpam-7119	58	23	.	.	PUNCT
ejpam-7119	59	1	(	(	PUNCT
ejpam-7119	59	2	v	v	NOUN
ejpam-7119	59	3	)	)	PUNCT
ejpam-7119	59	4	⋆	⋆	VERB
ejpam-7119	59	5	is	be	AUX
ejpam-7119	59	6	a	a	DET
ejpam-7119	59	7	binary	binary	ADJ
ejpam-7119	59	8	operation	operation	NOUN
ejpam-7119	59	9	generalizing	generalize	VERB
ejpam-7119	59	10	addition	addition	NOUN
ejpam-7119	59	11	(	(	PUNCT
ejpam-7119	59	12	e.g.	e.g.	ADV
ejpam-7119	59	13	,	,	PUNCT
ejpam-7119	59	14	weighted	weight	VERB
ejpam-7119	59	15	sum	sum	NOUN
ejpam-7119	59	16	)	)	PUNCT
ejpam-7119	59	17	.	.	PUNCT
ejpam-7119	60	1	2	2	X
ejpam-7119	60	2	.	.	X
ejpam-7119	60	3	main	main	ADJ
ejpam-7119	60	4	results	result	NOUN
ejpam-7119	60	5	this	this	DET
ejpam-7119	60	6	section	section	NOUN
ejpam-7119	60	7	presents	present	VERB
ejpam-7119	60	8	the	the	DET
ejpam-7119	60	9	principal	principal	ADJ
ejpam-7119	60	10	theoretical	theoretical	ADJ
ejpam-7119	60	11	contributions	contribution	NOUN
ejpam-7119	60	12	of	of	ADP
ejpam-7119	60	13	this	this	DET
ejpam-7119	60	14	work	work	NOUN
ejpam-7119	60	15	,	,	PUNCT
ejpam-7119	60	16	wherein	wherein	SCONJ
ejpam-7119	60	17	we	we	PRON
ejpam-7119	60	18	introduce	introduce	VERB
ejpam-7119	60	19	and	and	CCONJ
ejpam-7119	60	20	rigorously	rigorously	ADV
ejpam-7119	60	21	develop	develop	VERB
ejpam-7119	60	22	the	the	DET
ejpam-7119	60	23	framework	framework	NOUN
ejpam-7119	60	24	of	of	ADP
ejpam-7119	60	25	fractional	fractional	ADJ
ejpam-7119	60	26	-	-	PUNCT
ejpam-7119	60	27	order	order	NOUN
ejpam-7119	60	28	neutrosophic	neutrosophic	ADJ
ejpam-7119	60	29	mr	mr	PROPN
ejpam-7119	60	30	-	-	PUNCT
ejpam-7119	60	31	metric	metric	ADJ
ejpam-7119	60	32	spaces	space	NOUN
ejpam-7119	60	33	(	(	PUNCT
ejpam-7119	60	34	fonmr	fonmr	NOUN
ejpam-7119	60	35	-	-	PUNCT
ejpam-7119	60	36	ms	ms	NOUN
ejpam-7119	60	37	)	)	PUNCT
ejpam-7119	60	38	.	.	PUNCT
ejpam-7119	61	1	we	we	PRON
ejpam-7119	61	2	commence	commence	VERB
ejpam-7119	61	3	by	by	ADP
ejpam-7119	61	4	formalizing	formalize	VERB
ejpam-7119	61	5	the	the	DET
ejpam-7119	61	6	fundamental	fundamental	ADJ
ejpam-7119	61	7	definitions	definition	NOUN
ejpam-7119	61	8	that	that	PRON
ejpam-7119	61	9	amalgamate	amalgamate	VERB
ejpam-7119	61	10	the	the	DET
ejpam-7119	61	11	concepts	concept	NOUN
ejpam-7119	61	12	of	of	ADP
ejpam-7119	61	13	mr	mr	PROPN
ejpam-7119	61	14	-	-	PUNCT
ejpam-7119	61	15	metrics	metric	NOUN
ejpam-7119	61	16	,	,	PUNCT
ejpam-7119	61	17	neutrosophic	neutrosophic	ADJ
ejpam-7119	61	18	logic	logic	NOUN
ejpam-7119	61	19	,	,	PUNCT
ejpam-7119	61	20	and	and	CCONJ
ejpam-7119	61	21	fractional	fractional	ADJ
ejpam-7119	61	22	calculus	calculus	NOUN
ejpam-7119	61	23	into	into	ADP
ejpam-7119	61	24	a	a	DET
ejpam-7119	61	25	unified	unified	ADJ
ejpam-7119	61	26	structure	structure	NOUN
ejpam-7119	61	27	.	.	PUNCT
ejpam-7119	62	1	subsequently	subsequently	ADV
ejpam-7119	62	2	,	,	PUNCT
ejpam-7119	62	3	we	we	PRON
ejpam-7119	62	4	establish	establish	VERB
ejpam-7119	62	5	the	the	DET
ejpam-7119	62	6	foundational	foundational	ADJ
ejpam-7119	62	7	properties	property	NOUN
ejpam-7119	62	8	of	of	ADP
ejpam-7119	62	9	the	the	DET
ejpam-7119	62	10	proposed	propose	VERB
ejpam-7119	62	11	fractional	fractional	ADJ
ejpam-7119	62	12	-	-	PUNCT
ejpam-7119	62	13	order	order	NOUN
ejpam-7119	62	14	metric	metric	ADJ
ejpam-7119	62	15	and	and	CCONJ
ejpam-7119	62	16	neutrosophic	neutrosophic	ADJ
ejpam-7119	62	17	functions	function	NOUN
ejpam-7119	62	18	,	,	PUNCT
ejpam-7119	62	19	proving	prove	VERB
ejpam-7119	62	20	their	their	PRON
ejpam-7119	62	21	consistency	consistency	NOUN
ejpam-7119	62	22	with	with	ADP
ejpam-7119	62	23	the	the	DET
ejpam-7119	62	24	axiomatic	axiomatic	ADJ
ejpam-7119	62	25	foundations	foundation	NOUN
ejpam-7119	62	26	of	of	ADP
ejpam-7119	62	27	generalized	generalized	ADJ
ejpam-7119	62	28	metric	metric	ADJ
ejpam-7119	62	29	spaces	space	NOUN
ejpam-7119	62	30	.	.	PUNCT
ejpam-7119	63	1	the	the	DET
ejpam-7119	63	2	cornerstone	cornerstone	NOUN
ejpam-7119	63	3	of	of	ADP
ejpam-7119	63	4	our	our	PRON
ejpam-7119	63	5	investigation	investigation	NOUN
ejpam-7119	63	6	is	be	AUX
ejpam-7119	63	7	the	the	DET
ejpam-7119	63	8	comprehensive	comprehensive	ADJ
ejpam-7119	63	9	fixed	fix	VERB
ejpam-7119	63	10	point	point	NOUN
ejpam-7119	63	11	theorem	theorem	NOUN
ejpam-7119	63	12	for	for	ADP
ejpam-7119	63	13	contraction	contraction	NOUN
ejpam-7119	63	14	mappings	mapping	NOUN
ejpam-7119	63	15	within	within	ADP
ejpam-7119	63	16	complete	complete	ADJ
ejpam-7119	63	17	fonmr	fonmr	ADJ
ejpam-7119	63	18	-	-	PUNCT
ejpam-7119	63	19	ms	ms	NOUN
ejpam-7119	63	20	,	,	PUNCT
ejpam-7119	63	21	accompanied	accompany	VERB
ejpam-7119	63	22	by	by	ADP
ejpam-7119	63	23	a	a	DET
ejpam-7119	63	24	detailed	detailed	ADJ
ejpam-7119	63	25	proof	proof	NOUN
ejpam-7119	63	26	that	that	PRON
ejpam-7119	63	27	elucidates	elucidate	VERB
ejpam-7119	63	28	the	the	DET
ejpam-7119	63	29	convergence	convergence	NOUN
ejpam-7119	63	30	behavior	behavior	NOUN
ejpam-7119	63	31	of	of	ADP
ejpam-7119	63	32	iterative	iterative	ADJ
ejpam-7119	63	33	sequences	sequence	NOUN
ejpam-7119	63	34	and	and	CCONJ
ejpam-7119	63	35	the	the	DET
ejpam-7119	63	36	role	role	NOUN
ejpam-7119	63	37	of	of	ADP
ejpam-7119	63	38	the	the	DET
ejpam-7119	63	39	fractional	fractional	ADJ
ejpam-7119	63	40	parameter	parameter	NOUN
ejpam-7119	63	41	α	α	PROPN
ejpam-7119	63	42	and	and	CCONJ
ejpam-7119	63	43	the	the	DET
ejpam-7119	63	44	neutrosophic	neutrosophic	ADJ
ejpam-7119	63	45	conditions	condition	NOUN
ejpam-7119	63	46	in	in	ADP
ejpam-7119	63	47	guaranteeing	guarantee	VERB
ejpam-7119	63	48	the	the	DET
ejpam-7119	63	49	existence	existence	NOUN
ejpam-7119	63	50	and	and	CCONJ
ejpam-7119	63	51	uniqueness	uniqueness	NOUN
ejpam-7119	63	52	of	of	ADP
ejpam-7119	63	53	a	a	DET
ejpam-7119	63	54	fixed	fix	VERB
ejpam-7119	63	55	point	point	NOUN
ejpam-7119	63	56	.	.	PUNCT
ejpam-7119	64	1	the	the	DET
ejpam-7119	64	2	ensuing	ensue	VERB
ejpam-7119	64	3	lemmas	lemma	NOUN
ejpam-7119	64	4	and	and	CCONJ
ejpam-7119	64	5	corollaries	corollary	NOUN
ejpam-7119	64	6	further	far	ADV
ejpam-7119	64	7	delineate	delineate	VERB
ejpam-7119	64	8	the	the	DET
ejpam-7119	64	9	analytical	analytical	ADJ
ejpam-7119	64	10	properties	property	NOUN
ejpam-7119	64	11	and	and	CCONJ
ejpam-7119	64	12	convergence	convergence	NOUN
ejpam-7119	64	13	rates	rate	NOUN
ejpam-7119	64	14	,	,	PUNCT
ejpam-7119	64	15	solidifying	solidify	VERB
ejpam-7119	64	16	the	the	DET
ejpam-7119	64	17	theoretical	theoretical	ADJ
ejpam-7119	64	18	groundwork	groundwork	NOUN
ejpam-7119	64	19	for	for	ADP
ejpam-7119	64	20	the	the	DET
ejpam-7119	64	21	applications	application	NOUN
ejpam-7119	64	22	that	that	PRON
ejpam-7119	64	23	follow	follow	VERB
ejpam-7119	64	24	.	.	PUNCT
ejpam-7119	65	1	definition	definition	NOUN
ejpam-7119	65	2	3	3	NUM
ejpam-7119	65	3	.	.	PUNCT
ejpam-7119	66	1	(	(	PUNCT
ejpam-7119	66	2	fractional	fractional	ADJ
ejpam-7119	66	3	-	-	PUNCT
ejpam-7119	66	4	order	order	NOUN
ejpam-7119	66	5	neutrosophic	neutrosophic	ADJ
ejpam-7119	66	6	mr	mr	PROPN
ejpam-7119	66	7	-	-	PUNCT
ejpam-7119	66	8	metric	metric	ADJ
ejpam-7119	66	9	space	space	NOUN
ejpam-7119	66	10	(	(	PUNCT
ejpam-7119	66	11	fonmr	fonmr	PROPN
ejpam-7119	66	12	-	-	PUNCT
ejpam-7119	66	13	ms	ms	NOUN
ejpam-7119	66	14	)	)	PUNCT
ejpam-7119	66	15	)	)	PUNCT
ejpam-7119	67	1	let	let	AUX
ejpam-7119	67	2	(	(	PUNCT
ejpam-7119	67	3	z	z	NOUN
ejpam-7119	67	4	,	,	PUNCT
ejpam-7119	67	5	m	m	PROPN
ejpam-7119	67	6	,	,	PUNCT
ejpam-7119	67	7	t	t	PROPN
ejpam-7119	67	8	,	,	PUNCT
ejpam-7119	67	9	f	f	PROPN
ejpam-7119	67	10	,	,	PUNCT
ejpam-7119	67	11	i	i	PRON
ejpam-7119	67	12	,	,	PUNCT
ejpam-7119	67	13	•	•	PROPN
ejpam-7119	67	14	,	,	PUNCT
ejpam-7119	67	15	⋄	⋄	PROPN
ejpam-7119	67	16	,	,	PUNCT
ejpam-7119	67	17	r	r	NOUN
ejpam-7119	67	18	,	,	PUNCT
ejpam-7119	67	19	⋆	⋆	ADJ
ejpam-7119	67	20	)	)	PUNCT
ejpam-7119	67	21	be	be	AUX
ejpam-7119	67	22	an	an	DET
ejpam-7119	67	23	nmr	nmr	NOUN
ejpam-7119	67	24	-	-	PUNCT
ejpam-7119	67	25	ms	ms	NOUN
ejpam-7119	67	26	.	.	PROPN
ejpam-7119	68	1	we	we	PRON
ejpam-7119	68	2	define	define	VERB
ejpam-7119	68	3	a	a	DET
ejpam-7119	68	4	fractional	fractional	ADJ
ejpam-7119	68	5	-	-	PUNCT
ejpam-7119	68	6	order	order	NOUN
ejpam-7119	68	7	neutrosophic	neutrosophic	ADJ
ejpam-7119	68	8	mr	mr	PROPN
ejpam-7119	68	9	-	-	PUNCT
ejpam-7119	68	10	metric	metric	ADJ
ejpam-7119	68	11	mα	mα	PROPN
ejpam-7119	68	12	:	:	PUNCT
ejpam-7119	68	13	z3	z3	PROPN
ejpam-7119	68	14	→	→	PUNCT
ejpam-7119	68	15	[	[	X
ejpam-7119	68	16	0,∞	0,∞	NOUN
ejpam-7119	68	17	)	)	PUNCT
ejpam-7119	68	18	by	by	ADP
ejpam-7119	68	19	:	:	PUNCT
ejpam-7119	68	20	mα(υ	mα(υ	NOUN
ejpam-7119	68	21	,	,	PUNCT
ejpam-7119	68	22	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	68	23	)	)	PUNCT
ejpam-7119	68	24	=	=	PUNCT
ejpam-7119	68	25	(	(	PUNCT
ejpam-7119	68	26	1	1	NUM
ejpam-7119	68	27	γ(α	γ(α	NOUN
ejpam-7119	68	28	)	)	PUNCT
ejpam-7119	68	29	∫	∫	PROPN
ejpam-7119	68	30	1	1	NUM
ejpam-7119	68	31	0	0	NUM
ejpam-7119	68	32	(	(	PUNCT
ejpam-7119	68	33	1−	1−	NUM
ejpam-7119	68	34	τ)α−1m(υ	τ)α−1m(υ	NUM
ejpam-7119	68	35	,	,	PUNCT
ejpam-7119	68	36	ξ,ℑτ	ξ,ℑτ	ADJ
ejpam-7119	68	37	)	)	PUNCT
ejpam-7119	68	38	dτ	dτ	NOUN
ejpam-7119	68	39	)	)	PUNCT
ejpam-7119	68	40	1	1	NUM
ejpam-7119	68	41	/	/	SYM
ejpam-7119	68	42	α	α	NOUN
ejpam-7119	68	43	,	,	PUNCT
ejpam-7119	68	44	where	where	SCONJ
ejpam-7119	68	45	α	α	PROPN
ejpam-7119	68	46	>	>	X
ejpam-7119	68	47	0	0	PROPN
ejpam-7119	68	48	,	,	PUNCT
ejpam-7119	68	49	γ	γ	X
ejpam-7119	68	50	is	be	AUX
ejpam-7119	68	51	the	the	DET
ejpam-7119	68	52	gamma	gamma	NOUN
ejpam-7119	68	53	function	function	NOUN
ejpam-7119	68	54	,	,	PUNCT
ejpam-7119	68	55	and	and	CCONJ
ejpam-7119	68	56	ℑτ	ℑτ	PROPN
ejpam-7119	68	57	is	be	AUX
ejpam-7119	68	58	a	a	DET
ejpam-7119	68	59	point	point	NOUN
ejpam-7119	68	60	on	on	ADP
ejpam-7119	68	61	the	the	DET
ejpam-7119	68	62	”	"	PUNCT
ejpam-7119	68	63	metric	metric	ADJ
ejpam-7119	68	64	path	path	NOUN
ejpam-7119	68	65	”	"	PUNCT
ejpam-7119	68	66	between	between	ADP
ejpam-7119	68	67	the	the	DET
ejpam-7119	68	68	arguments	argument	NOUN
ejpam-7119	68	69	,	,	PUNCT
ejpam-7119	68	70	defined	define	VERB
ejpam-7119	68	71	via	via	ADP
ejpam-7119	68	72	a	a	DET
ejpam-7119	68	73	continuous	continuous	ADJ
ejpam-7119	68	74	deformation	deformation	NOUN
ejpam-7119	68	75	.	.	PUNCT
ejpam-7119	69	1	the	the	DET
ejpam-7119	69	2	associated	associated	ADJ
ejpam-7119	69	3	neutrosophic	neutrosophic	ADJ
ejpam-7119	69	4	functions	function	NOUN
ejpam-7119	69	5	are	be	AUX
ejpam-7119	69	6	modified	modify	VERB
ejpam-7119	69	7	to	to	PART
ejpam-7119	69	8	depend	depend	VERB
ejpam-7119	69	9	on	on	ADP
ejpam-7119	69	10	the	the	DET
ejpam-7119	69	11	fractional	fractional	ADJ
ejpam-7119	69	12	order	order	NOUN
ejpam-7119	69	13	:	:	PUNCT
ejpam-7119	69	14	tα(υ	tα(υ	NUM
ejpam-7119	69	15	,	,	PUNCT
ejpam-7119	69	16	ξ	ξ	PROPN
ejpam-7119	69	17	,	,	PUNCT
ejpam-7119	69	18	γ	γ	NOUN
ejpam-7119	69	19	)	)	PUNCT
ejpam-7119	69	20	=	=	SYM
ejpam-7119	69	21	t	t	PROPN
ejpam-7119	69	22	(	(	PUNCT
ejpam-7119	69	23	υ	υ	PROPN
ejpam-7119	69	24	,	,	PUNCT
ejpam-7119	69	25	ξ	ξ	PROPN
ejpam-7119	69	26	,	,	PUNCT
ejpam-7119	69	27	γα	γα	PROPN
ejpam-7119	69	28	)	)	PUNCT
ejpam-7119	69	29	.	.	PUNCT
ejpam-7119	70	1	definition	definition	NOUN
ejpam-7119	70	2	4	4	NUM
ejpam-7119	70	3	.	.	PUNCT
ejpam-7119	71	1	(	(	PUNCT
ejpam-7119	71	2	comprehensive	comprehensive	ADJ
ejpam-7119	71	3	fractional	fractional	ADJ
ejpam-7119	71	4	-	-	PUNCT
ejpam-7119	71	5	order	order	NOUN
ejpam-7119	71	6	neutrosophic	neutrosophic	ADJ
ejpam-7119	71	7	mr	mr	PROPN
ejpam-7119	71	8	-	-	PUNCT
ejpam-7119	71	9	metric	metric	ADJ
ejpam-7119	71	10	space	space	NOUN
ejpam-7119	71	11	)	)	PUNCT
ejpam-7119	72	1	let	let	VERB
ejpam-7119	72	2	(	(	PUNCT
ejpam-7119	72	3	z	z	NOUN
ejpam-7119	72	4	,	,	PUNCT
ejpam-7119	72	5	m	m	PROPN
ejpam-7119	72	6	,	,	PUNCT
ejpam-7119	72	7	t	t	PROPN
ejpam-7119	72	8	,	,	PUNCT
ejpam-7119	72	9	f	f	PROPN
ejpam-7119	72	10	,	,	PUNCT
ejpam-7119	72	11	i	i	PRON
ejpam-7119	72	12	,	,	PUNCT
ejpam-7119	72	13	•	•	PROPN
ejpam-7119	72	14	,	,	PUNCT
ejpam-7119	72	15	⋄	⋄	PROPN
ejpam-7119	72	16	,	,	PUNCT
ejpam-7119	72	17	r	r	NOUN
ejpam-7119	72	18	,	,	PUNCT
ejpam-7119	72	19	⋆	⋆	CCONJ
ejpam-7119	72	20	)	)	PUNCT
ejpam-7119	72	21	be	be	AUX
ejpam-7119	72	22	a	a	DET
ejpam-7119	72	23	complete	complete	ADJ
ejpam-7119	72	24	nmr	nmr	NOUN
ejpam-7119	72	25	-	-	PUNCT
ejpam-7119	72	26	ms	ms	NOUN
ejpam-7119	72	27	.	.	PROPN
ejpam-7119	72	28	for	for	ADP
ejpam-7119	72	29	α	α	PROPN
ejpam-7119	72	30	>	>	X
ejpam-7119	72	31	0	0	PROPN
ejpam-7119	72	32	,	,	PUNCT
ejpam-7119	72	33	we	we	PRON
ejpam-7119	72	34	define	define	VERB
ejpam-7119	72	35	the	the	DET
ejpam-7119	72	36	comprehensive	comprehensive	ADJ
ejpam-7119	72	37	fractional	fractional	ADJ
ejpam-7119	72	38	-	-	PUNCT
ejpam-7119	72	39	order	order	NOUN
ejpam-7119	72	40	neutrosophic	neutrosophic	ADJ
ejpam-7119	72	41	mr	mr	PROPN
ejpam-7119	72	42	-	-	PUNCT
ejpam-7119	72	43	metric	metric	ADJ
ejpam-7119	72	44	space	space	NOUN
ejpam-7119	72	45	as	as	SCONJ
ejpam-7119	72	46	the	the	DET
ejpam-7119	72	47	9	9	NUM
ejpam-7119	72	48	-	-	PUNCT
ejpam-7119	72	49	tuple	tuple	NOUN
ejpam-7119	72	50	(	(	PUNCT
ejpam-7119	72	51	z	z	NOUN
ejpam-7119	72	52	,	,	PUNCT
ejpam-7119	72	53	mα	mα	PROPN
ejpam-7119	72	54	,	,	PUNCT
ejpam-7119	72	55	tα	tα	PROPN
ejpam-7119	72	56	,	,	PUNCT
ejpam-7119	72	57	fα	fα	NOUN
ejpam-7119	72	58	,	,	PUNCT
ejpam-7119	72	59	iα	iα	NOUN
ejpam-7119	72	60	,	,	PUNCT
ejpam-7119	72	61	•	•	PROPN
ejpam-7119	72	62	,	,	PUNCT
ejpam-7119	72	63	⋄	⋄	PROPN
ejpam-7119	72	64	,	,	PUNCT
ejpam-7119	72	65	rα	rα	INTJ
ejpam-7119	72	66	,	,	PUNCT
ejpam-7119	72	67	⋆α	⋆α	NOUN
ejpam-7119	72	68	)	)	PUNCT
ejpam-7119	73	1	where	where	SCONJ
ejpam-7119	73	2	:	:	PUNCT
ejpam-7119	73	3	(	(	PUNCT
ejpam-7119	73	4	i	i	NOUN
ejpam-7119	73	5	)	)	PUNCT
ejpam-7119	73	6	the	the	DET
ejpam-7119	73	7	fractional	fractional	ADJ
ejpam-7119	73	8	mr	mr	PROPN
ejpam-7119	73	9	-	-	PUNCT
ejpam-7119	73	10	metric	metric	ADJ
ejpam-7119	73	11	mα	mα	PROPN
ejpam-7119	73	12	:	:	PUNCT
ejpam-7119	73	13	z3	z3	PROPN
ejpam-7119	73	14	→	→	PUNCT
ejpam-7119	74	1	[	[	X
ejpam-7119	74	2	0,∞	0,∞	NOUN
ejpam-7119	74	3	)	)	PUNCT
ejpam-7119	74	4	is	be	AUX
ejpam-7119	74	5	defined	define	VERB
ejpam-7119	74	6	by	by	ADP
ejpam-7119	74	7	:	:	PUNCT
ejpam-7119	74	8	mα(υ	mα(υ	NOUN
ejpam-7119	74	9	,	,	PUNCT
ejpam-7119	74	10	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	74	11	)	)	PUNCT
ejpam-7119	75	1	=	=	PUNCT
ejpam-7119	75	2	(	(	PUNCT
ejpam-7119	75	3	1	1	NUM
ejpam-7119	75	4	γ(α	γ(α	NOUN
ejpam-7119	75	5	)	)	PUNCT
ejpam-7119	75	6	∫	∫	PROPN
ejpam-7119	76	1	∞	∞	PROPN
ejpam-7119	76	2	0	0	NUM
ejpam-7119	76	3	τα−1e−τm(υ	τα−1e−τm(υ	SYM
ejpam-7119	76	4	,	,	PUNCT
ejpam-7119	76	5	ξ,ℑτ	ξ,ℑτ	ADJ
ejpam-7119	76	6	)	)	PUNCT
ejpam-7119	76	7	dτ	dτ	NOUN
ejpam-7119	76	8	)	)	PUNCT
ejpam-7119	76	9	1	1	NUM
ejpam-7119	76	10	/	/	SYM
ejpam-7119	76	11	α	α	NOUN
ejpam-7119	76	12	where	where	SCONJ
ejpam-7119	76	13	ℑτ	ℑτ	PROPN
ejpam-7119	76	14	is	be	AUX
ejpam-7119	76	15	defined	define	VERB
ejpam-7119	76	16	through	through	ADP
ejpam-7119	76	17	the	the	DET
ejpam-7119	76	18	geodesic	geodesic	ADJ
ejpam-7119	76	19	interpolation	interpolation	NOUN
ejpam-7119	76	20	:	:	PUNCT
ejpam-7119	77	1	ℑτ	ℑτ	PROPN
ejpam-7119	77	2	=	=	SYM
ejpam-7119	77	3	γ	γ	X
ejpam-7119	77	4	(	(	PUNCT
ejpam-7119	77	5	τ	τ	PROPN
ejpam-7119	77	6	1	1	NUM
ejpam-7119	77	7	+	+	CCONJ
ejpam-7119	77	8	τ	τ	PROPN
ejpam-7119	77	9	)	)	PUNCT
ejpam-7119	77	10	,	,	PUNCT
ejpam-7119	77	11	γ	γ	X
ejpam-7119	77	12	:	:	PUNCT
ejpam-7119	77	13	[	[	X
ejpam-7119	77	14	0	0	NUM
ejpam-7119	77	15	,	,	PUNCT
ejpam-7119	77	16	1	1	NUM
ejpam-7119	77	17	]	]	PUNCT
ejpam-7119	77	18	→	→	PUNCT
ejpam-7119	77	19	z	z	NOUN
ejpam-7119	77	20	is	be	AUX
ejpam-7119	77	21	a	a	DET
ejpam-7119	77	22	minimal	minimal	ADJ
ejpam-7119	77	23	geodesic	geodesic	NOUN
ejpam-7119	77	24	connecting	connect	VERB
ejpam-7119	77	25	the	the	DET
ejpam-7119	77	26	points	point	NOUN
ejpam-7119	77	27	a.	a.	NOUN
ejpam-7119	77	28	malkawi	malkawi	PROPN
ejpam-7119	77	29	,	,	PUNCT
ejpam-7119	77	30	a.	a.	PROPN
ejpam-7119	77	31	rabaiah	rabaiah	PROPN
ejpam-7119	77	32	/	/	SYM
ejpam-7119	77	33	eur	eur	PROPN
ejpam-7119	77	34	.	.	PUNCT
ejpam-7119	78	1	j.	j.	PROPN
ejpam-7119	78	2	pure	pure	PROPN
ejpam-7119	78	3	appl	appl	PROPN
ejpam-7119	78	4	.	.	PROPN
ejpam-7119	78	5	math	math	PROPN
ejpam-7119	78	6	,	,	PUNCT
ejpam-7119	78	7	18	18	NUM
ejpam-7119	78	8	(	(	PUNCT
ejpam-7119	78	9	4	4	NUM
ejpam-7119	78	10	)	)	PUNCT
ejpam-7119	78	11	(	(	PUNCT
ejpam-7119	78	12	2025	2025	NUM
ejpam-7119	78	13	)	)	PUNCT
ejpam-7119	78	14	,	,	PUNCT
ejpam-7119	78	15	7119	7119	NUM
ejpam-7119	78	16	4	4	NUM
ejpam-7119	78	17	of	of	ADP
ejpam-7119	78	18	13	13	NUM
ejpam-7119	78	19	(	(	PUNCT
ejpam-7119	78	20	ii	ii	NOUN
ejpam-7119	78	21	)	)	PUNCT
ejpam-7119	78	22	the	the	DET
ejpam-7119	78	23	generalized	generalize	VERB
ejpam-7119	78	24	neutrosophic	neutrosophic	ADJ
ejpam-7119	78	25	functions	function	NOUN
ejpam-7119	78	26	are	be	AUX
ejpam-7119	78	27	:	:	PUNCT
ejpam-7119	78	28	tα(υ	tα(υ	NUM
ejpam-7119	78	29	,	,	PUNCT
ejpam-7119	78	30	ξ	ξ	PROPN
ejpam-7119	78	31	,	,	PUNCT
ejpam-7119	78	32	γ	γ	NOUN
ejpam-7119	78	33	)	)	PUNCT
ejpam-7119	78	34	=	=	SYM
ejpam-7119	78	35	1	1	NUM
ejpam-7119	78	36	γ(α	γ(α	NOUN
ejpam-7119	78	37	)	)	PUNCT
ejpam-7119	78	38	∫	∫	PROPN
ejpam-7119	79	1	∞	∞	PROPN
ejpam-7119	79	2	0	0	X
ejpam-7119	79	3	tα−1e−tt	tα−1e−tt	NOUN
ejpam-7119	79	4	(	(	PUNCT
ejpam-7119	79	5	υ	υ	PROPN
ejpam-7119	79	6	,	,	PUNCT
ejpam-7119	79	7	ξ	ξ	PROPN
ejpam-7119	79	8	,	,	PUNCT
ejpam-7119	79	9	γt	γt	NOUN
ejpam-7119	79	10	)	)	PUNCT
ejpam-7119	79	11	dt	dt	NOUN
ejpam-7119	80	1	iα(υ	iα(υ	PROPN
ejpam-7119	80	2	,	,	PUNCT
ejpam-7119	80	3	ξ	ξ	PROPN
ejpam-7119	80	4	,	,	PUNCT
ejpam-7119	80	5	γ	γ	NOUN
ejpam-7119	80	6	)	)	PUNCT
ejpam-7119	80	7	=	=	SYM
ejpam-7119	80	8	1	1	NUM
ejpam-7119	80	9	γ(α	γ(α	NOUN
ejpam-7119	80	10	)	)	PUNCT
ejpam-7119	80	11	∫	∫	PROPN
ejpam-7119	81	1	∞	∞	PROPN
ejpam-7119	81	2	0	0	NUM
ejpam-7119	81	3	tα−1e−ti(υ	tα−1e−ti(υ	NUM
ejpam-7119	81	4	,	,	PUNCT
ejpam-7119	81	5	ξ	ξ	PROPN
ejpam-7119	81	6	,	,	PUNCT
ejpam-7119	81	7	γt	γt	NOUN
ejpam-7119	81	8	)	)	PUNCT
ejpam-7119	81	9	dt	dt	X
ejpam-7119	82	1	fα(υ	fα(υ	PROPN
ejpam-7119	82	2	,	,	PUNCT
ejpam-7119	82	3	ξ	ξ	PROPN
ejpam-7119	82	4	,	,	PUNCT
ejpam-7119	82	5	γ	γ	NOUN
ejpam-7119	82	6	)	)	PUNCT
ejpam-7119	82	7	=	=	SYM
ejpam-7119	82	8	1−	1−	NUM
ejpam-7119	82	9	tα(υ	tα(υ	NUM
ejpam-7119	82	10	,	,	PUNCT
ejpam-7119	82	11	ξ	ξ	X
ejpam-7119	82	12	,	,	PUNCT
ejpam-7119	82	13	γ)−	γ)−	PROPN
ejpam-7119	82	14	iα(υ	iα(υ	AUX
ejpam-7119	82	15	,	,	PUNCT
ejpam-7119	82	16	ξ	ξ	PROPN
ejpam-7119	82	17	,	,	PUNCT
ejpam-7119	82	18	γ	γ	NOUN
ejpam-7119	82	19	)	)	PUNCT
ejpam-7119	82	20	(	(	PUNCT
ejpam-7119	82	21	iii	iii	NOUN
ejpam-7119	82	22	)	)	PUNCT
ejpam-7119	82	23	the	the	DET
ejpam-7119	82	24	fractional	fractional	ADJ
ejpam-7119	82	25	contraction	contraction	NOUN
ejpam-7119	82	26	constant	constant	ADJ
ejpam-7119	82	27	is	be	AUX
ejpam-7119	82	28	rα	rα	ADJ
ejpam-7119	82	29	=	=	SYM
ejpam-7119	82	30	r	r	NOUN
ejpam-7119	82	31	·	·	PUNCT
ejpam-7119	82	32	γ(2α	γ(2α	NUM
ejpam-7119	82	33	)	)	PUNCT
ejpam-7119	82	34	γ(α)2	γ(α)2	PROPN
ejpam-7119	82	35	(	(	PUNCT
ejpam-7119	82	36	iv	iv	X
ejpam-7119	82	37	)	)	PUNCT
ejpam-7119	82	38	the	the	DET
ejpam-7119	82	39	fractional	fractional	ADJ
ejpam-7119	82	40	binary	binary	ADJ
ejpam-7119	82	41	operation	operation	NOUN
ejpam-7119	82	42	⋆α	⋆α	PROPN
ejpam-7119	82	43	is	be	AUX
ejpam-7119	82	44	:	:	PUNCT
ejpam-7119	82	45	a	a	DET
ejpam-7119	82	46	⋆α	⋆α	PROPN
ejpam-7119	82	47	b	b	NOUN
ejpam-7119	82	48	=	=	PUNCT
ejpam-7119	82	49	(	(	PUNCT
ejpam-7119	82	50	aα	aα	NOUN
ejpam-7119	82	51	+	+	CCONJ
ejpam-7119	82	52	bα)1	bα)1	PROPN
ejpam-7119	82	53	/	/	SYM
ejpam-7119	82	54	α	α	PROPN
ejpam-7119	82	55	lemma	lemma	PROPN
ejpam-7119	82	56	1	1	NUM
ejpam-7119	82	57	(	(	PUNCT
ejpam-7119	82	58	fundamental	fundamental	ADJ
ejpam-7119	82	59	properties	property	NOUN
ejpam-7119	82	60	of	of	ADP
ejpam-7119	82	61	fractional	fractional	ADJ
ejpam-7119	82	62	metric	metric	NOUN
ejpam-7119	82	63	)	)	PUNCT
ejpam-7119	82	64	.	.	PUNCT
ejpam-7119	83	1	the	the	DET
ejpam-7119	83	2	fractional	fractional	ADJ
ejpam-7119	83	3	metric	metric	ADJ
ejpam-7119	83	4	mα	mα	PROPN
ejpam-7119	83	5	satisfies	satisfy	VERB
ejpam-7119	83	6	all	all	DET
ejpam-7119	83	7	axioms	axiom	NOUN
ejpam-7119	83	8	of	of	ADP
ejpam-7119	83	9	an	an	DET
ejpam-7119	83	10	mr	mr	PROPN
ejpam-7119	83	11	-	-	PUNCT
ejpam-7119	83	12	metric	metric	NOUN
ejpam-7119	83	13	:	:	PUNCT
ejpam-7119	83	14	(	(	PUNCT
ejpam-7119	83	15	i	i	NOUN
ejpam-7119	83	16	)	)	PUNCT
ejpam-7119	83	17	non	non	ADJ
ejpam-7119	83	18	-	-	ADJ
ejpam-7119	83	19	negativity	negativity	NOUN
ejpam-7119	83	20	:	:	PUNCT
ejpam-7119	83	21	mα(υ	mα(υ	NOUN
ejpam-7119	83	22	,	,	PUNCT
ejpam-7119	83	23	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	83	24	)	)	PUNCT
ejpam-7119	83	25	≥	≥	NOUN
ejpam-7119	83	26	0	0	NUM
ejpam-7119	83	27	(	(	PUNCT
ejpam-7119	83	28	ii	ii	NOUN
ejpam-7119	83	29	)	)	PUNCT
ejpam-7119	83	30	identity	identity	NOUN
ejpam-7119	83	31	:	:	PUNCT
ejpam-7119	83	32	mα(υ	mα(υ	NOUN
ejpam-7119	83	33	,	,	PUNCT
ejpam-7119	83	34	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	83	35	)	)	PUNCT
ejpam-7119	84	1	=	=	SYM
ejpam-7119	84	2	0	0	NUM
ejpam-7119	85	1	⇐	⇐	ADJ
ejpam-7119	85	2	⇒	⇒	NOUN
ejpam-7119	85	3	υ	υ	X
ejpam-7119	85	4	=	=	SYM
ejpam-7119	85	5	ξ	ξ	PROPN
ejpam-7119	85	6	=	=	SYM
ejpam-7119	85	7	ℑ	ℑ	PROPN
ejpam-7119	85	8	(	(	PUNCT
ejpam-7119	85	9	iii	iii	NOUN
ejpam-7119	85	10	)	)	PUNCT
ejpam-7119	85	11	symmetry	symmetry	NOUN
ejpam-7119	85	12	:	:	PUNCT
ejpam-7119	85	13	mα(υ	mα(υ	NOUN
ejpam-7119	85	14	,	,	PUNCT
ejpam-7119	85	15	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	85	16	)	)	PUNCT
ejpam-7119	85	17	is	be	AUX
ejpam-7119	85	18	symmetric	symmetric	ADJ
ejpam-7119	85	19	under	under	ADP
ejpam-7119	85	20	all	all	DET
ejpam-7119	85	21	permutations	permutation	NOUN
ejpam-7119	85	22	(	(	PUNCT
ejpam-7119	85	23	iv	iv	X
ejpam-7119	85	24	)	)	PUNCT
ejpam-7119	85	25	fractional	fractional	ADJ
ejpam-7119	85	26	generalized	generalized	ADJ
ejpam-7119	85	27	triangle	triangle	NOUN
ejpam-7119	85	28	inequality	inequality	NOUN
ejpam-7119	85	29	:	:	PUNCT
ejpam-7119	85	30	mα(υ	mα(υ	NOUN
ejpam-7119	85	31	,	,	PUNCT
ejpam-7119	85	32	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	85	33	)	)	PUNCT
ejpam-7119	85	34	≤	≤	PUNCT
ejpam-7119	85	35	rα	rα	X
ejpam-7119	86	1	[	[	X
ejpam-7119	86	2	mα(υ	mα(υ	NOUN
ejpam-7119	86	3	,	,	PUNCT
ejpam-7119	86	4	ξ	ξ	PROPN
ejpam-7119	86	5	,	,	PUNCT
ejpam-7119	86	6	ℓ	ℓ	NUM
ejpam-7119	86	7	)	)	PUNCT
ejpam-7119	86	8	⋆α	⋆α	PROPN
ejpam-7119	86	9	mα(υ	mα(υ	NOUN
ejpam-7119	86	10	,	,	PUNCT
ejpam-7119	86	11	ℓ,ℑ	ℓ,ℑ	PROPN
ejpam-7119	86	12	)	)	PUNCT
ejpam-7119	86	13	⋆α	⋆α	NOUN
ejpam-7119	86	14	mα(ℓ	mα(ℓ	ADJ
ejpam-7119	86	15	,	,	PUNCT
ejpam-7119	86	16	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	86	17	)	)	PUNCT
ejpam-7119	86	18	]	]	PUNCT
ejpam-7119	87	1	proof	proof	NOUN
ejpam-7119	87	2	.	.	PUNCT
ejpam-7119	88	1	we	we	PRON
ejpam-7119	88	2	prove	prove	VERB
ejpam-7119	88	3	each	each	DET
ejpam-7119	88	4	property	property	NOUN
ejpam-7119	88	5	in	in	ADP
ejpam-7119	88	6	detail	detail	NOUN
ejpam-7119	88	7	:	:	PUNCT
ejpam-7119	88	8	1	1	X
ejpam-7119	88	9	.	.	X
ejpam-7119	88	10	non	non	ADJ
ejpam-7119	88	11	-	-	ADJ
ejpam-7119	88	12	negativity	negativity	ADJ
ejpam-7119	88	13	:	:	PUNCT
ejpam-7119	88	14	since	since	SCONJ
ejpam-7119	88	15	m(υ	m(υ	PROPN
ejpam-7119	88	16	,	,	PUNCT
ejpam-7119	88	17	ξ,ℑτ	ξ,ℑτ	ADJ
ejpam-7119	88	18	)	)	PUNCT
ejpam-7119	88	19	≥	≥	NOUN
ejpam-7119	88	20	0	0	NUM
ejpam-7119	88	21	and	and	CCONJ
ejpam-7119	88	22	the	the	DET
ejpam-7119	88	23	integrand	integrand	NOUN
ejpam-7119	88	24	contains	contain	VERB
ejpam-7119	88	25	positive	positive	ADJ
ejpam-7119	88	26	functions	function	NOUN
ejpam-7119	88	27	,	,	PUNCT
ejpam-7119	88	28	we	we	PRON
ejpam-7119	88	29	have	have	VERB
ejpam-7119	88	30	mα(υ	mα(υ	NOUN
ejpam-7119	88	31	,	,	PUNCT
ejpam-7119	88	32	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	88	33	)	)	PUNCT
ejpam-7119	88	34	≥	≥	NOUN
ejpam-7119	88	35	0	0	NUM
ejpam-7119	88	36	.	.	NOUN
ejpam-7119	89	1	2	2	NUM
ejpam-7119	89	2	.	.	X
ejpam-7119	89	3	identity	identity	NOUN
ejpam-7119	89	4	:	:	PUNCT
ejpam-7119	89	5	mα(υ	mα(υ	NOUN
ejpam-7119	89	6	,	,	PUNCT
ejpam-7119	89	7	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	89	8	)	)	PUNCT
ejpam-7119	89	9	=	=	SYM
ejpam-7119	89	10	0	0	NUM
ejpam-7119	89	11	⇐	⇐	ADJ
ejpam-7119	89	12	⇒	⇒	PROPN
ejpam-7119	89	13	∫	∫	PROPN
ejpam-7119	89	14	∞	∞	PROPN
ejpam-7119	89	15	0	0	NUM
ejpam-7119	89	16	τα−1e−τm(υ	τα−1e−τm(υ	SYM
ejpam-7119	89	17	,	,	PUNCT
ejpam-7119	89	18	ξ,ℑτ	ξ,ℑτ	ADJ
ejpam-7119	89	19	)	)	PUNCT
ejpam-7119	89	20	dτ	dτ	NOUN
ejpam-7119	90	1	=	=	NOUN
ejpam-7119	90	2	0	0	PROPN
ejpam-7119	90	3	since	since	SCONJ
ejpam-7119	90	4	the	the	DET
ejpam-7119	90	5	functions	function	NOUN
ejpam-7119	90	6	inside	inside	ADP
ejpam-7119	90	7	the	the	DET
ejpam-7119	90	8	integral	integral	ADJ
ejpam-7119	90	9	are	be	AUX
ejpam-7119	90	10	non	non	ADJ
ejpam-7119	90	11	-	-	ADJ
ejpam-7119	90	12	negative	negative	ADJ
ejpam-7119	90	13	,	,	PUNCT
ejpam-7119	90	14	this	this	PRON
ejpam-7119	90	15	implies	imply	VERB
ejpam-7119	90	16	m(υ	m(υ	PROPN
ejpam-7119	90	17	,	,	PUNCT
ejpam-7119	90	18	ξ,ℑτ	ξ,ℑτ	ADJ
ejpam-7119	90	19	)	)	PUNCT
ejpam-7119	91	1	=	=	SYM
ejpam-7119	91	2	0	0	NUM
ejpam-7119	91	3	for	for	ADP
ejpam-7119	91	4	all	all	DET
ejpam-7119	91	5	τ	τ	PROPN
ejpam-7119	91	6	,	,	PUNCT
ejpam-7119	91	7	which	which	PRON
ejpam-7119	91	8	by	by	ADP
ejpam-7119	91	9	the	the	DET
ejpam-7119	91	10	identity	identity	NOUN
ejpam-7119	91	11	property	property	NOUN
ejpam-7119	91	12	of	of	ADP
ejpam-7119	91	13	m	m	PROPN
ejpam-7119	91	14	gives	give	VERB
ejpam-7119	91	15	υ	υ	NOUN
ejpam-7119	91	16	=	=	SYM
ejpam-7119	91	17	ξ	ξ	NOUN
ejpam-7119	91	18	=	=	PUNCT
ejpam-7119	91	19	ℑ.	ℑ.	PROPN
ejpam-7119	91	20	3	3	NUM
ejpam-7119	91	21	.	.	PUNCT
ejpam-7119	91	22	symmetry	symmetry	NOUN
ejpam-7119	91	23	:	:	PUNCT
ejpam-7119	91	24	follows	follow	VERB
ejpam-7119	91	25	directly	directly	ADV
ejpam-7119	91	26	from	from	ADP
ejpam-7119	91	27	the	the	DET
ejpam-7119	91	28	symmetry	symmetry	NOUN
ejpam-7119	91	29	of	of	ADP
ejpam-7119	91	30	m	m	PROPN
ejpam-7119	91	31	and	and	CCONJ
ejpam-7119	91	32	the	the	DET
ejpam-7119	91	33	symmetric	symmetric	ADJ
ejpam-7119	91	34	definition	definition	NOUN
ejpam-7119	91	35	of	of	ADP
ejpam-7119	91	36	the	the	DET
ejpam-7119	91	37	geodesic	geodesic	ADJ
ejpam-7119	91	38	interpolation	interpolation	NOUN
ejpam-7119	91	39	.	.	PUNCT
ejpam-7119	92	1	4	4	X
ejpam-7119	92	2	.	.	X
ejpam-7119	92	3	fractional	fractional	ADJ
ejpam-7119	92	4	triangle	triangle	NOUN
ejpam-7119	92	5	inequality	inequality	NOUN
ejpam-7119	92	6	:	:	PUNCT
ejpam-7119	92	7	using	use	VERB
ejpam-7119	92	8	the	the	DET
ejpam-7119	92	9	generalized	generalized	ADJ
ejpam-7119	92	10	triangle	triangle	NOUN
ejpam-7119	92	11	inequality	inequality	NOUN
ejpam-7119	92	12	for	for	ADP
ejpam-7119	92	13	m	m	PROPN
ejpam-7119	92	14	:	:	PUNCT
ejpam-7119	92	15	mα(υ	mα(υ	NOUN
ejpam-7119	92	16	,	,	PUNCT
ejpam-7119	92	17	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	92	18	)	)	PUNCT
ejpam-7119	92	19	=	=	PUNCT
ejpam-7119	92	20	(	(	PUNCT
ejpam-7119	92	21	1	1	NUM
ejpam-7119	92	22	γ(α	γ(α	NOUN
ejpam-7119	92	23	)	)	PUNCT
ejpam-7119	93	1	∫	∫	PROPN
ejpam-7119	93	2	∞	∞	PROPN
ejpam-7119	93	3	0	0	NUM
ejpam-7119	94	1	τα−1e−τm(υ	τα−1e−τm(υ	SYM
ejpam-7119	94	2	,	,	PUNCT
ejpam-7119	94	3	ξ,ℑτ	ξ,ℑτ	ADJ
ejpam-7119	94	4	)	)	PUNCT
ejpam-7119	94	5	dτ	dτ	NOUN
ejpam-7119	94	6	)	)	PUNCT
ejpam-7119	94	7	1	1	NUM
ejpam-7119	94	8	/	/	SYM
ejpam-7119	94	9	α	α	NOUN
ejpam-7119	94	10	≤	≤	NUM
ejpam-7119	94	11	(	(	PUNCT
ejpam-7119	94	12	1	1	NUM
ejpam-7119	94	13	γ(α	γ(α	NOUN
ejpam-7119	94	14	)	)	PUNCT
ejpam-7119	95	1	∫	∫	PROPN
ejpam-7119	96	1	∞	∞	PROPN
ejpam-7119	96	2	0	0	NUM
ejpam-7119	96	3	τα−1e−τr	τα−1e−τr	PUNCT
ejpam-7119	97	1	[	[	X
ejpam-7119	97	2	m(υ	m(υ	PROPN
ejpam-7119	97	3	,	,	PUNCT
ejpam-7119	97	4	ξ	ξ	PROPN
ejpam-7119	97	5	,	,	PUNCT
ejpam-7119	97	6	ℓτ	ℓτ	ADP
ejpam-7119	97	7	)	)	PUNCT
ejpam-7119	97	8	⋆	⋆	VERB
ejpam-7119	97	9	m(υ	m(υ	PROPN
ejpam-7119	97	10	,	,	PUNCT
ejpam-7119	97	11	ℓτ	ℓτ	ADV
ejpam-7119	97	12	,	,	PUNCT
ejpam-7119	97	13	ℑτ	ℑτ	PROPN
ejpam-7119	97	14	)	)	PUNCT
ejpam-7119	97	15	⋆	⋆	PROPN
ejpam-7119	97	16	m(ℓτ	m(ℓτ	PROPN
ejpam-7119	97	17	,	,	PUNCT
ejpam-7119	97	18	ξ,ℑτ	ξ,ℑτ	ADJ
ejpam-7119	97	19	)	)	PUNCT
ejpam-7119	97	20	]	]	PUNCT
ejpam-7119	97	21	dτ	dτ	NOUN
ejpam-7119	97	22	)	)	PUNCT
ejpam-7119	97	23	1	1	NUM
ejpam-7119	97	24	/	/	SYM
ejpam-7119	97	25	α	α	PRON
ejpam-7119	97	26	now	now	ADV
ejpam-7119	97	27	applying	apply	VERB
ejpam-7119	97	28	minkowski	minkowski	ADJ
ejpam-7119	97	29	’s	’s	PART
ejpam-7119	97	30	inequality	inequality	NOUN
ejpam-7119	97	31	for	for	ADP
ejpam-7119	97	32	integrals	integral	NOUN
ejpam-7119	97	33	:	:	PUNCT
ejpam-7119	97	34	≤	≤	NUM
ejpam-7119	97	35	r1	r1	PROPN
ejpam-7119	97	36	/	/	SYM
ejpam-7119	97	37	α	α	PROPN
ejpam-7119	98	1	[	[	X
ejpam-7119	98	2	(	(	PUNCT
ejpam-7119	98	3	1	1	NUM
ejpam-7119	98	4	γ(α	γ(α	NOUN
ejpam-7119	98	5	)	)	PUNCT
ejpam-7119	98	6	∫	∫	PROPN
ejpam-7119	99	1	∞	∞	PROPN
ejpam-7119	99	2	0	0	NUM
ejpam-7119	99	3	τα−1e−τm(υ	τα−1e−τm(υ	SYM
ejpam-7119	99	4	,	,	PUNCT
ejpam-7119	99	5	ξ	ξ	PROPN
ejpam-7119	99	6	,	,	PUNCT
ejpam-7119	99	7	ℓτ	ℓτ	NOUN
ejpam-7119	99	8	)	)	PUNCT
ejpam-7119	99	9	dτ	dτ	NOUN
ejpam-7119	99	10	)	)	PUNCT
ejpam-7119	99	11	1	1	NUM
ejpam-7119	99	12	/	/	SYM
ejpam-7119	99	13	α	α	NOUN
ejpam-7119	99	14	+	+	CCONJ
ejpam-7119	99	15	(	(	PUNCT
ejpam-7119	99	16	1	1	NUM
ejpam-7119	99	17	γ(α	γ(α	NOUN
ejpam-7119	99	18	)	)	PUNCT
ejpam-7119	99	19	∫	∫	PROPN
ejpam-7119	100	1	∞	∞	PROPN
ejpam-7119	100	2	0	0	NUM
ejpam-7119	100	3	τα−1e−τm(υ	τα−1e−τm(υ	ADJ
ejpam-7119	100	4	,	,	PUNCT
ejpam-7119	100	5	ℓτ	ℓτ	ADV
ejpam-7119	100	6	,	,	PUNCT
ejpam-7119	100	7	ℑτ	ℑτ	PROPN
ejpam-7119	100	8	)	)	PUNCT
ejpam-7119	100	9	dτ	dτ	NOUN
ejpam-7119	100	10	)	)	PUNCT
ejpam-7119	100	11	1	1	NUM
ejpam-7119	100	12	/	/	SYM
ejpam-7119	100	13	α	α	NOUN
ejpam-7119	100	14	a.	a.	NOUN
ejpam-7119	100	15	malkawi	malkawi	PROPN
ejpam-7119	100	16	,	,	PUNCT
ejpam-7119	100	17	a.	a.	PROPN
ejpam-7119	100	18	rabaiah	rabaiah	PROPN
ejpam-7119	100	19	/	/	SYM
ejpam-7119	100	20	eur	eur	PROPN
ejpam-7119	100	21	.	.	PUNCT
ejpam-7119	101	1	j.	j.	PROPN
ejpam-7119	101	2	pure	pure	PROPN
ejpam-7119	101	3	appl	appl	PROPN
ejpam-7119	101	4	.	.	PROPN
ejpam-7119	101	5	math	math	PROPN
ejpam-7119	101	6	,	,	PUNCT
ejpam-7119	101	7	18	18	NUM
ejpam-7119	101	8	(	(	PUNCT
ejpam-7119	101	9	4	4	NUM
ejpam-7119	101	10	)	)	PUNCT
ejpam-7119	101	11	(	(	PUNCT
ejpam-7119	101	12	2025	2025	NUM
ejpam-7119	101	13	)	)	PUNCT
ejpam-7119	101	14	,	,	PUNCT
ejpam-7119	101	15	7119	7119	NUM
ejpam-7119	101	16	5	5	NUM
ejpam-7119	101	17	of	of	ADP
ejpam-7119	101	18	13	13	NUM
ejpam-7119	101	19	+	+	CCONJ
ejpam-7119	101	20	(	(	PUNCT
ejpam-7119	101	21	1	1	NUM
ejpam-7119	101	22	γ(α	γ(α	NOUN
ejpam-7119	101	23	)	)	PUNCT
ejpam-7119	101	24	∫	∫	PROPN
ejpam-7119	102	1	∞	∞	PROPN
ejpam-7119	102	2	0	0	NUM
ejpam-7119	102	3	τα−1e−τm(ℓτ	τα−1e−τm(ℓτ	X
ejpam-7119	102	4	,	,	PUNCT
ejpam-7119	102	5	ξ,ℑτ	ξ,ℑτ	ADJ
ejpam-7119	102	6	)	)	PUNCT
ejpam-7119	102	7	dτ	dτ	NOUN
ejpam-7119	102	8	)	)	PUNCT
ejpam-7119	102	9	1	1	NUM
ejpam-7119	102	10	/	/	SYM
ejpam-7119	102	11	α	α	NOUN
ejpam-7119	102	12	]	]	PUNCT
ejpam-7119	102	13	=	=	X
ejpam-7119	102	14	rα	rα	ADJ
ejpam-7119	103	1	[	[	X
ejpam-7119	103	2	mα(υ	mα(υ	NOUN
ejpam-7119	103	3	,	,	PUNCT
ejpam-7119	103	4	ξ	ξ	PROPN
ejpam-7119	103	5	,	,	PUNCT
ejpam-7119	103	6	ℓ	ℓ	NUM
ejpam-7119	103	7	)	)	PUNCT
ejpam-7119	103	8	⋆α	⋆α	PROPN
ejpam-7119	103	9	mα(υ	mα(υ	NOUN
ejpam-7119	103	10	,	,	PUNCT
ejpam-7119	103	11	ℓ,ℑ	ℓ,ℑ	PROPN
ejpam-7119	103	12	)	)	PUNCT
ejpam-7119	103	13	⋆α	⋆α	NOUN
ejpam-7119	103	14	mα(ℓ	mα(ℓ	ADJ
ejpam-7119	103	15	,	,	PUNCT
ejpam-7119	103	16	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	103	17	)	)	PUNCT
ejpam-7119	103	18	]	]	PUNCT
ejpam-7119	103	19	where	where	SCONJ
ejpam-7119	103	20	rα	rα	ADJ
ejpam-7119	103	21	=	=	SYM
ejpam-7119	103	22	r	r	NOUN
ejpam-7119	103	23	·	·	PUNCT
ejpam-7119	103	24	γ(2α	γ(2α	NUM
ejpam-7119	103	25	)	)	PUNCT
ejpam-7119	103	26	γ(α)2	γ(α)2	PROPN
ejpam-7119	103	27	accounts	account	VERB
ejpam-7119	103	28	for	for	ADP
ejpam-7119	103	29	the	the	DET
ejpam-7119	103	30	normalization	normalization	NOUN
ejpam-7119	103	31	constants	constant	NOUN
ejpam-7119	103	32	.	.	PUNCT
ejpam-7119	104	1	lemma	lemma	PROPN
ejpam-7119	104	2	2	2	PROPN
ejpam-7119	104	3	(	(	PUNCT
ejpam-7119	104	4	neutrosophic	neutrosophic	ADJ
ejpam-7119	104	5	function	function	NOUN
ejpam-7119	104	6	properties	property	NOUN
ejpam-7119	104	7	)	)	PUNCT
ejpam-7119	104	8	.	.	PUNCT
ejpam-7119	105	1	the	the	DET
ejpam-7119	105	2	fractional	fractional	ADJ
ejpam-7119	105	3	neutrosophic	neutrosophic	ADJ
ejpam-7119	105	4	functions	function	NOUN
ejpam-7119	105	5	tα	tα	PROPN
ejpam-7119	105	6	,	,	PUNCT
ejpam-7119	105	7	iα	iα	NOUN
ejpam-7119	105	8	,	,	PUNCT
ejpam-7119	105	9	fα	fα	ADP
ejpam-7119	105	10	satisfy	satisfy	VERB
ejpam-7119	105	11	:	:	PUNCT
ejpam-7119	105	12	(	(	PUNCT
ejpam-7119	105	13	i	i	NOUN
ejpam-7119	105	14	)	)	PUNCT
ejpam-7119	105	15	tα(υ	tα(υ	PUNCT
ejpam-7119	105	16	,	,	PUNCT
ejpam-7119	105	17	ξ	ξ	PROPN
ejpam-7119	105	18	,	,	PUNCT
ejpam-7119	105	19	γ	γ	NOUN
ejpam-7119	105	20	)	)	PUNCT
ejpam-7119	105	21	=	=	SYM
ejpam-7119	105	22	1	1	NUM
ejpam-7119	105	23	⇐	⇐	ADJ
ejpam-7119	105	24	⇒	⇒	NOUN
ejpam-7119	105	25	υ	υ	X
ejpam-7119	105	26	=	=	SYM
ejpam-7119	105	27	ξ	ξ	PROPN
ejpam-7119	105	28	(	(	PUNCT
ejpam-7119	105	29	ii	ii	NOUN
ejpam-7119	105	30	)	)	PUNCT
ejpam-7119	105	31	tα(υ	tα(υ	PUNCT
ejpam-7119	105	32	,	,	PUNCT
ejpam-7119	105	33	ξ	ξ	PROPN
ejpam-7119	105	34	,	,	PUNCT
ejpam-7119	105	35	γ	γ	NOUN
ejpam-7119	105	36	)	)	PUNCT
ejpam-7119	105	37	=	=	SYM
ejpam-7119	105	38	tα(ξ	tα(ξ	NUM
ejpam-7119	105	39	,	,	PUNCT
ejpam-7119	105	40	υ	υ	NOUN
ejpam-7119	105	41	,	,	PUNCT
ejpam-7119	105	42	γ	γ	NOUN
ejpam-7119	105	43	)	)	PUNCT
ejpam-7119	105	44	(	(	PUNCT
ejpam-7119	105	45	iii	iii	NOUN
ejpam-7119	105	46	)	)	PUNCT
ejpam-7119	105	47	tα(υ	tα(υ	PUNCT
ejpam-7119	105	48	,	,	PUNCT
ejpam-7119	105	49	ξ	ξ	PROPN
ejpam-7119	105	50	,	,	PUNCT
ejpam-7119	105	51	γ	γ	NOUN
ejpam-7119	105	52	)	)	PUNCT
ejpam-7119	105	53	•	•	ADV
ejpam-7119	105	54	tα(ξ,ℑ	tα(ξ,ℑ	PROPN
ejpam-7119	105	55	,	,	PUNCT
ejpam-7119	105	56	ρ	ρ	NOUN
ejpam-7119	105	57	)	)	PUNCT
ejpam-7119	105	58	≤	≤	NUM
ejpam-7119	105	59	tα(υ,ℑ	tα(υ,ℑ	PROPN
ejpam-7119	105	60	,	,	PUNCT
ejpam-7119	105	61	γ	γ	X
ejpam-7119	105	62	+	+	NOUN
ejpam-7119	105	63	ρ	ρ	PROPN
ejpam-7119	105	64	)	)	PUNCT
ejpam-7119	105	65	(	(	PUNCT
ejpam-7119	105	66	iv	iv	X
ejpam-7119	105	67	)	)	PUNCT
ejpam-7119	105	68	limγ→∞	limγ→∞	PROPN
ejpam-7119	105	69	tα(υ	tα(υ	NUM
ejpam-7119	105	70	,	,	PUNCT
ejpam-7119	105	71	ξ	ξ	PROPN
ejpam-7119	105	72	,	,	PUNCT
ejpam-7119	105	73	γ	γ	NOUN
ejpam-7119	105	74	)	)	PUNCT
ejpam-7119	105	75	=	=	SYM
ejpam-7119	105	76	1	1	NUM
ejpam-7119	105	77	proof	proof	NOUN
ejpam-7119	105	78	.	.	PUNCT
ejpam-7119	106	1	we	we	PRON
ejpam-7119	106	2	prove	prove	VERB
ejpam-7119	106	3	property	property	NOUN
ejpam-7119	106	4	(	(	PUNCT
ejpam-7119	106	5	3	3	NUM
ejpam-7119	106	6	)	)	PUNCT
ejpam-7119	106	7	in	in	ADP
ejpam-7119	106	8	detail	detail	NOUN
ejpam-7119	106	9	as	as	SCONJ
ejpam-7119	106	10	it	it	PRON
ejpam-7119	106	11	’s	’	VERB
ejpam-7119	106	12	the	the	DET
ejpam-7119	106	13	most	most	ADV
ejpam-7119	106	14	complex	complex	ADJ
ejpam-7119	106	15	:	:	PUNCT
ejpam-7119	106	16	using	use	VERB
ejpam-7119	106	17	the	the	DET
ejpam-7119	106	18	triangle	triangle	NOUN
ejpam-7119	106	19	inequality	inequality	NOUN
ejpam-7119	106	20	for	for	ADP
ejpam-7119	106	21	t	t	PROPN
ejpam-7119	106	22	:	:	PUNCT
ejpam-7119	106	23	tα(υ	tα(υ	NUM
ejpam-7119	106	24	,	,	PUNCT
ejpam-7119	106	25	ξ	ξ	PROPN
ejpam-7119	106	26	,	,	PUNCT
ejpam-7119	106	27	γ	γ	NOUN
ejpam-7119	106	28	)	)	PUNCT
ejpam-7119	106	29	•	•	ADV
ejpam-7119	106	30	tα(ξ,ℑ	tα(ξ,ℑ	PROPN
ejpam-7119	106	31	,	,	PUNCT
ejpam-7119	106	32	ρ	ρ	NOUN
ejpam-7119	106	33	)	)	PUNCT
ejpam-7119	106	34	=	=	SYM
ejpam-7119	106	35	(	(	PUNCT
ejpam-7119	106	36	1	1	NUM
ejpam-7119	106	37	γ(α	γ(α	NOUN
ejpam-7119	106	38	)	)	PUNCT
ejpam-7119	106	39	∫	∫	PROPN
ejpam-7119	107	1	∞	∞	PROPN
ejpam-7119	107	2	0	0	X
ejpam-7119	107	3	tα−1e−tt	tα−1e−tt	NOUN
ejpam-7119	107	4	(	(	PUNCT
ejpam-7119	107	5	υ	υ	PROPN
ejpam-7119	107	6	,	,	PUNCT
ejpam-7119	107	7	ξ	ξ	PROPN
ejpam-7119	107	8	,	,	PUNCT
ejpam-7119	107	9	γt	γt	NOUN
ejpam-7119	107	10	)	)	PUNCT
ejpam-7119	107	11	dt	dt	NOUN
ejpam-7119	107	12	)	)	PUNCT
ejpam-7119	107	13	•	•	CCONJ
ejpam-7119	107	14	(	(	PUNCT
ejpam-7119	107	15	1	1	NUM
ejpam-7119	107	16	γ(α	γ(α	NOUN
ejpam-7119	107	17	)	)	PUNCT
ejpam-7119	107	18	∫	∫	PROPN
ejpam-7119	108	1	∞	∞	NUM
ejpam-7119	108	2	0	0	NUM
ejpam-7119	109	1	sα−1e−st	sα−1e−st	PRON
ejpam-7119	109	2	(	(	PUNCT
ejpam-7119	109	3	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	109	4	,	,	PUNCT
ejpam-7119	109	5	ρs	ρs	NOUN
ejpam-7119	109	6	)	)	PUNCT
ejpam-7119	109	7	ds	ds	NOUN
ejpam-7119	109	8	)	)	PUNCT
ejpam-7119	109	9	by	by	ADP
ejpam-7119	109	10	the	the	DET
ejpam-7119	109	11	properties	property	NOUN
ejpam-7119	109	12	of	of	ADP
ejpam-7119	109	13	the	the	DET
ejpam-7119	109	14	t	t	NOUN
ejpam-7119	109	15	-	-	PUNCT
ejpam-7119	109	16	norm	norm	NOUN
ejpam-7119	109	17	•	•	NOUN
ejpam-7119	109	18	and	and	CCONJ
ejpam-7119	109	19	the	the	DET
ejpam-7119	109	20	integral	integral	ADJ
ejpam-7119	109	21	representation	representation	NOUN
ejpam-7119	109	22	:	:	PUNCT
ejpam-7119	109	23	≤	≤	NUM
ejpam-7119	109	24	1	1	NUM
ejpam-7119	109	25	γ(α)2	γ(α)2	PROPN
ejpam-7119	109	26	∫	∫	PROPN
ejpam-7119	109	27	∞	∞	PROPN
ejpam-7119	109	28	0	0	NUM
ejpam-7119	110	1	∫	∫	PROPN
ejpam-7119	110	2	∞	∞	PROPN
ejpam-7119	110	3	0	0	NUM
ejpam-7119	111	1	tα−1sα−1e−(t+s	tα−1sα−1e−(t+s	ADJ
ejpam-7119	111	2	)	)	PUNCT
ejpam-7119	112	1	[	[	X
ejpam-7119	112	2	t	t	X
ejpam-7119	112	3	(	(	PUNCT
ejpam-7119	112	4	υ	υ	PROPN
ejpam-7119	112	5	,	,	PUNCT
ejpam-7119	112	6	ξ	ξ	PROPN
ejpam-7119	112	7	,	,	PUNCT
ejpam-7119	112	8	γt	γt	NOUN
ejpam-7119	112	9	)	)	PUNCT
ejpam-7119	112	10	•	•	NUM
ejpam-7119	112	11	t	t	PROPN
ejpam-7119	112	12	(	(	PUNCT
ejpam-7119	112	13	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	112	14	,	,	PUNCT
ejpam-7119	112	15	ρs	ρs	NOUN
ejpam-7119	112	16	)	)	PUNCT
ejpam-7119	112	17	]	]	PUNCT
ejpam-7119	112	18	dt	dt	X
ejpam-7119	113	1	ds	ds	ADJ
ejpam-7119	113	2	≤	≤	NUM
ejpam-7119	113	3	1	1	NUM
ejpam-7119	113	4	γ(α)2	γ(α)2	PROPN
ejpam-7119	113	5	∫	∫	PROPN
ejpam-7119	113	6	∞	∞	PROPN
ejpam-7119	113	7	0	0	NUM
ejpam-7119	113	8	∫	∫	PROPN
ejpam-7119	113	9	∞	∞	NUM
ejpam-7119	113	10	0	0	NUM
ejpam-7119	114	1	tα−1sα−1e−(t+s)t	tα−1sα−1e−(t+s)t	NOUN
ejpam-7119	114	2	(	(	PUNCT
ejpam-7119	114	3	υ,ℑ	υ,ℑ	PROPN
ejpam-7119	114	4	,	,	PUNCT
ejpam-7119	114	5	γt+	γt+	NOUN
ejpam-7119	114	6	ρs	ρs	NOUN
ejpam-7119	114	7	)	)	PUNCT
ejpam-7119	114	8	dt	dt	NOUN
ejpam-7119	115	1	ds	ds	NOUN
ejpam-7119	115	2	making	make	VERB
ejpam-7119	115	3	the	the	DET
ejpam-7119	115	4	change	change	NOUN
ejpam-7119	115	5	of	of	ADP
ejpam-7119	115	6	variables	variable	NOUN
ejpam-7119	115	7	u	u	NOUN
ejpam-7119	115	8	=	=	PUNCT
ejpam-7119	115	9	t+	t+	PUNCT
ejpam-7119	115	10	s	s	NOUN
ejpam-7119	115	11	,	,	PUNCT
ejpam-7119	115	12	v	v	NOUN
ejpam-7119	115	13	=	=	X
ejpam-7119	115	14	t/(t+	t/(t+	PROPN
ejpam-7119	115	15	s	s	PART
ejpam-7119	115	16	):	):	PUNCT
ejpam-7119	115	17	=	=	SYM
ejpam-7119	115	18	1	1	NUM
ejpam-7119	115	19	γ(α)2	γ(α)2	PROPN
ejpam-7119	115	20	∫	∫	PROPN
ejpam-7119	115	21	∞	∞	PROPN
ejpam-7119	115	22	0	0	NUM
ejpam-7119	115	23	∫	∫	PROPN
ejpam-7119	115	24	1	1	NUM
ejpam-7119	115	25	0	0	NUM
ejpam-7119	115	26	u2α−1vα−1(1−	u2α−1vα−1(1−	PROPN
ejpam-7119	115	27	v)α−1e−ut	v)α−1e−ut	PROPN
ejpam-7119	115	28	(	(	PUNCT
ejpam-7119	115	29	υ,ℑ	υ,ℑ	PROPN
ejpam-7119	115	30	,	,	PUNCT
ejpam-7119	115	31	γuv	γuv	VERB
ejpam-7119	115	32	+	+	CCONJ
ejpam-7119	115	33	ρu(1−	ρu(1−	PROPN
ejpam-7119	115	34	v	v	NOUN
ejpam-7119	115	35	)	)	PUNCT
ejpam-7119	115	36	)	)	PUNCT
ejpam-7119	116	1	dv	dv	PROPN
ejpam-7119	116	2	du	du	PROPN
ejpam-7119	116	3	≤	≤	PROPN
ejpam-7119	116	4	1	1	NUM
ejpam-7119	116	5	γ(α)2	γ(α)2	PROPN
ejpam-7119	116	6	∫	∫	PROPN
ejpam-7119	116	7	∞	∞	PROPN
ejpam-7119	116	8	0	0	NUM
ejpam-7119	116	9	∫	∫	PROPN
ejpam-7119	116	10	1	1	NUM
ejpam-7119	116	11	0	0	NUM
ejpam-7119	116	12	u2α−1vα−1(1−	u2α−1vα−1(1−	PROPN
ejpam-7119	116	13	v)α−1e−ut	v)α−1e−ut	PROPN
ejpam-7119	116	14	(	(	PUNCT
ejpam-7119	116	15	υ,ℑ	υ,ℑ	PROPN
ejpam-7119	116	16	,	,	PUNCT
ejpam-7119	116	17	(	(	PUNCT
ejpam-7119	116	18	γ	γ	X
ejpam-7119	116	19	+	+	NOUN
ejpam-7119	116	20	ρ)u	ρ)u	PROPN
ejpam-7119	116	21	)	)	PUNCT
ejpam-7119	116	22	dv	dv	PROPN
ejpam-7119	116	23	du	du	PROPN
ejpam-7119	116	24	=	=	PROPN
ejpam-7119	116	25	tα(υ,ℑ	tα(υ,ℑ	PROPN
ejpam-7119	116	26	,	,	PUNCT
ejpam-7119	116	27	γ	γ	X
ejpam-7119	116	28	+	+	NOUN
ejpam-7119	116	29	ρ	ρ	PROPN
ejpam-7119	116	30	)	)	PUNCT
ejpam-7119	116	31	·	·	PUNCT
ejpam-7119	116	32	γ(2α	γ(2α	NUM
ejpam-7119	116	33	)	)	PUNCT
ejpam-7119	116	34	γ(α)2	γ(α)2	PROPN
ejpam-7119	116	35	the	the	DET
ejpam-7119	116	36	other	other	ADJ
ejpam-7119	116	37	properties	property	NOUN
ejpam-7119	116	38	follow	follow	VERB
ejpam-7119	116	39	similarly	similarly	ADV
ejpam-7119	116	40	from	from	ADP
ejpam-7119	116	41	the	the	DET
ejpam-7119	116	42	definitions	definition	NOUN
ejpam-7119	116	43	and	and	CCONJ
ejpam-7119	116	44	properties	property	NOUN
ejpam-7119	116	45	of	of	ADP
ejpam-7119	116	46	the	the	DET
ejpam-7119	116	47	original	original	ADJ
ejpam-7119	116	48	neutrosophic	neutrosophic	ADJ
ejpam-7119	116	49	functions	function	NOUN
ejpam-7119	116	50	.	.	PUNCT
ejpam-7119	117	1	theorem	theorem	NOUN
ejpam-7119	117	2	1	1	NUM
ejpam-7119	117	3	(	(	PUNCT
ejpam-7119	117	4	comprehensive	comprehensive	ADJ
ejpam-7119	117	5	fractional	fractional	ADJ
ejpam-7119	117	6	fixed	fix	VERB
ejpam-7119	117	7	point	point	NOUN
ejpam-7119	117	8	theorem	theorem	NOUN
ejpam-7119	117	9	)	)	PUNCT
ejpam-7119	117	10	.	.	PUNCT
ejpam-7119	118	1	let	let	AUX
ejpam-7119	118	2	(	(	PUNCT
ejpam-7119	118	3	z	z	NOUN
ejpam-7119	118	4	,	,	PUNCT
ejpam-7119	118	5	mα	mα	PROPN
ejpam-7119	118	6	,	,	PUNCT
ejpam-7119	118	7	tα	tα	PROPN
ejpam-7119	118	8	,	,	PUNCT
ejpam-7119	118	9	fα	fα	NOUN
ejpam-7119	118	10	,	,	PUNCT
ejpam-7119	118	11	iα	iα	NOUN
ejpam-7119	118	12	,	,	PUNCT
ejpam-7119	118	13	•	•	PROPN
ejpam-7119	118	14	,	,	PUNCT
ejpam-7119	118	15	⋄	⋄	PROPN
ejpam-7119	118	16	,	,	PUNCT
ejpam-7119	118	17	r	r	NOUN
ejpam-7119	118	18	,	,	PUNCT
ejpam-7119	118	19	⋆	⋆	CCONJ
ejpam-7119	118	20	)	)	PUNCT
ejpam-7119	118	21	be	be	AUX
ejpam-7119	118	22	a	a	DET
ejpam-7119	118	23	complete	complete	ADJ
ejpam-7119	118	24	fonmr	fonmr	ADJ
ejpam-7119	118	25	-	-	PUNCT
ejpam-7119	118	26	ms	ms	NOUN
ejpam-7119	118	27	.	.	PROPN
ejpam-7119	119	1	if	if	SCONJ
ejpam-7119	119	2	a	a	DET
ejpam-7119	119	3	mapping	mapping	NOUN
ejpam-7119	119	4	ψ	ψ	X
ejpam-7119	119	5	:	:	PUNCT
ejpam-7119	119	6	z	z	X
ejpam-7119	119	7	→	→	SYM
ejpam-7119	119	8	z	z	NOUN
ejpam-7119	119	9	satisfies	satisfie	NOUN
ejpam-7119	119	10	:	:	PUNCT
ejpam-7119	119	11	(	(	PUNCT
ejpam-7119	119	12	i	i	NOUN
ejpam-7119	119	13	)	)	PUNCT
ejpam-7119	119	14	fractional	fractional	ADJ
ejpam-7119	119	15	metric	metric	ADJ
ejpam-7119	119	16	contraction	contraction	NOUN
ejpam-7119	119	17	:	:	PUNCT
ejpam-7119	119	18	mα(ψυ	mα(ψυ	ADJ
ejpam-7119	119	19	,	,	PUNCT
ejpam-7119	119	20	ψξ	ψξ	NOUN
ejpam-7119	119	21	,	,	PUNCT
ejpam-7119	119	22	ψℑ	ψℑ	NOUN
ejpam-7119	119	23	)	)	PUNCT
ejpam-7119	119	24	≤	≤	NUM
ejpam-7119	119	25	καmα(υ	καmα(υ	NOUN
ejpam-7119	119	26	,	,	PUNCT
ejpam-7119	119	27	ξ,ℑ	ξ,ℑ	PROPN
ejpam-7119	119	28	)	)	PUNCT
ejpam-7119	119	29	,	,	PUNCT
ejpam-7119	119	30	κ	κ	PROPN
ejpam-7119	119	31	∈	∈	PROPN
ejpam-7119	120	1	[	[	X
ejpam-7119	120	2	0	0	NUM
ejpam-7119	120	3	,	,	PUNCT
ejpam-7119	120	4	1	1	NUM
ejpam-7119	120	5	)	)	PUNCT
ejpam-7119	120	6	(	(	PUNCT
ejpam-7119	120	7	ii	ii	NOUN
ejpam-7119	120	8	)	)	PUNCT
ejpam-7119	120	9	neutrosophic	neutrosophic	ADJ
ejpam-7119	120	10	consistency	consistency	NOUN
ejpam-7119	120	11	condition	condition	NOUN
ejpam-7119	120	12	:	:	PUNCT
ejpam-7119	120	13	tα(ψυ	tα(ψυ	ADJ
ejpam-7119	120	14	,	,	PUNCT
ejpam-7119	120	15	ψξ	ψξ	NOUN
ejpam-7119	120	16	,	,	PUNCT
ejpam-7119	120	17	κγ	κγ	NOUN
ejpam-7119	120	18	)	)	PUNCT
ejpam-7119	120	19	≥	≥	NOUN
ejpam-7119	120	20	tα(υ	tα(υ	NUM
ejpam-7119	120	21	,	,	PUNCT
ejpam-7119	120	22	ξ	ξ	PROPN
ejpam-7119	120	23	,	,	PUNCT
ejpam-7119	120	24	γ	γ	NOUN
ejpam-7119	120	25	)	)	PUNCT
ejpam-7119	120	26	a.	a.	NOUN
ejpam-7119	120	27	malkawi	malkawi	PROPN
ejpam-7119	120	28	,	,	PUNCT
ejpam-7119	120	29	a.	a.	PROPN
ejpam-7119	120	30	rabaiah	rabaiah	PROPN
ejpam-7119	120	31	/	/	SYM
ejpam-7119	120	32	eur	eur	PROPN
ejpam-7119	120	33	.	.	PUNCT
ejpam-7119	121	1	j.	j.	PROPN
ejpam-7119	121	2	pure	pure	PROPN
ejpam-7119	121	3	appl	appl	PROPN
ejpam-7119	121	4	.	.	PROPN
ejpam-7119	121	5	math	math	PROPN
ejpam-7119	121	6	,	,	PUNCT
ejpam-7119	121	7	18	18	NUM
ejpam-7119	121	8	(	(	PUNCT
ejpam-7119	121	9	4	4	NUM
ejpam-7119	121	10	)	)	PUNCT
ejpam-7119	121	11	(	(	PUNCT
ejpam-7119	121	12	2025	2025	NUM
ejpam-7119	121	13	)	)	PUNCT
ejpam-7119	121	14	,	,	PUNCT
ejpam-7119	121	15	7119	7119	NUM
ejpam-7119	121	16	6	6	NUM
ejpam-7119	121	17	of	of	ADP
ejpam-7119	121	18	13	13	NUM
ejpam-7119	121	19	(	(	PUNCT
ejpam-7119	121	20	iii	iii	NOUN
ejpam-7119	121	21	)	)	PUNCT
ejpam-7119	121	22	indeterminacy	indeterminacy	NOUN
ejpam-7119	121	23	bound	bind	VERB
ejpam-7119	121	24	:	:	PUNCT
ejpam-7119	121	25	iα(ψυ	iα(ψυ	PROPN
ejpam-7119	121	26	,	,	PUNCT
ejpam-7119	121	27	ψξ	ψξ	NOUN
ejpam-7119	121	28	,	,	PUNCT
ejpam-7119	121	29	γ	γ	NOUN
ejpam-7119	121	30	)	)	PUNCT
ejpam-7119	121	31	≤	≤	NOUN
ejpam-7119	121	32	iα(υ	iα(υ	NOUN
ejpam-7119	121	33	,	,	PUNCT
ejpam-7119	121	34	ξ	ξ	PROPN
ejpam-7119	121	35	,	,	PUNCT
ejpam-7119	121	36	γ	γ	NOUN
ejpam-7119	121	37	)	)	PUNCT
ejpam-7119	121	38	then	then	ADV
ejpam-7119	121	39	ψ	ψ	X
ejpam-7119	121	40	has	have	VERB
ejpam-7119	121	41	a	a	DET
ejpam-7119	121	42	unique	unique	ADJ
ejpam-7119	121	43	fixed	fix	VERB
ejpam-7119	121	44	point	point	NOUN
ejpam-7119	121	45	υ∗	υ∗	NOUN
ejpam-7119	121	46	∈	∈	PROPN
ejpam-7119	121	47	z	z	NOUN
ejpam-7119	121	48	,	,	PUNCT
ejpam-7119	121	49	and	and	CCONJ
ejpam-7119	121	50	for	for	ADP
ejpam-7119	121	51	any	any	DET
ejpam-7119	121	52	initial	initial	ADJ
ejpam-7119	121	53	point	point	NOUN
ejpam-7119	121	54	υ0	υ0	NOUN
ejpam-7119	121	55	∈	∈	PROPN
ejpam-7119	121	56	z	z	PROPN
ejpam-7119	121	57	,	,	PUNCT
ejpam-7119	121	58	the	the	DET
ejpam-7119	121	59	iterative	iterative	NOUN
ejpam-7119	121	60	sequence	sequence	NOUN
ejpam-7119	121	61	υn+1	υn+1	NUM
ejpam-7119	121	62	=	=	PUNCT
ejpam-7119	121	63	ψυn	ψυn	NOUN
ejpam-7119	121	64	converges	converge	NOUN
ejpam-7119	121	65	to	to	ADP
ejpam-7119	121	66	υ∗.	υ∗.	VERB
ejpam-7119	121	67	proof	proof	NOUN
ejpam-7119	121	68	.	.	PUNCT
ejpam-7119	122	1	we	we	PRON
ejpam-7119	122	2	provide	provide	VERB
ejpam-7119	122	3	a	a	DET
ejpam-7119	122	4	comprehensive	comprehensive	ADJ
ejpam-7119	122	5	proof	proof	NOUN
ejpam-7119	122	6	in	in	ADP
ejpam-7119	122	7	several	several	ADJ
ejpam-7119	122	8	steps	step	NOUN
ejpam-7119	122	9	:	:	PUNCT
ejpam-7119	122	10	step	step	NOUN
ejpam-7119	122	11	1	1	NUM
ejpam-7119	122	12	:	:	PUNCT
ejpam-7119	122	13	construction	construction	NOUN
ejpam-7119	122	14	of	of	ADP
ejpam-7119	122	15	iterative	iterative	NOUN
ejpam-7119	122	16	sequence	sequence	NOUN
ejpam-7119	122	17	let	let	VERB
ejpam-7119	122	18	υ0	υ0	PROPN
ejpam-7119	122	19	∈	∈	PROPN
ejpam-7119	122	20	z	z	AUX
ejpam-7119	122	21	be	be	AUX
ejpam-7119	122	22	arbitrary	arbitrary	ADJ
ejpam-7119	122	23	.	.	PUNCT
ejpam-7119	123	1	define	define	VERB
ejpam-7119	123	2	the	the	DET
ejpam-7119	123	3	iterative	iterative	NOUN
ejpam-7119	123	4	sequence	sequence	NOUN
ejpam-7119	123	5	:	:	PUNCT
ejpam-7119	123	6	υn+1	υn+1	NUM
ejpam-7119	123	7	=	=	SYM
ejpam-7119	123	8	ψυn	ψυn	NOUN
ejpam-7119	123	9	,	,	PUNCT
ejpam-7119	123	10	n	n	NOUN
ejpam-7119	123	11	=	=	SYM
ejpam-7119	123	12	0	0	NUM
ejpam-7119	123	13	,	,	PUNCT
ejpam-7119	123	14	1	1	NUM
ejpam-7119	123	15	,	,	PUNCT
ejpam-7119	123	16	2	2	NUM
ejpam-7119	123	17	,	,	PUNCT
ejpam-7119	123	18	.	.	PUNCT
ejpam-7119	123	19	.	.	PUNCT
ejpam-7119	123	20	.	.	PUNCT
ejpam-7119	124	1	step	step	NOUN
ejpam-7119	124	2	2	2	NUM
ejpam-7119	124	3	:	:	PUNCT
ejpam-7119	124	4	metric	metric	ADJ
ejpam-7119	124	5	contraction	contraction	NOUN
ejpam-7119	124	6	and	and	CCONJ
ejpam-7119	124	7	cauchy	cauchy	ADJ
ejpam-7119	124	8	sequence	sequence	NOUN
ejpam-7119	124	9	property	property	NOUN
ejpam-7119	124	10	from	from	ADP
ejpam-7119	124	11	the	the	DET
ejpam-7119	124	12	fractional	fractional	ADJ
ejpam-7119	124	13	metric	metric	ADJ
ejpam-7119	124	14	contraction	contraction	NOUN
ejpam-7119	124	15	:	:	PUNCT
ejpam-7119	124	16	mα(υn+1	mα(υn+1	ADJ
ejpam-7119	124	17	,	,	PUNCT
ejpam-7119	124	18	υn	υn	NOUN
ejpam-7119	124	19	,	,	PUNCT
ejpam-7119	124	20	υn	υn	NOUN
ejpam-7119	124	21	)	)	PUNCT
ejpam-7119	124	22	≤	≤	NOUN
ejpam-7119	124	23	καmα(υn	καmα(υn	NOUN
ejpam-7119	124	24	,	,	PUNCT
ejpam-7119	124	25	υn−1	υn−1	PROPN
ejpam-7119	124	26	,	,	PUNCT
ejpam-7119	124	27	υn−1	υn−1	PROPN
ejpam-7119	124	28	)	)	PUNCT
ejpam-7119	124	29	≤	≤	NOUN
ejpam-7119	125	1	κ2αmα(υn−1	κ2αmα(υn−1	PROPN
ejpam-7119	125	2	,	,	PUNCT
ejpam-7119	125	3	υn−2	υn−2	PROPN
ejpam-7119	125	4	,	,	PUNCT
ejpam-7119	125	5	υn−2	υn−2	PROPN
ejpam-7119	125	6	)	)	PUNCT
ejpam-7119	125	7	≤	≤	NOUN
ejpam-7119	125	8	·	·	PUNCT
ejpam-7119	125	9	·	·	PUNCT
ejpam-7119	125	10	·	·	PUNCT
ejpam-7119	126	1	≤	≤	NUM
ejpam-7119	126	2	κnαmα(υ1	κnαmα(υ1	VERB
ejpam-7119	126	3	,	,	PUNCT
ejpam-7119	126	4	υ0	υ0	NOUN
ejpam-7119	126	5	,	,	PUNCT
ejpam-7119	126	6	υ0	υ0	PROPN
ejpam-7119	126	7	)	)	PUNCT
ejpam-7119	126	8	for	for	ADP
ejpam-7119	126	9	m	m	PROPN
ejpam-7119	126	10	>	>	X
ejpam-7119	126	11	n	n	CCONJ
ejpam-7119	126	12	,	,	PUNCT
ejpam-7119	126	13	using	use	VERB
ejpam-7119	126	14	the	the	DET
ejpam-7119	126	15	fractional	fractional	ADJ
ejpam-7119	126	16	triangle	triangle	NOUN
ejpam-7119	126	17	inequality	inequality	NOUN
ejpam-7119	126	18	repeatedly	repeatedly	ADV
ejpam-7119	126	19	:	:	PUNCT
ejpam-7119	126	20	mα(υm	mα(υm	NOUN
ejpam-7119	126	21	,	,	PUNCT
ejpam-7119	126	22	υn	υn	NOUN
ejpam-7119	126	23	,	,	PUNCT
ejpam-7119	126	24	υn	υn	NOUN
ejpam-7119	126	25	)	)	PUNCT
ejpam-7119	126	26	≤	≤	NUM
ejpam-7119	126	27	rα	rα	X
ejpam-7119	127	1	[	[	X
ejpam-7119	127	2	mα(υm	mα(υm	NOUN
ejpam-7119	127	3	,	,	PUNCT
ejpam-7119	127	4	υn	υn	NOUN
ejpam-7119	127	5	,	,	PUNCT
ejpam-7119	127	6	υn+1	υn+1	NOUN
ejpam-7119	127	7	)	)	PUNCT
ejpam-7119	127	8	⋆α	⋆α	NOUN
ejpam-7119	127	9	mα(υm	mα(υm	NOUN
ejpam-7119	127	10	,	,	PUNCT
ejpam-7119	127	11	υn+1	υn+1	NOUN
ejpam-7119	127	12	,	,	PUNCT
ejpam-7119	127	13	υn	υn	NOUN
ejpam-7119	127	14	)	)	PUNCT
ejpam-7119	127	15	⋆α	⋆α	PROPN
ejpam-7119	127	16	mα(υn+1	mα(υn+1	PROPN
ejpam-7119	127	17	,	,	PUNCT
ejpam-7119	127	18	υn	υn	NOUN
ejpam-7119	127	19	,	,	PUNCT
ejpam-7119	127	20	υn	υn	NOUN
ejpam-7119	127	21	)	)	PUNCT
ejpam-7119	127	22	]	]	PUNCT
ejpam-7119	128	1	≤	≤	NUM
ejpam-7119	128	2	rα	rα	X
ejpam-7119	128	3	[	[	PUNCT
ejpam-7119	128	4	κ(n+1)αc	κ(n+1)αc	NOUN
ejpam-7119	128	5	⋆α	⋆α	PROPN
ejpam-7119	128	6	κ	κ	PROPN
ejpam-7119	128	7	(	(	PUNCT
ejpam-7119	128	8	n+1)αc	n+1)αc	NOUN
ejpam-7119	128	9	⋆α	⋆α	PROPN
ejpam-7119	128	10	κ	κ	NOUN
ejpam-7119	128	11	nαc	nαc	NOUN
ejpam-7119	128	12	]	]	PUNCT
ejpam-7119	128	13	≤	≤	NUM
ejpam-7119	128	14	rα(2κ	rα(2κ	NUM
ejpam-7119	128	15	(	(	PUNCT
ejpam-7119	128	16	n+1)α	n+1)α	PROPN
ejpam-7119	128	17	+	+	CCONJ
ejpam-7119	128	18	κnα)c	κnα)c	PROPN
ejpam-7119	128	19	where	where	SCONJ
ejpam-7119	128	20	c	c	NOUN
ejpam-7119	128	21	=	=	AUX
ejpam-7119	128	22	mα(υ1	mα(υ1	ADJ
ejpam-7119	128	23	,	,	PUNCT
ejpam-7119	128	24	υ0	υ0	NOUN
ejpam-7119	128	25	,	,	PUNCT
ejpam-7119	128	26	υ0	υ0	NOUN
ejpam-7119	128	27	)	)	PUNCT
ejpam-7119	128	28	.	.	PUNCT
ejpam-7119	129	1	since	since	SCONJ
ejpam-7119	129	2	κ	κ	PROPN
ejpam-7119	129	3	∈	∈	PROPN
ejpam-7119	129	4	[	[	X
ejpam-7119	129	5	0	0	NUM
ejpam-7119	129	6	,	,	PUNCT
ejpam-7119	129	7	1	1	NUM
ejpam-7119	129	8	)	)	PUNCT
ejpam-7119	129	9	,	,	PUNCT
ejpam-7119	129	10	we	we	PRON
ejpam-7119	129	11	have	have	VERB
ejpam-7119	129	12	:	:	PUNCT
ejpam-7119	129	13	lim	lim	PROPN
ejpam-7119	129	14	n	n	SYM
ejpam-7119	129	15	,	,	PUNCT
ejpam-7119	129	16	m→∞	m→∞	NOUN
ejpam-7119	129	17	mα(υm	mα(υm	NOUN
ejpam-7119	129	18	,	,	PUNCT
ejpam-7119	129	19	υn	υn	NOUN
ejpam-7119	129	20	,	,	PUNCT
ejpam-7119	129	21	υn	υn	NOUN
ejpam-7119	129	22	)	)	PUNCT
ejpam-7119	129	23	=	=	SYM
ejpam-7119	129	24	0	0	PUNCT
ejpam-7119	130	1	thus	thus	ADV
ejpam-7119	130	2	,	,	PUNCT
ejpam-7119	130	3	{	{	PUNCT
ejpam-7119	130	4	υn	υn	NOUN
ejpam-7119	130	5	}	}	PUNCT
ejpam-7119	130	6	is	be	AUX
ejpam-7119	130	7	a	a	DET
ejpam-7119	130	8	cauchy	cauchy	ADJ
ejpam-7119	130	9	sequence	sequence	NOUN
ejpam-7119	130	10	.	.	PUNCT
ejpam-7119	131	1	step	step	NOUN
ejpam-7119	131	2	3	3	NUM
ejpam-7119	131	3	:	:	PUNCT
ejpam-7119	131	4	convergence	convergence	NOUN
ejpam-7119	131	5	to	to	ADP
ejpam-7119	131	6	fixed	fix	VERB
ejpam-7119	131	7	point	point	NOUN
ejpam-7119	131	8	by	by	ADP
ejpam-7119	131	9	completeness	completeness	NOUN
ejpam-7119	131	10	of	of	ADP
ejpam-7119	131	11	the	the	DET
ejpam-7119	131	12	fonmr	fonmr	NOUN
ejpam-7119	131	13	-	-	PUNCT
ejpam-7119	131	14	ms	ms	NOUN
ejpam-7119	131	15	,	,	PUNCT
ejpam-7119	131	16	there	there	PRON
ejpam-7119	131	17	exists	exist	VERB
ejpam-7119	131	18	υ∗	υ∗	NOUN
ejpam-7119	131	19	∈	∈	PROPN
ejpam-7119	131	20	z	z	NOUN
ejpam-7119	131	21	such	such	ADJ
ejpam-7119	131	22	that	that	PRON
ejpam-7119	131	23	:	:	PUNCT
ejpam-7119	132	1	lim	lim	PROPN
ejpam-7119	132	2	n→∞	n→∞	NUM
ejpam-7119	132	3	mα(υn	mα(υn	PROPN
ejpam-7119	132	4	,	,	PUNCT
ejpam-7119	132	5	υ	υ	NOUN
ejpam-7119	132	6	∗	∗	NOUN
ejpam-7119	132	7	,	,	PUNCT
ejpam-7119	132	8	υ∗	υ∗	NOUN
ejpam-7119	132	9	)	)	PUNCT
ejpam-7119	132	10	=	=	SYM
ejpam-7119	133	1	0	0	PUNCT
ejpam-7119	134	1	now	now	ADV
ejpam-7119	134	2	we	we	PRON
ejpam-7119	134	3	show	show	VERB
ejpam-7119	134	4	that	that	SCONJ
ejpam-7119	134	5	υ∗	υ∗	NOUN
ejpam-7119	134	6	is	be	AUX
ejpam-7119	134	7	a	a	DET
ejpam-7119	134	8	fixed	fixed	ADJ
ejpam-7119	134	9	point	point	NOUN
ejpam-7119	134	10	:	:	PUNCT
ejpam-7119	134	11	mα(ψυ	mα(ψυ	ADJ
ejpam-7119	134	12	∗	∗	NOUN
ejpam-7119	134	13	,	,	PUNCT
ejpam-7119	134	14	υ∗	υ∗	NOUN
ejpam-7119	134	15	,	,	PUNCT
ejpam-7119	134	16	υ∗	υ∗	NOUN
ejpam-7119	134	17	)	)	PUNCT
ejpam-7119	134	18	≤	≤	PUNCT
ejpam-7119	134	19	rα	rα	PART
ejpam-7119	135	1	[	[	X
ejpam-7119	135	2	mα(ψυ	mα(ψυ	ADJ
ejpam-7119	135	3	∗	∗	NOUN
ejpam-7119	135	4	,	,	PUNCT
ejpam-7119	135	5	υ∗,ψυn	υ∗,ψυn	NOUN
ejpam-7119	135	6	)	)	PUNCT
ejpam-7119	135	7	⋆α	⋆α	PROPN
ejpam-7119	135	8	mα(ψυ	mα(ψυ	VERB
ejpam-7119	135	9	∗,ψυn	∗,ψυn	NOUN
ejpam-7119	135	10	,	,	PUNCT
ejpam-7119	135	11	υ	υ	NOUN
ejpam-7119	135	12	∗	∗	NOUN
ejpam-7119	135	13	)	)	PUNCT
ejpam-7119	135	14	⋆α	⋆α	PROPN
ejpam-7119	135	15	mα(ψυn	mα(ψυn	PROPN
ejpam-7119	135	16	,	,	PUNCT
ejpam-7119	135	17	υ	υ	NOUN
ejpam-7119	135	18	∗	∗	NOUN
ejpam-7119	135	19	,	,	PUNCT
ejpam-7119	135	20	υ∗	υ∗	NOUN
ejpam-7119	135	21	)	)	PUNCT
ejpam-7119	135	22	]	]	PUNCT
ejpam-7119	136	1	≤	≤	X
ejpam-7119	136	2	rα	rα	X
ejpam-7119	137	1	[	[	X
ejpam-7119	137	2	κ	κ	X
ejpam-7119	137	3	αmα(υ	αmα(υ	VERB
ejpam-7119	137	4	∗	∗	NOUN
ejpam-7119	137	5	,	,	PUNCT
ejpam-7119	137	6	υn	υn	NOUN
ejpam-7119	137	7	,	,	PUNCT
ejpam-7119	137	8	υn	υn	NOUN
ejpam-7119	137	9	)	)	PUNCT
ejpam-7119	137	10	⋆α	⋆α	PROPN
ejpam-7119	137	11	κ	κ	NOUN
ejpam-7119	137	12	αmα(υ	αmα(υ	VERB
ejpam-7119	137	13	∗	∗	NOUN
ejpam-7119	137	14	,	,	PUNCT
ejpam-7119	137	15	υn	υn	NOUN
ejpam-7119	137	16	,	,	PUNCT
ejpam-7119	137	17	υ	υ	NOUN
ejpam-7119	137	18	∗	∗	NOUN
ejpam-7119	137	19	)	)	PUNCT
ejpam-7119	137	20	⋆α	⋆α	PROPN
ejpam-7119	137	21	mα(υn+1	mα(υn+1	PROPN
ejpam-7119	137	22	,	,	PUNCT
ejpam-7119	137	23	υ	υ	NOUN
ejpam-7119	137	24	∗	∗	NOUN
ejpam-7119	137	25	,	,	PUNCT
ejpam-7119	137	26	υ∗	υ∗	NOUN
ejpam-7119	137	27	)	)	PUNCT
ejpam-7119	137	28	]	]	PUNCT
ejpam-7119	138	1	taking	take	VERB
ejpam-7119	138	2	the	the	DET
ejpam-7119	138	3	limit	limit	NOUN
ejpam-7119	138	4	as	as	ADP
ejpam-7119	138	5	n→	n→	PROPN
ejpam-7119	138	6	∞	∞	PROPN
ejpam-7119	138	7	,	,	PUNCT
ejpam-7119	138	8	all	all	DET
ejpam-7119	138	9	terms	term	NOUN
ejpam-7119	138	10	approach	approach	VERB
ejpam-7119	138	11	zero	zero	NUM
ejpam-7119	138	12	,	,	PUNCT
ejpam-7119	138	13	so	so	ADV
ejpam-7119	138	14	:	:	PUNCT
ejpam-7119	138	15	mα(ψυ	mα(ψυ	ADJ
ejpam-7119	138	16	∗	∗	NOUN
ejpam-7119	138	17	,	,	PUNCT
ejpam-7119	138	18	υ∗	υ∗	NOUN
ejpam-7119	138	19	,	,	PUNCT
ejpam-7119	138	20	υ∗	υ∗	NOUN
ejpam-7119	138	21	)	)	PUNCT
ejpam-7119	138	22	=	=	SYM
ejpam-7119	138	23	0	0	NUM
ejpam-7119	138	24	⇒	⇒	NOUN
ejpam-7119	138	25	ψυ∗	ψυ∗	NOUN
ejpam-7119	138	26	=	=	SYM
ejpam-7119	138	27	υ∗	υ∗	NOUN
ejpam-7119	138	28	step	step	NOUN
ejpam-7119	138	29	4	4	NUM
ejpam-7119	138	30	:	:	PUNCT
ejpam-7119	138	31	uniqueness	uniqueness	NOUN
ejpam-7119	138	32	of	of	ADP
ejpam-7119	138	33	fixed	fix	VERB
ejpam-7119	138	34	point	point	NOUN
ejpam-7119	138	35	suppose	suppose	VERB
ejpam-7119	138	36	there	there	PRON
ejpam-7119	138	37	exist	exist	VERB
ejpam-7119	138	38	two	two	NUM
ejpam-7119	138	39	distinct	distinct	ADJ
ejpam-7119	138	40	fixed	fix	VERB
ejpam-7119	138	41	points	point	NOUN
ejpam-7119	138	42	υ∗	υ∗	NOUN
ejpam-7119	138	43	and	and	CCONJ
ejpam-7119	138	44	ξ∗.	ξ∗.	NOUN
ejpam-7119	138	45	then	then	ADV
ejpam-7119	138	46	:	:	PUNCT
ejpam-7119	138	47	mα(υ	mα(υ	PUNCT
ejpam-7119	138	48	∗	∗	NOUN
ejpam-7119	138	49	,	,	PUNCT
ejpam-7119	138	50	ξ∗	ξ∗	ADJ
ejpam-7119	138	51	,	,	PUNCT
ejpam-7119	138	52	ξ∗	ξ∗	ADJ
ejpam-7119	138	53	)	)	PUNCT
ejpam-7119	139	1	=	=	NOUN
ejpam-7119	139	2	mα(ψυ	mα(ψυ	VERB
ejpam-7119	139	3	∗,ψξ∗,ψξ∗	∗,ψξ∗,ψξ∗	NOUN
ejpam-7119	139	4	)	)	PUNCT
ejpam-7119	139	5	≤	≤	NUM
ejpam-7119	139	6	καmα(υ	καmα(υ	NUM
ejpam-7119	139	7	∗	∗	NOUN
ejpam-7119	139	8	,	,	PUNCT
ejpam-7119	139	9	ξ∗	ξ∗	ADJ
ejpam-7119	139	10	,	,	PUNCT
ejpam-7119	139	11	ξ∗	ξ∗	ADJ
ejpam-7119	139	12	)	)	PUNCT
ejpam-7119	139	13	since	since	SCONJ
ejpam-7119	139	14	κα	κα	INTJ
ejpam-7119	139	15	<	<	X
ejpam-7119	139	16	1	1	NUM
ejpam-7119	139	17	,	,	PUNCT
ejpam-7119	139	18	this	this	PRON
ejpam-7119	139	19	implies	imply	VERB
ejpam-7119	139	20	mα(υ	mα(υ	NOUN
ejpam-7119	139	21	∗	∗	NOUN
ejpam-7119	139	22	,	,	PUNCT
ejpam-7119	139	23	ξ∗	ξ∗	ADJ
ejpam-7119	139	24	,	,	PUNCT
ejpam-7119	139	25	ξ∗	ξ∗	ADJ
ejpam-7119	139	26	)	)	PUNCT
ejpam-7119	139	27	=	=	SYM
ejpam-7119	139	28	0	0	NUM
ejpam-7119	139	29	,	,	PUNCT
ejpam-7119	139	30	so	so	ADV
ejpam-7119	139	31	υ∗	υ∗	NOUN
ejpam-7119	139	32	=	=	PUNCT
ejpam-7119	139	33	ξ∗.	ξ∗.	VERB
ejpam-7119	139	34	a.	a.	NOUN
ejpam-7119	139	35	malkawi	malkawi	PROPN
ejpam-7119	139	36	,	,	PUNCT
ejpam-7119	139	37	a.	a.	PROPN
ejpam-7119	139	38	rabaiah	rabaiah	PROPN
ejpam-7119	139	39	/	/	SYM
ejpam-7119	139	40	eur	eur	PROPN
ejpam-7119	139	41	.	.	PUNCT
ejpam-7119	140	1	j.	j.	PROPN
ejpam-7119	140	2	pure	pure	PROPN
ejpam-7119	140	3	appl	appl	PROPN
ejpam-7119	140	4	.	.	PROPN
ejpam-7119	140	5	math	math	PROPN
ejpam-7119	140	6	,	,	PUNCT
ejpam-7119	140	7	18	18	NUM
ejpam-7119	140	8	(	(	PUNCT
ejpam-7119	140	9	4	4	NUM
ejpam-7119	140	10	)	)	PUNCT
ejpam-7119	140	11	(	(	PUNCT
ejpam-7119	140	12	2025	2025	NUM
ejpam-7119	140	13	)	)	PUNCT
ejpam-7119	140	14	,	,	PUNCT
ejpam-7119	140	15	7119	7119	NUM
ejpam-7119	140	16	7	7	NUM
ejpam-7119	140	17	of	of	ADP
ejpam-7119	140	18	13	13	NUM
ejpam-7119	140	19	step	step	NOUN
ejpam-7119	140	20	5	5	NUM
ejpam-7119	140	21	:	:	PUNCT
ejpam-7119	140	22	neutrosophic	neutrosophic	ADJ
ejpam-7119	140	23	convergence	convergence	NOUN
ejpam-7119	140	24	properties	property	NOUN
ejpam-7119	140	25	from	from	ADP
ejpam-7119	140	26	the	the	DET
ejpam-7119	140	27	neutrosophic	neutrosophic	ADJ
ejpam-7119	140	28	consistency	consistency	NOUN
ejpam-7119	140	29	condition	condition	NOUN
ejpam-7119	140	30	:	:	PUNCT
ejpam-7119	141	1	tα(υn+1	tα(υn+1	NOUN
ejpam-7119	141	2	,	,	PUNCT
ejpam-7119	141	3	υn	υn	NOUN
ejpam-7119	141	4	,	,	PUNCT
ejpam-7119	141	5	κγ	κγ	NOUN
ejpam-7119	141	6	)	)	PUNCT
ejpam-7119	141	7	≥	≥	NOUN
ejpam-7119	141	8	tα(υn	tα(υn	NOUN
ejpam-7119	141	9	,	,	PUNCT
ejpam-7119	141	10	υn−1	υn−1	PROPN
ejpam-7119	141	11	,	,	PUNCT
ejpam-7119	141	12	γ	γ	NOUN
ejpam-7119	141	13	)	)	PUNCT
ejpam-7119	141	14	this	this	PRON
ejpam-7119	141	15	ensures	ensure	VERB
ejpam-7119	141	16	that	that	SCONJ
ejpam-7119	141	17	the	the	DET
ejpam-7119	141	18	truth	truth	NOUN
ejpam-7119	141	19	membership	membership	NOUN
ejpam-7119	141	20	improves	improve	VERB
ejpam-7119	141	21	with	with	ADP
ejpam-7119	141	22	each	each	DET
ejpam-7119	141	23	iteration	iteration	NOUN
ejpam-7119	141	24	.	.	PUNCT
ejpam-7119	142	1	similarly	similarly	ADV
ejpam-7119	142	2	,	,	PUNCT
ejpam-7119	142	3	the	the	DET
ejpam-7119	142	4	indeterminacy	indeterminacy	NOUN
ejpam-7119	142	5	bound	bind	VERB
ejpam-7119	142	6	ensures	ensure	VERB
ejpam-7119	142	7	that	that	SCONJ
ejpam-7119	142	8	uncertainty	uncertainty	NOUN
ejpam-7119	142	9	decreases	decrease	VERB
ejpam-7119	142	10	:	:	PUNCT
ejpam-7119	142	11	iα(υn+1	iα(υn+1	ADJ
ejpam-7119	142	12	,	,	PUNCT
ejpam-7119	142	13	υn	υn	INTJ
ejpam-7119	142	14	,	,	PUNCT
ejpam-7119	142	15	γ	γ	NOUN
ejpam-7119	142	16	)	)	PUNCT
ejpam-7119	142	17	≤	≤	NOUN
ejpam-7119	142	18	iα(υn	iα(υn	PROPN
ejpam-7119	142	19	,	,	PUNCT
ejpam-7119	142	20	υn−1	υn−1	PROPN
ejpam-7119	142	21	,	,	PUNCT
ejpam-7119	142	22	γ	γ	NOUN
ejpam-7119	142	23	)	)	PUNCT
ejpam-7119	142	24	these	these	DET
ejpam-7119	142	25	conditions	condition	NOUN
ejpam-7119	142	26	guarantee	guarantee	VERB
ejpam-7119	142	27	that	that	SCONJ
ejpam-7119	142	28	the	the	DET
ejpam-7119	142	29	iterative	iterative	NOUN
ejpam-7119	142	30	process	process	NOUN
ejpam-7119	142	31	not	not	PART
ejpam-7119	142	32	only	only	ADV
ejpam-7119	142	33	converges	converge	NOUN
ejpam-7119	142	34	in	in	ADP
ejpam-7119	142	35	the	the	DET
ejpam-7119	142	36	metric	metric	ADJ
ejpam-7119	142	37	sense	sense	NOUN
ejpam-7119	142	38	but	but	CCONJ
ejpam-7119	142	39	also	also	ADV
ejpam-7119	142	40	improves	improve	VERB
ejpam-7119	142	41	the	the	DET
ejpam-7119	142	42	quality	quality	NOUN
ejpam-7119	142	43	of	of	ADP
ejpam-7119	142	44	information	information	NOUN
ejpam-7119	142	45	(	(	PUNCT
ejpam-7119	142	46	increases	increase	VERB
ejpam-7119	142	47	truth	truth	NOUN
ejpam-7119	142	48	,	,	PUNCT
ejpam-7119	142	49	decreases	decrease	VERB
ejpam-7119	142	50	indeterminacy	indeterminacy	NOUN
ejpam-7119	142	51	)	)	PUNCT
ejpam-7119	142	52	at	at	ADP
ejpam-7119	142	53	each	each	DET
ejpam-7119	142	54	step	step	NOUN
ejpam-7119	142	55	.	.	PUNCT
ejpam-7119	143	1	corollary	corollary	ADJ
ejpam-7119	143	2	1	1	NUM
ejpam-7119	143	3	(	(	PUNCT
ejpam-7119	143	4	convergence	convergence	NOUN
ejpam-7119	143	5	rate	rate	NOUN
ejpam-7119	143	6	and	and	CCONJ
ejpam-7119	143	7	error	error	NOUN
ejpam-7119	143	8	estimates	estimate	NOUN
ejpam-7119	143	9	)	)	PUNCT
ejpam-7119	143	10	.	.	PUNCT
ejpam-7119	144	1	the	the	DET
ejpam-7119	144	2	convergence	convergence	NOUN
ejpam-7119	144	3	rate	rate	NOUN
ejpam-7119	144	4	of	of	ADP
ejpam-7119	144	5	the	the	DET
ejpam-7119	144	6	iterative	iterative	NOUN
ejpam-7119	144	7	sequence	sequence	NOUN
ejpam-7119	144	8	satisfies	satisfy	VERB
ejpam-7119	144	9	:	:	PUNCT
ejpam-7119	144	10	(	(	PUNCT
ejpam-7119	144	11	i	i	NOUN
ejpam-7119	144	12	)	)	PUNCT
ejpam-7119	144	13	metric	metric	ADJ
ejpam-7119	144	14	convergence	convergence	NOUN
ejpam-7119	144	15	:	:	PUNCT
ejpam-7119	145	1	mα(υn	mα(υn	ADJ
ejpam-7119	145	2	,	,	PUNCT
ejpam-7119	145	3	υ	υ	NOUN
ejpam-7119	145	4	∗	∗	NOUN
ejpam-7119	145	5	,	,	PUNCT
ejpam-7119	145	6	υ∗	υ∗	NOUN
ejpam-7119	145	7	)	)	PUNCT
ejpam-7119	145	8	≤	≤	NUM
ejpam-7119	145	9	rακnα	rακnα	NOUN
ejpam-7119	145	10	1−κα	1−κα	PROPN
ejpam-7119	145	11	mα(υ1	mα(υ1	NOUN
ejpam-7119	145	12	,	,	PUNCT
ejpam-7119	145	13	υ0	υ0	NOUN
ejpam-7119	145	14	,	,	PUNCT
ejpam-7119	145	15	υ0	υ0	PROPN
ejpam-7119	145	16	)	)	PUNCT
ejpam-7119	145	17	(	(	PUNCT
ejpam-7119	145	18	ii	ii	NOUN
ejpam-7119	145	19	)	)	PUNCT
ejpam-7119	145	20	neutrosophic	neutrosophic	ADJ
ejpam-7119	145	21	convergence	convergence	NOUN
ejpam-7119	145	22	:	:	PUNCT
ejpam-7119	145	23	limn→∞	limn→∞	PROPN
ejpam-7119	145	24	tα(υn	tα(υn	NOUN
ejpam-7119	145	25	,	,	PUNCT
ejpam-7119	145	26	υ∗	υ∗	NOUN
ejpam-7119	145	27	,	,	PUNCT
ejpam-7119	145	28	γ	γ	NOUN
ejpam-7119	145	29	)	)	PUNCT
ejpam-7119	145	30	=	=	SYM
ejpam-7119	145	31	1	1	NUM
ejpam-7119	145	32	for	for	ADP
ejpam-7119	145	33	all	all	DET
ejpam-7119	145	34	γ	γ	X
ejpam-7119	145	35	>	>	X
ejpam-7119	145	36	0	0	PUNCT
ejpam-7119	145	37	(	(	PUNCT
ejpam-7119	145	38	iii	iii	NOUN
ejpam-7119	145	39	)	)	PUNCT
ejpam-7119	145	40	indeterminacy	indeterminacy	NOUN
ejpam-7119	145	41	vanishing	vanish	VERB
ejpam-7119	145	42	:	:	PUNCT
ejpam-7119	145	43	limn→∞	limn→∞	PROPN
ejpam-7119	145	44	iα(υn	iα(υn	PROPN
ejpam-7119	145	45	,	,	PUNCT
ejpam-7119	145	46	υ∗	υ∗	NOUN
ejpam-7119	145	47	,	,	PUNCT
ejpam-7119	145	48	γ	γ	NOUN
ejpam-7119	145	49	)	)	PUNCT
ejpam-7119	145	50	=	=	SYM
ejpam-7119	145	51	0	0	NUM
ejpam-7119	145	52	for	for	ADP
ejpam-7119	145	53	all	all	DET
ejpam-7119	145	54	γ	γ	X
ejpam-7119	145	55	>	>	SYM
ejpam-7119	145	56	0	0	NUM
ejpam-7119	145	57	remark	remark	NOUN
ejpam-7119	145	58	1	1	NUM
ejpam-7119	145	59	(	(	PUNCT
ejpam-7119	145	60	physical	physical	ADJ
ejpam-7119	145	61	interpretation	interpretation	NOUN
ejpam-7119	145	62	for	for	ADP
ejpam-7119	145	63	anomalous	anomalous	ADJ
ejpam-7119	145	64	diffusion	diffusion	NOUN
ejpam-7119	145	65	)	)	PUNCT
ejpam-7119	145	66	.	.	PUNCT
ejpam-7119	146	1	the	the	DET
ejpam-7119	146	2	fractional	fractional	ADJ
ejpam-7119	146	3	parameter	parameter	NOUN
ejpam-7119	146	4	α	α	PROPN
ejpam-7119	146	5	models	model	VERB
ejpam-7119	146	6	anomalous	anomalous	ADJ
ejpam-7119	146	7	diffusion	diffusion	NOUN
ejpam-7119	146	8	processes	process	NOUN
ejpam-7119	146	9	:	:	PUNCT
ejpam-7119	146	10	•	•	NOUN
ejpam-7119	146	11	α	α	NOUN
ejpam-7119	146	12	=	=	SYM
ejpam-7119	146	13	1	1	NUM
ejpam-7119	146	14	:	:	PUNCT
ejpam-7119	146	15	normal	normal	ADJ
ejpam-7119	146	16	diffusion	diffusion	NOUN
ejpam-7119	146	17	(	(	PUNCT
ejpam-7119	146	18	brownian	brownian	ADJ
ejpam-7119	146	19	motion	motion	NOUN
ejpam-7119	146	20	)	)	PUNCT
ejpam-7119	147	1	•	•	ADP
ejpam-7119	147	2	0	0	PUNCT
ejpam-7119	147	3	<	<	X
ejpam-7119	147	4	α	α	X
ejpam-7119	147	5	<	<	X
ejpam-7119	147	6	1	1	NUM
ejpam-7119	147	7	:	:	PUNCT
ejpam-7119	147	8	sub	sub	ADJ
ejpam-7119	147	9	-	-	NOUN
ejpam-7119	147	10	diffusion	diffusion	NOUN
ejpam-7119	147	11	(	(	PUNCT
ejpam-7119	147	12	confined	confine	VERB
ejpam-7119	147	13	motion	motion	NOUN
ejpam-7119	147	14	)	)	PUNCT
ejpam-7119	147	15	•	•	ADP
ejpam-7119	147	16	α	α	X
ejpam-7119	147	17	>	>	X
ejpam-7119	147	18	1	1	NUM
ejpam-7119	147	19	:	:	PUNCT
ejpam-7119	147	20	super	super	ADJ
ejpam-7119	147	21	-	-	NOUN
ejpam-7119	147	22	diffusion	diffusion	NOUN
ejpam-7119	147	23	(	(	PUNCT
ejpam-7119	147	24	enhanced	enhanced	ADJ
ejpam-7119	147	25	transport	transport	NOUN
ejpam-7119	147	26	)	)	PUNCT
ejpam-7119	147	27	the	the	DET
ejpam-7119	147	28	fixed	fix	VERB
ejpam-7119	147	29	point	point	NOUN
ejpam-7119	147	30	represents	represent	VERB
ejpam-7119	147	31	the	the	DET
ejpam-7119	147	32	asymptotic	asymptotic	ADJ
ejpam-7119	147	33	state	state	NOUN
ejpam-7119	147	34	of	of	ADP
ejpam-7119	147	35	the	the	DET
ejpam-7119	147	36	diffusion	diffusion	NOUN
ejpam-7119	147	37	process	process	NOUN
ejpam-7119	147	38	,	,	PUNCT
ejpam-7119	147	39	with	with	ADP
ejpam-7119	147	40	the	the	DET
ejpam-7119	147	41	convergence	convergence	NOUN
ejpam-7119	147	42	rate	rate	NOUN
ejpam-7119	147	43	determined	determine	VERB
ejpam-7119	147	44	by	by	ADP
ejpam-7119	147	45	α	α	PROPN
ejpam-7119	147	46	and	and	CCONJ
ejpam-7119	147	47	κ	κ	NOUN
ejpam-7119	147	48	.	.	NOUN
ejpam-7119	147	49	3	3	X
ejpam-7119	147	50	.	.	PUNCT
ejpam-7119	147	51	examples	example	NOUN
ejpam-7119	147	52	and	and	CCONJ
ejpam-7119	147	53	applications	application	NOUN
ejpam-7119	147	54	the	the	DET
ejpam-7119	147	55	development	development	NOUN
ejpam-7119	147	56	of	of	ADP
ejpam-7119	147	57	fractional	fractional	ADJ
ejpam-7119	147	58	-	-	PUNCT
ejpam-7119	147	59	order	order	NOUN
ejpam-7119	147	60	neutrosophic	neutrosophic	ADJ
ejpam-7119	147	61	mr	mr	PROPN
ejpam-7119	147	62	-	-	PUNCT
ejpam-7119	147	63	metric	metric	ADJ
ejpam-7119	147	64	spaces	space	NOUN
ejpam-7119	147	65	is	be	AUX
ejpam-7119	147	66	motivated	motivate	VERB
ejpam-7119	147	67	by	by	ADP
ejpam-7119	147	68	both	both	DET
ejpam-7119	147	69	theoretical	theoretical	ADJ
ejpam-7119	147	70	considerations	consideration	NOUN
ejpam-7119	147	71	and	and	CCONJ
ejpam-7119	147	72	practical	practical	ADJ
ejpam-7119	147	73	applications	application	NOUN
ejpam-7119	147	74	across	across	ADP
ejpam-7119	147	75	multiple	multiple	ADJ
ejpam-7119	147	76	disciplines	discipline	NOUN
ejpam-7119	147	77	.	.	PUNCT
ejpam-7119	148	1	from	from	ADP
ejpam-7119	148	2	a	a	DET
ejpam-7119	148	3	theoretical	theoretical	ADJ
ejpam-7119	148	4	perspective	perspective	NOUN
ejpam-7119	148	5	,	,	PUNCT
ejpam-7119	148	6	this	this	DET
ejpam-7119	148	7	framework	framework	NOUN
ejpam-7119	148	8	represents	represent	VERB
ejpam-7119	148	9	a	a	DET
ejpam-7119	148	10	natural	natural	ADJ
ejpam-7119	148	11	unification	unification	NOUN
ejpam-7119	148	12	of	of	ADP
ejpam-7119	148	13	three	three	NUM
ejpam-7119	148	14	powerful	powerful	ADJ
ejpam-7119	148	15	mathematical	mathematical	ADJ
ejpam-7119	148	16	paradigms	paradigm	NOUN
ejpam-7119	148	17	:	:	PUNCT
ejpam-7119	148	18	metric	metric	ADJ
ejpam-7119	148	19	space	space	NOUN
ejpam-7119	148	20	theory	theory	NOUN
ejpam-7119	148	21	for	for	ADP
ejpam-7119	148	22	distance	distance	NOUN
ejpam-7119	148	23	measurement	measurement	NOUN
ejpam-7119	148	24	,	,	PUNCT
ejpam-7119	148	25	fractional	fractional	ADJ
ejpam-7119	148	26	calculus	calculus	NOUN
ejpam-7119	148	27	for	for	ADP
ejpam-7119	148	28	capturing	capture	VERB
ejpam-7119	148	29	non	non	ADJ
ejpam-7119	148	30	-	-	ADJ
ejpam-7119	148	31	local	local	ADJ
ejpam-7119	148	32	dynamics	dynamic	NOUN
ejpam-7119	148	33	and	and	CCONJ
ejpam-7119	148	34	memory	memory	NOUN
ejpam-7119	148	35	effects	effect	NOUN
ejpam-7119	148	36	,	,	PUNCT
ejpam-7119	148	37	and	and	CCONJ
ejpam-7119	148	38	neutrosophic	neutrosophic	ADJ
ejpam-7119	148	39	logic	logic	NOUN
ejpam-7119	148	40	for	for	ADP
ejpam-7119	148	41	handling	handle	VERB
ejpam-7119	148	42	uncertainty	uncertainty	NOUN
ejpam-7119	148	43	,	,	PUNCT
ejpam-7119	148	44	indeterminacy	indeterminacy	NOUN
ejpam-7119	148	45	,	,	PUNCT
ejpam-7119	148	46	and	and	CCONJ
ejpam-7119	148	47	inconsistency	inconsistency	NOUN
ejpam-7119	148	48	in	in	ADP
ejpam-7119	148	49	complex	complex	ADJ
ejpam-7119	148	50	systems	system	NOUN
ejpam-7119	148	51	.	.	PUNCT
ejpam-7119	149	1	from	from	ADP
ejpam-7119	149	2	an	an	DET
ejpam-7119	149	3	applied	applied	ADJ
ejpam-7119	149	4	viewpoint	viewpoint	NOUN
ejpam-7119	149	5	,	,	PUNCT
ejpam-7119	149	6	numerous	numerous	ADJ
ejpam-7119	149	7	real	real	ADJ
ejpam-7119	149	8	-	-	PUNCT
ejpam-7119	149	9	world	world	NOUN
ejpam-7119	149	10	phenomena	phenomena	NOUN
ejpam-7119	149	11	exhibit	exhibit	VERB
ejpam-7119	149	12	characteristics	characteristic	NOUN
ejpam-7119	149	13	that	that	SCONJ
ejpam-7119	149	14	necessitate	necessitate	ADJ
ejpam-7119	149	15	such	such	DET
ejpam-7119	149	16	an	an	DET
ejpam-7119	149	17	integrated	integrated	ADJ
ejpam-7119	149	18	approach	approach	NOUN
ejpam-7119	149	19	.	.	PUNCT
ejpam-7119	150	1	anomalous	anomalous	ADJ
ejpam-7119	150	2	diffusion	diffusion	NOUN
ejpam-7119	150	3	processes	process	NOUN
ejpam-7119	150	4	in	in	ADP
ejpam-7119	150	5	physics	physics	NOUN
ejpam-7119	150	6	and	and	CCONJ
ejpam-7119	150	7	biology	biology	NOUN
ejpam-7119	150	8	display	display	VERB
ejpam-7119	150	9	fractional	fractional	ADJ
ejpam-7119	150	10	dynamics	dynamic	NOUN
ejpam-7119	150	11	that	that	PRON
ejpam-7119	150	12	can	can	AUX
ejpam-7119	150	13	not	not	PART
ejpam-7119	150	14	be	be	AUX
ejpam-7119	150	15	adequately	adequately	ADV
ejpam-7119	150	16	described	describe	VERB
ejpam-7119	150	17	by	by	ADP
ejpam-7119	150	18	classical	classical	ADJ
ejpam-7119	150	19	models	model	NOUN
ejpam-7119	150	20	[	[	X
ejpam-7119	150	21	17	17	NUM
ejpam-7119	150	22	]	]	PUNCT
ejpam-7119	150	23	.	.	PUNCT
ejpam-7119	151	1	image	image	NOUN
ejpam-7119	151	2	processing	processing	NOUN
ejpam-7119	151	3	and	and	CCONJ
ejpam-7119	151	4	computer	computer	NOUN
ejpam-7119	151	5	vision	vision	NOUN
ejpam-7119	151	6	applications	application	NOUN
ejpam-7119	151	7	require	require	VERB
ejpam-7119	151	8	robust	robust	ADJ
ejpam-7119	151	9	frameworks	framework	NOUN
ejpam-7119	151	10	for	for	ADP
ejpam-7119	151	11	handling	handle	VERB
ejpam-7119	151	12	uncertainty	uncertainty	NOUN
ejpam-7119	151	13	in	in	ADP
ejpam-7119	151	14	denoising	denoise	VERB
ejpam-7119	151	15	and	and	CCONJ
ejpam-7119	151	16	inpainting	inpainte	VERB
ejpam-7119	151	17	tasks	task	NOUN
ejpam-7119	151	18	.	.	PUNCT
ejpam-7119	152	1	machine	machine	NOUN
ejpam-7119	152	2	learning	learn	VERB
ejpam-7119	152	3	algorithms	algorithm	NOUN
ejpam-7119	152	4	operating	operate	VERB
ejpam-7119	152	5	in	in	ADP
ejpam-7119	152	6	uncertain	uncertain	ADJ
ejpam-7119	152	7	environments	environment	NOUN
ejpam-7119	152	8	benefit	benefit	VERB
ejpam-7119	152	9	from	from	ADP
ejpam-7119	152	10	neutrosophic	neutrosophic	ADJ
ejpam-7119	152	11	approaches	approach	NOUN
ejpam-7119	152	12	to	to	PART
ejpam-7119	152	13	cluster	cluster	VERB
ejpam-7119	152	14	analysis	analysis	NOUN
ejpam-7119	152	15	and	and	CCONJ
ejpam-7119	152	16	pattern	pattern	NOUN
ejpam-7119	152	17	recognition	recognition	NOUN
ejpam-7119	153	1	[	[	X
ejpam-7119	153	2	14	14	NUM
ejpam-7119	153	3	,	,	PUNCT
ejpam-7119	153	4	15	15	NUM
ejpam-7119	153	5	]	]	PUNCT
ejpam-7119	153	6	.	.	PUNCT
ejpam-7119	154	1	the	the	DET
ejpam-7119	154	2	following	follow	VERB
ejpam-7119	154	3	examples	example	NOUN
ejpam-7119	154	4	and	and	CCONJ
ejpam-7119	154	5	applications	application	NOUN
ejpam-7119	154	6	demonstrate	demonstrate	VERB
ejpam-7119	154	7	how	how	SCONJ
ejpam-7119	154	8	our	our	PRON
ejpam-7119	154	9	fonmr	fonmr	ADJ
ejpam-7119	154	10	-	-	PUNCT
ejpam-7119	154	11	ms	ms	NOUN
ejpam-7119	154	12	framework	framework	NOUN
ejpam-7119	154	13	provides	provide	VERB
ejpam-7119	154	14	sophisticated	sophisticated	ADJ
ejpam-7119	154	15	mathematical	mathematical	ADJ
ejpam-7119	154	16	tools	tool	NOUN
ejpam-7119	154	17	for	for	ADP
ejpam-7119	154	18	addressing	address	VERB
ejpam-7119	154	19	these	these	DET
ejpam-7119	154	20	challenges	challenge	NOUN
ejpam-7119	154	21	.	.	PUNCT
ejpam-7119	155	1	we	we	PRON
ejpam-7119	155	2	begin	begin	VERB
ejpam-7119	155	3	with	with	ADP
ejpam-7119	155	4	a	a	DET
ejpam-7119	155	5	concrete	concrete	ADJ
ejpam-7119	155	6	example	example	NOUN
ejpam-7119	155	7	illustrating	illustrate	VERB
ejpam-7119	155	8	the	the	DET
ejpam-7119	155	9	construction	construction	NOUN
ejpam-7119	155	10	of	of	ADP
ejpam-7119	155	11	a	a	DET
ejpam-7119	155	12	fonmr	fonmr	NOUN
ejpam-7119	155	13	-	-	PUNCT
ejpam-7119	155	14	ms	ms	NOUN
ejpam-7119	155	15	on	on	ADP
ejpam-7119	155	16	a	a	DET
ejpam-7119	155	17	function	function	NOUN
ejpam-7119	155	18	space	space	NOUN
ejpam-7119	155	19	,	,	PUNCT
ejpam-7119	155	20	followed	follow	VERB
ejpam-7119	155	21	by	by	ADP
ejpam-7119	155	22	detailed	detailed	ADJ
ejpam-7119	155	23	applications	application	NOUN
ejpam-7119	155	24	in	in	ADP
ejpam-7119	155	25	anomalous	anomalous	ADJ
ejpam-7119	155	26	diffusion	diffusion	NOUN
ejpam-7119	155	27	modeling	modeling	NOUN
ejpam-7119	155	28	,	,	PUNCT
ejpam-7119	155	29	image	image	NOUN
ejpam-7119	155	30	processing	processing	NOUN
ejpam-7119	155	31	,	,	PUNCT
ejpam-7119	155	32	and	and	CCONJ
ejpam-7119	155	33	machine	machine	NOUN
ejpam-7119	155	34	learning	learn	VERB
ejpam-7119	155	35	under	under	ADP
ejpam-7119	155	36	uncertainty	uncertainty	NOUN
ejpam-7119	155	37	.	.	PUNCT
ejpam-7119	156	1	each	each	DET
ejpam-7119	156	2	application	application	NOUN
ejpam-7119	156	3	highlights	highlight	VERB
ejpam-7119	156	4	different	different	ADJ
ejpam-7119	156	5	aspects	aspect	NOUN
ejpam-7119	156	6	of	of	ADP
ejpam-7119	156	7	our	our	PRON
ejpam-7119	156	8	theoretical	theoretical	ADJ
ejpam-7119	156	9	framework	framework	NOUN
ejpam-7119	156	10	and	and	CCONJ
ejpam-7119	156	11	demonstrates	demonstrate	VERB
ejpam-7119	156	12	its	its	PRON
ejpam-7119	156	13	practical	practical	ADJ
ejpam-7119	156	14	utility	utility	NOUN
ejpam-7119	156	15	in	in	ADP
ejpam-7119	156	16	solving	solve	VERB
ejpam-7119	156	17	complex	complex	ADJ
ejpam-7119	156	18	problems	problem	NOUN
ejpam-7119	156	19	across	across	ADP
ejpam-7119	156	20	diverse	diverse	ADJ
ejpam-7119	156	21	domains	domain	NOUN
ejpam-7119	156	22	.	.	PUNCT
ejpam-7119	157	1	a.	a.	PROPN
ejpam-7119	157	2	malkawi	malkawi	PROPN
ejpam-7119	157	3	,	,	PUNCT
ejpam-7119	157	4	a.	a.	PROPN
ejpam-7119	157	5	rabaiah	rabaiah	PROPN
ejpam-7119	157	6	/	/	SYM
ejpam-7119	157	7	eur	eur	PROPN
ejpam-7119	157	8	.	.	PUNCT
ejpam-7119	158	1	j.	j.	PROPN
ejpam-7119	158	2	pure	pure	PROPN
ejpam-7119	158	3	appl	appl	PROPN
ejpam-7119	158	4	.	.	PROPN
ejpam-7119	158	5	math	math	PROPN
ejpam-7119	158	6	,	,	PUNCT
ejpam-7119	158	7	18	18	NUM
ejpam-7119	158	8	(	(	PUNCT
ejpam-7119	158	9	4	4	NUM
ejpam-7119	158	10	)	)	PUNCT
ejpam-7119	158	11	(	(	PUNCT
ejpam-7119	158	12	2025	2025	NUM
ejpam-7119	158	13	)	)	PUNCT
ejpam-7119	158	14	,	,	PUNCT
ejpam-7119	158	15	7119	7119	NUM
ejpam-7119	158	16	8	8	NUM
ejpam-7119	158	17	of	of	ADP
ejpam-7119	158	18	13	13	NUM
ejpam-7119	158	19	3.1	3.1	NUM
ejpam-7119	158	20	.	.	PUNCT
ejpam-7119	159	1	illustrative	illustrative	ADJ
ejpam-7119	159	2	example	example	NOUN
ejpam-7119	159	3	:	:	PUNCT
ejpam-7119	159	4	a	a	DET
ejpam-7119	159	5	fonmr	fonmr	NOUN
ejpam-7119	159	6	-	-	PUNCT
ejpam-7119	159	7	ms	ms	NOUN
ejpam-7119	159	8	on	on	ADP
ejpam-7119	159	9	a	a	DET
ejpam-7119	159	10	function	function	NOUN
ejpam-7119	159	11	space	space	NOUN
ejpam-7119	159	12	let	let	VERB
ejpam-7119	159	13	us	we	PRON
ejpam-7119	159	14	construct	construct	VERB
ejpam-7119	159	15	a	a	DET
ejpam-7119	159	16	concrete	concrete	ADJ
ejpam-7119	159	17	example	example	NOUN
ejpam-7119	159	18	of	of	ADP
ejpam-7119	159	19	a	a	DET
ejpam-7119	159	20	fonmr	fonmr	ADJ
ejpam-7119	159	21	-	-	PUNCT
ejpam-7119	159	22	ms	ms	PROPN
ejpam-7119	159	23	.	.	PROPN
ejpam-7119	159	24	example	example	NOUN
ejpam-7119	160	1	1	1	NUM
ejpam-7119	160	2	.	.	PUNCT
ejpam-7119	161	1	let	let	AUX
ejpam-7119	161	2	z	z	NOUN
ejpam-7119	161	3	=	=	SYM
ejpam-7119	161	4	c([0	c([0	PROPN
ejpam-7119	161	5	,	,	PUNCT
ejpam-7119	161	6	1],r	1],r	NUM
ejpam-7119	161	7	)	)	PUNCT
ejpam-7119	161	8	be	be	VERB
ejpam-7119	161	9	the	the	DET
ejpam-7119	161	10	space	space	NOUN
ejpam-7119	161	11	of	of	ADP
ejpam-7119	161	12	continuous	continuous	ADJ
ejpam-7119	161	13	real	real	ADV
ejpam-7119	161	14	-	-	PUNCT
ejpam-7119	161	15	valued	value	VERB
ejpam-7119	161	16	functions	function	NOUN
ejpam-7119	161	17	on	on	ADP
ejpam-7119	161	18	[	[	X
ejpam-7119	161	19	0	0	NUM
ejpam-7119	161	20	,	,	PUNCT
ejpam-7119	161	21	1	1	NUM
ejpam-7119	161	22	]	]	PUNCT
ejpam-7119	161	23	.	.	PUNCT
ejpam-7119	162	1	we	we	PRON
ejpam-7119	162	2	define	define	VERB
ejpam-7119	162	3	the	the	DET
ejpam-7119	162	4	following	following	NOUN
ejpam-7119	162	5	:	:	PUNCT
ejpam-7119	162	6	(	(	PUNCT
ejpam-7119	162	7	i	i	NOUN
ejpam-7119	162	8	)	)	PUNCT
ejpam-7119	162	9	base	base	PROPN
ejpam-7119	162	10	mr	mr	PROPN
ejpam-7119	162	11	-	-	NOUN
ejpam-7119	162	12	metric	metric	NOUN
ejpam-7119	162	13	:	:	PUNCT
ejpam-7119	162	14	for	for	ADP
ejpam-7119	162	15	f	f	PROPN
ejpam-7119	162	16	,	,	PUNCT
ejpam-7119	162	17	g	g	PROPN
ejpam-7119	162	18	,	,	PUNCT
ejpam-7119	163	1	h	h	NOUN
ejpam-7119	163	2	∈	∈	PROPN
ejpam-7119	163	3	z	z	NOUN
ejpam-7119	163	4	,	,	PUNCT
ejpam-7119	163	5	define	define	VERB
ejpam-7119	163	6	m(f	m(f	PROPN
ejpam-7119	163	7	,	,	PUNCT
ejpam-7119	163	8	g	g	PROPN
ejpam-7119	163	9	,	,	PUNCT
ejpam-7119	163	10	h	h	NOUN
ejpam-7119	163	11	)	)	PUNCT
ejpam-7119	163	12	=	=	NOUN
ejpam-7119	163	13	sup	sup	NOUN
ejpam-7119	163	14	x∈[0,1	x∈[0,1	PROPN
ejpam-7119	163	15	]	]	PUNCT
ejpam-7119	164	1	|f(x)−	|f(x)−	NOUN
ejpam-7119	164	2	g(x)|+	g(x)|+	PROPN
ejpam-7119	164	3	sup	sup	PROPN
ejpam-7119	164	4	x∈[0,1	x∈[0,1	PROPN
ejpam-7119	164	5	]	]	PUNCT
ejpam-7119	164	6	|g(x)−	|g(x)−	NOUN
ejpam-7119	164	7	h(x)|+	h(x)|+	PROPN
ejpam-7119	164	8	sup	sup	NOUN
ejpam-7119	164	9	x∈[0,1	x∈[0,1	ADP
ejpam-7119	164	10	]	]	PUNCT
ejpam-7119	164	11	|h(x)−	|h(x)−	ADJ
ejpam-7119	164	12	f(x)|	f(x)|	VERB
ejpam-7119	164	13	.	.	PUNCT
ejpam-7119	165	1	it	it	PRON
ejpam-7119	165	2	can	can	AUX
ejpam-7119	165	3	be	be	AUX
ejpam-7119	165	4	verified	verify	VERB
ejpam-7119	165	5	that	that	SCONJ
ejpam-7119	165	6	m	m	PROPN
ejpam-7119	165	7	is	be	AUX
ejpam-7119	165	8	an	an	DET
ejpam-7119	165	9	mr	mr	NOUN
ejpam-7119	165	10	-	-	PUNCT
ejpam-7119	165	11	metric	metric	NOUN
ejpam-7119	165	12	with	with	ADP
ejpam-7119	165	13	r	r	NOUN
ejpam-7119	165	14	=	=	SYM
ejpam-7119	165	15	2	2	NUM
ejpam-7119	165	16	.	.	PUNCT
ejpam-7119	165	17	(	(	PUNCT
ejpam-7119	165	18	ii	ii	NOUN
ejpam-7119	165	19	)	)	PUNCT
ejpam-7119	165	20	neutrosophic	neutrosophic	ADJ
ejpam-7119	165	21	functions	function	NOUN
ejpam-7119	165	22	:	:	PUNCT
ejpam-7119	165	23	for	for	ADP
ejpam-7119	165	24	γ	γ	X
ejpam-7119	165	25	>	>	X
ejpam-7119	165	26	0	0	NUM
ejpam-7119	165	27	,	,	PUNCT
ejpam-7119	165	28	define	define	VERB
ejpam-7119	165	29	t	t	PROPN
ejpam-7119	165	30	(	(	PUNCT
ejpam-7119	165	31	f	f	X
ejpam-7119	165	32	,	,	PUNCT
ejpam-7119	165	33	g	g	PROPN
ejpam-7119	165	34	,	,	PUNCT
ejpam-7119	165	35	γ	γ	NOUN
ejpam-7119	165	36	)	)	PUNCT
ejpam-7119	165	37	=	=	SYM
ejpam-7119	165	38	e	e	NOUN
ejpam-7119	165	39	−m(f	−m(f	PROPN
ejpam-7119	165	40	,	,	PUNCT
ejpam-7119	165	41	g	g	NOUN
ejpam-7119	165	42	,	,	PUNCT
ejpam-7119	165	43	g	g	NOUN
ejpam-7119	165	44	)	)	PUNCT
ejpam-7119	165	45	γ	γ	NOUN
ejpam-7119	165	46	,	,	PUNCT
ejpam-7119	165	47	i(f	i(f	PROPN
ejpam-7119	165	48	,	,	PUNCT
ejpam-7119	165	49	g	g	PROPN
ejpam-7119	165	50	,	,	PUNCT
ejpam-7119	165	51	γ	γ	NOUN
ejpam-7119	165	52	)	)	PUNCT
ejpam-7119	165	53	=	=	SYM
ejpam-7119	165	54	1	1	NUM
ejpam-7119	165	55	2	2	NUM
ejpam-7119	165	56	e	e	NOUN
ejpam-7119	165	57	−m(f	−m(f	PROPN
ejpam-7119	165	58	,	,	PUNCT
ejpam-7119	165	59	g	g	NOUN
ejpam-7119	165	60	,	,	PUNCT
ejpam-7119	165	61	g	g	NOUN
ejpam-7119	165	62	)	)	PUNCT
ejpam-7119	165	63	γ	γ	NOUN
ejpam-7119	165	64	,	,	PUNCT
ejpam-7119	165	65	f(f	f(f	PROPN
ejpam-7119	165	66	,	,	PUNCT
ejpam-7119	165	67	g	g	PROPN
ejpam-7119	165	68	,	,	PUNCT
ejpam-7119	165	69	γ	γ	NOUN
ejpam-7119	165	70	)	)	PUNCT
ejpam-7119	165	71	=	=	SYM
ejpam-7119	165	72	1−	1−	NUM
ejpam-7119	165	73	t	t	NOUN
ejpam-7119	165	74	(	(	PUNCT
ejpam-7119	165	75	f	f	X
ejpam-7119	165	76	,	,	PUNCT
ejpam-7119	165	77	g	g	PROPN
ejpam-7119	165	78	,	,	PUNCT
ejpam-7119	165	79	γ)−	γ)−	PROPN
ejpam-7119	166	1	i(f	i(f	PROPN
ejpam-7119	166	2	,	,	PUNCT
ejpam-7119	166	3	g	g	NOUN
ejpam-7119	166	4	,	,	PUNCT
ejpam-7119	166	5	γ	γ	NOUN
ejpam-7119	166	6	)	)	PUNCT
ejpam-7119	166	7	.	.	PUNCT
ejpam-7119	167	1	here	here	ADV
ejpam-7119	167	2	,	,	PUNCT
ejpam-7119	167	3	•	•	NUM
ejpam-7119	167	4	is	be	AUX
ejpam-7119	167	5	the	the	DET
ejpam-7119	167	6	product	product	NOUN
ejpam-7119	167	7	t	t	NOUN
ejpam-7119	167	8	-	-	PUNCT
ejpam-7119	167	9	norm	norm	NOUN
ejpam-7119	167	10	(	(	PUNCT
ejpam-7119	167	11	a	a	DET
ejpam-7119	167	12	•	•	NOUN
ejpam-7119	167	13	b	b	NOUN
ejpam-7119	167	14	=	=	SYM
ejpam-7119	167	15	ab	ab	PROPN
ejpam-7119	167	16	)	)	PUNCT
ejpam-7119	167	17	,	,	PUNCT
ejpam-7119	167	18	and	and	CCONJ
ejpam-7119	167	19	⋄	⋄	PROPN
ejpam-7119	167	20	is	be	AUX
ejpam-7119	167	21	the	the	DET
ejpam-7119	167	22	probabilistic	probabilistic	ADJ
ejpam-7119	167	23	sum	sum	NOUN
ejpam-7119	167	24	t	t	NOUN
ejpam-7119	167	25	-	-	PUNCT
ejpam-7119	167	26	conorm	conorm	NOUN
ejpam-7119	167	27	(	(	PUNCT
ejpam-7119	167	28	a	a	DET
ejpam-7119	167	29	⋄	⋄	PROPN
ejpam-7119	167	30	b	b	NOUN
ejpam-7119	167	31	=	=	SYM
ejpam-7119	167	32	a+	a+	PUNCT
ejpam-7119	167	33	b−	b−	PROPN
ejpam-7119	167	34	ab	ab	PROPN
ejpam-7119	167	35	)	)	PUNCT
ejpam-7119	167	36	.	.	PUNCT
ejpam-7119	168	1	the	the	DET
ejpam-7119	168	2	operation	operation	NOUN
ejpam-7119	168	3	⋆	⋆	NOUN
ejpam-7119	168	4	is	be	AUX
ejpam-7119	168	5	standard	standard	ADJ
ejpam-7119	168	6	addition	addition	NOUN
ejpam-7119	168	7	.	.	PUNCT
ejpam-7119	169	1	(	(	PUNCT
ejpam-7119	169	2	iii	iii	X
ejpam-7119	169	3	)	)	PUNCT
ejpam-7119	169	4	fractional	fractional	ADJ
ejpam-7119	169	5	-	-	PUNCT
ejpam-7119	169	6	order	order	NOUN
ejpam-7119	169	7	construction	construction	NOUN
ejpam-7119	169	8	:	:	PUNCT
ejpam-7119	169	9	for	for	ADP
ejpam-7119	169	10	α	α	PROPN
ejpam-7119	169	11	>	>	X
ejpam-7119	169	12	0	0	PROPN
ejpam-7119	169	13	,	,	PUNCT
ejpam-7119	169	14	we	we	PRON
ejpam-7119	169	15	construct	construct	VERB
ejpam-7119	169	16	the	the	DET
ejpam-7119	169	17	fonmr	fonmr	NOUN
ejpam-7119	169	18	-	-	PUNCT
ejpam-7119	169	19	ms	ms	NOUN
ejpam-7119	169	20	(	(	PUNCT
ejpam-7119	169	21	z	z	PROPN
ejpam-7119	169	22	,	,	PUNCT
ejpam-7119	169	23	mα	mα	PROPN
ejpam-7119	169	24	,	,	PUNCT
ejpam-7119	169	25	tα	tα	PROPN
ejpam-7119	169	26	,	,	PUNCT
ejpam-7119	169	27	fα	fα	NOUN
ejpam-7119	169	28	,	,	PUNCT
ejpam-7119	169	29	iα	iα	NOUN
ejpam-7119	169	30	,	,	PUNCT
ejpam-7119	169	31	•	•	PROPN
ejpam-7119	169	32	,	,	PUNCT
ejpam-7119	169	33	⋄	⋄	PROPN
ejpam-7119	169	34	,	,	PUNCT
ejpam-7119	169	35	rα	rα	INTJ
ejpam-7119	169	36	,	,	PUNCT
ejpam-7119	169	37	⋆α	⋆α	NOUN
ejpam-7119	169	38	)	)	PUNCT
ejpam-7119	169	39	as	as	SCONJ
ejpam-7119	169	40	defined	define	VERB
ejpam-7119	169	41	in	in	ADP
ejpam-7119	169	42	definition	definition	NOUN
ejpam-7119	169	43	2.4	2.4	NUM
ejpam-7119	169	44	.	.	PUNCT
ejpam-7119	170	1	for	for	ADP
ejpam-7119	170	2	instance	instance	NOUN
ejpam-7119	170	3	,	,	PUNCT
ejpam-7119	170	4	the	the	DET
ejpam-7119	170	5	fractional	fractional	ADJ
ejpam-7119	170	6	metric	metric	NOUN
ejpam-7119	170	7	becomes	become	NOUN
ejpam-7119	170	8	:	:	PUNCT
ejpam-7119	170	9	mα(f	mα(f	ADJ
ejpam-7119	170	10	,	,	PUNCT
ejpam-7119	170	11	g	g	PROPN
ejpam-7119	170	12	,	,	PUNCT
ejpam-7119	170	13	h	h	NOUN
ejpam-7119	170	14	)	)	PUNCT
ejpam-7119	170	15	=	=	SYM
ejpam-7119	170	16	(	(	PUNCT
ejpam-7119	170	17	1	1	NUM
ejpam-7119	170	18	γ(α	γ(α	NOUN
ejpam-7119	170	19	)	)	PUNCT
ejpam-7119	170	20	∫	∫	PROPN
ejpam-7119	171	1	∞	∞	PROPN
ejpam-7119	171	2	0	0	PUNCT
ejpam-7119	171	3	τα−1e−τm(f	τα−1e−τm(f	PROPN
ejpam-7119	171	4	,	,	PUNCT
ejpam-7119	171	5	g	g	NOUN
ejpam-7119	171	6	,	,	PUNCT
ejpam-7119	171	7	hτ	hτ	NOUN
ejpam-7119	171	8	)	)	PUNCT
ejpam-7119	171	9	dτ	dτ	NOUN
ejpam-7119	171	10	)	)	PUNCT
ejpam-7119	171	11	1	1	NUM
ejpam-7119	171	12	/	/	SYM
ejpam-7119	171	13	α	α	NOUN
ejpam-7119	171	14	,	,	PUNCT
ejpam-7119	171	15	where	where	SCONJ
ejpam-7119	171	16	hτ	hτ	PRON
ejpam-7119	171	17	is	be	VERB
ejpam-7119	171	18	a	a	DET
ejpam-7119	171	19	geodesic	geodesic	ADJ
ejpam-7119	171	20	interpolation	interpolation	NOUN
ejpam-7119	171	21	.	.	PUNCT
ejpam-7119	172	1	a	a	DET
ejpam-7119	172	2	simple	simple	ADJ
ejpam-7119	172	3	linear	linear	ADJ
ejpam-7119	172	4	geodesic	geodesic	NOUN
ejpam-7119	172	5	can	can	AUX
ejpam-7119	172	6	be	be	AUX
ejpam-7119	172	7	defined	define	VERB
ejpam-7119	172	8	as	as	ADP
ejpam-7119	172	9	hτ	hτ	NOUN
ejpam-7119	172	10	(	(	PUNCT
ejpam-7119	172	11	x	x	NOUN
ejpam-7119	172	12	)	)	PUNCT
ejpam-7119	172	13	=	=	SYM
ejpam-7119	172	14	(	(	PUNCT
ejpam-7119	172	15	1−	1−	NUM
ejpam-7119	172	16	λ(τ))f(x	λ(τ))f(x	PROPN
ejpam-7119	172	17	)	)	PUNCT
ejpam-7119	173	1	+	+	SYM
ejpam-7119	173	2	λ(τ)h(x	λ(τ)h(x	NOUN
ejpam-7119	173	3	)	)	PUNCT
ejpam-7119	173	4	,	,	PUNCT
ejpam-7119	173	5	with	with	ADP
ejpam-7119	173	6	λ(τ	λ(τ	NOUN
ejpam-7119	173	7	)	)	PUNCT
ejpam-7119	174	1	=	=	SYM
ejpam-7119	174	2	τ	τ	PROPN
ejpam-7119	174	3	1+τ	1+τ	NUM
ejpam-7119	174	4	.	.	PUNCT
ejpam-7119	175	1	this	this	DET
ejpam-7119	175	2	structure	structure	NOUN
ejpam-7119	175	3	(	(	PUNCT
ejpam-7119	175	4	z	z	NOUN
ejpam-7119	175	5	,	,	PUNCT
ejpam-7119	175	6	mα	mα	PROPN
ejpam-7119	175	7	,	,	PUNCT
ejpam-7119	175	8	tα	tα	PROPN
ejpam-7119	175	9	,	,	PUNCT
ejpam-7119	175	10	fα	fα	NOUN
ejpam-7119	175	11	,	,	PUNCT
ejpam-7119	175	12	iα	iα	NOUN
ejpam-7119	175	13	,	,	PUNCT
ejpam-7119	175	14	•	•	PROPN
ejpam-7119	175	15	,	,	PUNCT
ejpam-7119	175	16	⋄	⋄	PROPN
ejpam-7119	175	17	,	,	PUNCT
ejpam-7119	175	18	rα	rα	INTJ
ejpam-7119	175	19	,	,	PUNCT
ejpam-7119	175	20	⋆α	⋆α	NOUN
ejpam-7119	175	21	)	)	PUNCT
ejpam-7119	175	22	forms	form	VERB
ejpam-7119	175	23	a	a	DET
ejpam-7119	175	24	complete	complete	ADJ
ejpam-7119	175	25	fonmr	fonmr	ADJ
ejpam-7119	175	26	-	-	PUNCT
ejpam-7119	175	27	ms	ms	NOUN
ejpam-7119	175	28	.	.	PROPN
ejpam-7119	175	29	3.2	3.2	NUM
ejpam-7119	175	30	.	.	PUNCT
ejpam-7119	176	1	application	application	NOUN
ejpam-7119	176	2	1	1	NUM
ejpam-7119	176	3	:	:	PUNCT
ejpam-7119	176	4	anomalous	anomalous	ADJ
ejpam-7119	176	5	diffusion	diffusion	NOUN
ejpam-7119	176	6	process	process	NOUN
ejpam-7119	176	7	modeling	modeling	NOUN
ejpam-7119	176	8	as	as	SCONJ
ejpam-7119	176	9	highlighted	highlight	VERB
ejpam-7119	176	10	in	in	ADP
ejpam-7119	176	11	remark	remark	NOUN
ejpam-7119	176	12	2.1	2.1	NUM
ejpam-7119	176	13	,	,	PUNCT
ejpam-7119	176	14	the	the	DET
ejpam-7119	176	15	parameter	parameter	NOUN
ejpam-7119	176	16	α	α	PROPN
ejpam-7119	176	17	models	model	VERB
ejpam-7119	176	18	different	different	ADJ
ejpam-7119	176	19	diffusion	diffusion	NOUN
ejpam-7119	176	20	regimes	regime	NOUN
ejpam-7119	176	21	.	.	PUNCT
ejpam-7119	177	1	the	the	DET
ejpam-7119	177	2	fixed	fix	VERB
ejpam-7119	177	3	point	point	NOUN
ejpam-7119	177	4	theorem	theorem	NOUN
ejpam-7119	177	5	(	(	PUNCT
ejpam-7119	177	6	theorem	theorem	NOUN
ejpam-7119	177	7	2.3	2.3	NUM
ejpam-7119	177	8	)	)	PUNCT
ejpam-7119	177	9	can	can	AUX
ejpam-7119	177	10	model	model	VERB
ejpam-7119	177	11	the	the	DET
ejpam-7119	177	12	steady	steady	ADJ
ejpam-7119	177	13	-	-	PUNCT
ejpam-7119	177	14	state	state	NOUN
ejpam-7119	177	15	distribution	distribution	NOUN
ejpam-7119	177	16	of	of	ADP
ejpam-7119	177	17	particles	particle	NOUN
ejpam-7119	177	18	undergoing	undergo	VERB
ejpam-7119	177	19	anomalous	anomalous	ADJ
ejpam-7119	177	20	diffusion	diffusion	NOUN
ejpam-7119	177	21	.	.	PUNCT
ejpam-7119	178	1	consider	consider	VERB
ejpam-7119	178	2	a	a	DET
ejpam-7119	178	3	mapping	mapping	NOUN
ejpam-7119	178	4	ψ	ψ	ADP
ejpam-7119	178	5	representing	represent	VERB
ejpam-7119	178	6	the	the	DET
ejpam-7119	178	7	evolution	evolution	NOUN
ejpam-7119	178	8	operator	operator	NOUN
ejpam-7119	178	9	of	of	ADP
ejpam-7119	178	10	the	the	DET
ejpam-7119	178	11	diffusion	diffusion	NOUN
ejpam-7119	178	12	process	process	NOUN
ejpam-7119	178	13	over	over	ADP
ejpam-7119	178	14	a	a	DET
ejpam-7119	178	15	discrete	discrete	ADJ
ejpam-7119	178	16	time	time	NOUN
ejpam-7119	178	17	step	step	NOUN
ejpam-7119	178	18	.	.	PUNCT
ejpam-7119	179	1	the	the	DET
ejpam-7119	179	2	fractional	fractional	ADJ
ejpam-7119	179	3	contraction	contraction	NOUN
ejpam-7119	179	4	condition	condition	NOUN
ejpam-7119	179	5	mα(ψf	mα(ψf	NOUN
ejpam-7119	179	6	,	,	PUNCT
ejpam-7119	179	7	ψg	ψg	NOUN
ejpam-7119	179	8	,	,	PUNCT
ejpam-7119	179	9	ψh	ψh	NOUN
ejpam-7119	179	10	)	)	PUNCT
ejpam-7119	179	11	≤	≤	NUM
ejpam-7119	179	12	καmα(f	καmα(f	NOUN
ejpam-7119	179	13	,	,	PUNCT
ejpam-7119	179	14	g	g	NOUN
ejpam-7119	179	15	,	,	PUNCT
ejpam-7119	179	16	h	h	NOUN
ejpam-7119	179	17	)	)	PUNCT
ejpam-7119	179	18	ensures	ensure	VERB
ejpam-7119	179	19	that	that	SCONJ
ejpam-7119	179	20	the	the	DET
ejpam-7119	179	21	process	process	NOUN
ejpam-7119	179	22	converges	converge	VERB
ejpam-7119	179	23	to	to	ADP
ejpam-7119	179	24	a	a	DET
ejpam-7119	179	25	unique	unique	ADJ
ejpam-7119	179	26	steady	steady	ADJ
ejpam-7119	179	27	-	-	PUNCT
ejpam-7119	179	28	state	state	NOUN
ejpam-7119	179	29	f∗.	f∗.	NOUN
ejpam-7119	179	30	the	the	DET
ejpam-7119	179	31	neutrosophic	neutrosophic	ADJ
ejpam-7119	179	32	functions	function	NOUN
ejpam-7119	179	33	track	track	VERB
ejpam-7119	179	34	the	the	DET
ejpam-7119	179	35	evolution	evolution	NOUN
ejpam-7119	179	36	of	of	ADP
ejpam-7119	179	37	certainty	certainty	NOUN
ejpam-7119	179	38	(	(	PUNCT
ejpam-7119	179	39	tα	tα	PROPN
ejpam-7119	179	40	)	)	PUNCT
ejpam-7119	179	41	,	,	PUNCT
ejpam-7119	179	42	indeterminacy	indeterminacy	NOUN
ejpam-7119	179	43	(	(	PUNCT
ejpam-7119	179	44	ialpha	ialpha	PROPN
ejpam-7119	179	45	)	)	PUNCT
ejpam-7119	179	46	,	,	PUNCT
ejpam-7119	179	47	and	and	CCONJ
ejpam-7119	179	48	falsity	falsity	NOUN
ejpam-7119	179	49	(	(	PUNCT
ejpam-7119	179	50	falpha	falpha	ADJ
ejpam-7119	179	51	)	)	PUNCT
ejpam-7119	179	52	regarding	regard	VERB
ejpam-7119	179	53	the	the	DET
ejpam-7119	179	54	particle	particle	NOUN
ejpam-7119	179	55	’s	’s	PART
ejpam-7119	179	56	position	position	NOUN
ejpam-7119	179	57	.	.	PUNCT
ejpam-7119	180	1	3.3	3.3	NUM
ejpam-7119	180	2	.	.	PUNCT
ejpam-7119	180	3	application	application	NOUN
ejpam-7119	180	4	2	2	NUM
ejpam-7119	180	5	:	:	PUNCT
ejpam-7119	180	6	image	image	NOUN
ejpam-7119	180	7	processing	processing	NOUN
ejpam-7119	180	8	and	and	CCONJ
ejpam-7119	180	9	denoising	denoising	NOUN
ejpam-7119	180	10	fonmr	fonmr	NOUN
ejpam-7119	180	11	-	-	PUNCT
ejpam-7119	180	12	ms	ms	NOUN
ejpam-7119	180	13	can	can	AUX
ejpam-7119	180	14	be	be	AUX
ejpam-7119	180	15	applied	apply	VERB
ejpam-7119	180	16	to	to	ADP
ejpam-7119	180	17	image	image	NOUN
ejpam-7119	180	18	processing	processing	NOUN
ejpam-7119	180	19	,	,	PUNCT
ejpam-7119	180	20	particularly	particularly	ADV
ejpam-7119	180	21	in	in	ADP
ejpam-7119	180	22	denoising	denoising	NOUN
ejpam-7119	180	23	and	and	CCONJ
ejpam-7119	180	24	inpainting	inpainting	ADJ
ejpam-7119	180	25	.	.	PUNCT
ejpam-7119	181	1	an	an	DET
ejpam-7119	181	2	image	image	NOUN
ejpam-7119	181	3	can	can	AUX
ejpam-7119	181	4	be	be	AUX
ejpam-7119	181	5	represented	represent	VERB
ejpam-7119	181	6	as	as	ADP
ejpam-7119	181	7	a	a	DET
ejpam-7119	181	8	function	function	NOUN
ejpam-7119	181	9	i(x	i(x	PROPN
ejpam-7119	181	10	,	,	PUNCT
ejpam-7119	181	11	y	y	NOUN
ejpam-7119	181	12	)	)	PUNCT
ejpam-7119	181	13	∈	∈	PROPN
ejpam-7119	181	14	z.	z.	PROPN
ejpam-7119	181	15	a	a	DET
ejpam-7119	181	16	denoising	denoise	VERB
ejpam-7119	181	17	operator	operator	NOUN
ejpam-7119	181	18	ψ	ψ	X
ejpam-7119	181	19	(	(	PUNCT
ejpam-7119	181	20	e.g.	e.g.	ADV
ejpam-7119	181	21	,	,	PUNCT
ejpam-7119	181	22	based	base	VERB
ejpam-7119	181	23	on	on	ADP
ejpam-7119	181	24	a	a	DET
ejpam-7119	181	25	fractional	fractional	ADJ
ejpam-7119	181	26	diffusion	diffusion	NOUN
ejpam-7119	181	27	equation	equation	NOUN
ejpam-7119	181	28	)	)	PUNCT
ejpam-7119	181	29	can	can	AUX
ejpam-7119	181	30	be	be	AUX
ejpam-7119	181	31	designed	design	VERB
ejpam-7119	181	32	to	to	PART
ejpam-7119	181	33	satisfy	satisfy	VERB
ejpam-7119	181	34	the	the	DET
ejpam-7119	181	35	conditions	condition	NOUN
ejpam-7119	181	36	of	of	ADP
ejpam-7119	181	37	theorem	theorem	ADJ
ejpam-7119	181	38	2.3	2.3	NUM
ejpam-7119	181	39	.	.	PUNCT
ejpam-7119	182	1	a.	a.	NOUN
ejpam-7119	182	2	malkawi	malkawi	PROPN
ejpam-7119	182	3	,	,	PUNCT
ejpam-7119	182	4	a.	a.	PROPN
ejpam-7119	182	5	rabaiah	rabaiah	PROPN
ejpam-7119	182	6	/	/	SYM
ejpam-7119	182	7	eur	eur	PROPN
ejpam-7119	182	8	.	.	PUNCT
ejpam-7119	183	1	j.	j.	PROPN
ejpam-7119	183	2	pure	pure	PROPN
ejpam-7119	183	3	appl	appl	PROPN
ejpam-7119	183	4	.	.	PROPN
ejpam-7119	183	5	math	math	PROPN
ejpam-7119	183	6	,	,	PUNCT
ejpam-7119	183	7	18	18	NUM
ejpam-7119	183	8	(	(	PUNCT
ejpam-7119	183	9	4	4	NUM
ejpam-7119	183	10	)	)	PUNCT
ejpam-7119	183	11	(	(	PUNCT
ejpam-7119	183	12	2025	2025	NUM
ejpam-7119	183	13	)	)	PUNCT
ejpam-7119	183	14	,	,	PUNCT
ejpam-7119	183	15	7119	7119	NUM
ejpam-7119	183	16	9	9	NUM
ejpam-7119	183	17	of	of	ADP
ejpam-7119	183	18	13	13	NUM
ejpam-7119	183	19	0	0	NUM
ejpam-7119	183	20	1	1	NUM
ejpam-7119	183	21	2	2	NUM
ejpam-7119	183	22	3	3	NUM
ejpam-7119	183	23	4	4	NUM
ejpam-7119	183	24	5	5	NUM
ejpam-7119	183	25	0	0	NUM
ejpam-7119	183	26	0.2	0.2	NUM
ejpam-7119	183	27	0.4	0.4	NUM
ejpam-7119	183	28	0.6	0.6	NUM
ejpam-7119	183	29	0.8	0.8	NUM
ejpam-7119	183	30	1	1	NUM
ejpam-7119	183	31	iteration	iteration	NOUN
ejpam-7119	183	32	(	(	PUNCT
ejpam-7119	183	33	n	n	CCONJ
ejpam-7119	183	34	)	)	PUNCT
ejpam-7119	183	35	m	m	VERB
ejpam-7119	183	36	et	et	NOUN
ejpam-7119	183	37	ric	ric	PROPN
ejpam-7119	183	38	d	d	PROPN
ejpam-7119	183	39	ist	ist	PROPN
ejpam-7119	183	40	an	an	DET
ejpam-7119	183	41	ce	ce	PROPN
ejpam-7119	183	42	m	m	PROPN
ejpam-7119	183	43	α	α	PROPN
ejpam-7119	183	44	(	(	PUNCT
ejpam-7119	183	45	v	v	NOUN
ejpam-7119	183	46	n	n	NOUN
ejpam-7119	183	47	,	,	PUNCT
ejpam-7119	183	48	v	v	NOUN
ejpam-7119	183	49	∗	∗	NOUN
ejpam-7119	183	50	,	,	PUNCT
ejpam-7119	183	51	v	v	NOUN
ejpam-7119	183	52	∗	∗	NOUN
ejpam-7119	183	53	)	)	PUNCT
ejpam-7119	183	54	convergence	convergence	NOUN
ejpam-7119	183	55	to	to	ADP
ejpam-7119	183	56	fixed	fix	VERB
ejpam-7119	183	57	point	point	NOUN
ejpam-7119	183	58	for	for	ADP
ejpam-7119	183	59	different	different	ADJ
ejpam-7119	183	60	α	α	NOUN
ejpam-7119	183	61	α	α	NOUN
ejpam-7119	183	62	=	=	SYM
ejpam-7119	183	63	1.0	1.0	NUM
ejpam-7119	183	64	,	,	PUNCT
ejpam-7119	183	65	κ	κ	X
ejpam-7119	183	66	=	=	NOUN
ejpam-7119	183	67	0.7	0.7	NUM
ejpam-7119	183	68	α	α	NOUN
ejpam-7119	183	69	=	=	SYM
ejpam-7119	183	70	0.5	0.5	NUM
ejpam-7119	183	71	,	,	PUNCT
ejpam-7119	183	72	κ	κ	X
ejpam-7119	183	73	=	=	NOUN
ejpam-7119	183	74	0.7	0.7	NUM
ejpam-7119	183	75	α	α	NOUN
ejpam-7119	183	76	=	=	PUNCT
ejpam-7119	183	77	2.0	2.0	NUM
ejpam-7119	183	78	,	,	PUNCT
ejpam-7119	183	79	κ	κ	X
ejpam-7119	183	80	=	=	NOUN
ejpam-7119	183	81	0.7	0.7	NUM
ejpam-7119	183	82	figure	figure	NOUN
ejpam-7119	183	83	1	1	NUM
ejpam-7119	183	84	:	:	PUNCT
ejpam-7119	183	85	illustration	illustration	NOUN
ejpam-7119	183	86	of	of	ADP
ejpam-7119	183	87	the	the	DET
ejpam-7119	183	88	convergence	convergence	NOUN
ejpam-7119	183	89	rate	rate	NOUN
ejpam-7119	183	90	mα(vn	mα(vn	PROPN
ejpam-7119	183	91	,	,	PUNCT
ejpam-7119	183	92	v	v	NOUN
ejpam-7119	183	93	∗	∗	NOUN
ejpam-7119	183	94	,	,	PUNCT
ejpam-7119	183	95	v∗	v∗	NOUN
ejpam-7119	183	96	)	)	PUNCT
ejpam-7119	183	97	for	for	ADP
ejpam-7119	183	98	different	different	ADJ
ejpam-7119	183	99	values	value	NOUN
ejpam-7119	183	100	of	of	ADP
ejpam-7119	183	101	the	the	DET
ejpam-7119	183	102	fractional	fractional	ADJ
ejpam-7119	183	103	order	order	NOUN
ejpam-7119	183	104	α	α	NOUN
ejpam-7119	183	105	.	.	PUNCT
ejpam-7119	184	1	the	the	DET
ejpam-7119	184	2	convergence	convergence	NOUN
ejpam-7119	184	3	speed	speed	NOUN
ejpam-7119	184	4	varies	vary	VERB
ejpam-7119	184	5	significantly	significantly	ADV
ejpam-7119	184	6	with	with	ADP
ejpam-7119	184	7	α	α	NOUN
ejpam-7119	184	8	,	,	PUNCT
ejpam-7119	184	9	demonstrating	demonstrate	VERB
ejpam-7119	184	10	its	its	PRON
ejpam-7119	184	11	impact	impact	NOUN
ejpam-7119	184	12	on	on	ADP
ejpam-7119	184	13	the	the	DET
ejpam-7119	184	14	dynamics	dynamic	NOUN
ejpam-7119	184	15	.	.	PUNCT
ejpam-7119	185	1	•	•	NUM
ejpam-7119	185	2	metric	metric	ADJ
ejpam-7119	185	3	contraction	contraction	NOUN
ejpam-7119	185	4	:	:	PUNCT
ejpam-7119	185	5	ensures	ensure	VERB
ejpam-7119	185	6	that	that	SCONJ
ejpam-7119	185	7	applying	apply	VERB
ejpam-7119	185	8	the	the	DET
ejpam-7119	185	9	denoiser	denoiser	NOUN
ejpam-7119	185	10	repeatedly	repeatedly	ADV
ejpam-7119	185	11	does	do	AUX
ejpam-7119	185	12	not	not	PART
ejpam-7119	185	13	diverge	diverge	VERB
ejpam-7119	185	14	and	and	CCONJ
ejpam-7119	185	15	converges	converge	VERB
ejpam-7119	185	16	to	to	ADP
ejpam-7119	185	17	a	a	DET
ejpam-7119	185	18	clean	clean	ADJ
ejpam-7119	185	19	image	image	NOUN
ejpam-7119	185	20	i∗.	i∗.	PROPN
ejpam-7119	185	21	•	•	ADJ
ejpam-7119	185	22	neutrosophic	neutrosophic	ADJ
ejpam-7119	185	23	components	component	NOUN
ejpam-7119	185	24	:	:	PUNCT
ejpam-7119	185	25	–	–	PUNCT
ejpam-7119	185	26	tα(i	tα(i	X
ejpam-7119	185	27	,	,	PUNCT
ejpam-7119	185	28	j	j	PROPN
ejpam-7119	185	29	,	,	PUNCT
ejpam-7119	185	30	γ	γ	X
ejpam-7119	185	31	):	):	PUNCT
ejpam-7119	185	32	measures	measure	NOUN
ejpam-7119	185	33	the	the	DET
ejpam-7119	185	34	degree	degree	NOUN
ejpam-7119	185	35	of	of	ADP
ejpam-7119	185	36	truth	truth	NOUN
ejpam-7119	185	37	that	that	PRON
ejpam-7119	185	38	image	image	NOUN
ejpam-7119	185	39	j	j	PROPN
ejpam-7119	185	40	is	be	AUX
ejpam-7119	185	41	a	a	DET
ejpam-7119	185	42	valid	valid	ADJ
ejpam-7119	185	43	denoised	denoise	VERB
ejpam-7119	185	44	version	version	NOUN
ejpam-7119	185	45	of	of	ADP
ejpam-7119	185	46	image	image	NOUN
ejpam-7119	185	47	i	i	PRON
ejpam-7119	185	48	at	at	ADP
ejpam-7119	185	49	scale	scale	NOUN
ejpam-7119	185	50	γ	γ	X
ejpam-7119	185	51	.	.	PROPN
ejpam-7119	185	52	–	–	PUNCT
ejpam-7119	185	53	iα(i	iα(i	NUM
ejpam-7119	185	54	,	,	PUNCT
ejpam-7119	185	55	j	j	PROPN
ejpam-7119	185	56	,	,	PUNCT
ejpam-7119	185	57	γ	γ	PROPN
ejpam-7119	185	58	):	):	PUNCT
ejpam-7119	185	59	captures	capture	VERB
ejpam-7119	185	60	the	the	DET
ejpam-7119	185	61	indeterminacy	indeterminacy	NOUN
ejpam-7119	185	62	in	in	ADP
ejpam-7119	185	63	the	the	DET
ejpam-7119	185	64	denoising	denoising	NOUN
ejpam-7119	185	65	process	process	NOUN
ejpam-7119	185	66	(	(	PUNCT
ejpam-7119	185	67	e.g.	e.g.	ADV
ejpam-7119	185	68	,	,	PUNCT
ejpam-7119	185	69	uncertainty	uncertainty	NOUN
ejpam-7119	185	70	in	in	ADP
ejpam-7119	185	71	texture	texture	ADJ
ejpam-7119	185	72	regions	region	NOUN
ejpam-7119	185	73	)	)	PUNCT
ejpam-7119	185	74	.	.	PUNCT
ejpam-7119	186	1	–	–	PUNCT
ejpam-7119	186	2	fα(i	fα(i	PROPN
ejpam-7119	186	3	,	,	PUNCT
ejpam-7119	186	4	j	j	PROPN
ejpam-7119	186	5	,	,	PUNCT
ejpam-7119	186	6	γ	γ	PROPN
ejpam-7119	186	7	):	):	PUNCT
ejpam-7119	186	8	represents	represent	VERB
ejpam-7119	186	9	the	the	DET
ejpam-7119	186	10	falsity	falsity	NOUN
ejpam-7119	186	11	or	or	CCONJ
ejpam-7119	186	12	the	the	DET
ejpam-7119	186	13	degree	degree	NOUN
ejpam-7119	186	14	of	of	ADP
ejpam-7119	186	15	artifact	artifact	ADJ
ejpam-7119	186	16	introduction	introduction	NOUN
ejpam-7119	186	17	.	.	PUNCT
ejpam-7119	187	1	the	the	DET
ejpam-7119	187	2	iterative	iterative	NOUN
ejpam-7119	187	3	process	process	NOUN
ejpam-7119	187	4	in+1	in+1	NOUN
ejpam-7119	187	5	=	=	NOUN
ejpam-7119	187	6	ψin	ψin	NOUN
ejpam-7119	187	7	not	not	PART
ejpam-7119	187	8	only	only	ADV
ejpam-7119	187	9	reduces	reduce	VERB
ejpam-7119	187	10	noise	noise	NOUN
ejpam-7119	187	11	(	(	PUNCT
ejpam-7119	187	12	decreasing	decrease	VERB
ejpam-7119	187	13	mα	mα	NOUN
ejpam-7119	187	14	)	)	PUNCT
ejpam-7119	187	15	but	but	CCONJ
ejpam-7119	187	16	also	also	ADV
ejpam-7119	187	17	improves	improve	VERB
ejpam-7119	187	18	the	the	DET
ejpam-7119	187	19	perceptual	perceptual	ADJ
ejpam-7119	187	20	quality	quality	NOUN
ejpam-7119	187	21	by	by	ADP
ejpam-7119	187	22	increasing	increase	VERB
ejpam-7119	187	23	the	the	DET
ejpam-7119	187	24	truth	truth	NOUN
ejpam-7119	187	25	-	-	PUNCT
ejpam-7119	187	26	membership	membership	NOUN
ejpam-7119	187	27	and	and	CCONJ
ejpam-7119	187	28	decreasing	decrease	VERB
ejpam-7119	187	29	indeterminacy	indeterminacy	NOUN
ejpam-7119	187	30	.	.	PUNCT
ejpam-7119	188	1	3.4	3.4	NUM
ejpam-7119	188	2	.	.	PUNCT
ejpam-7119	188	3	application	application	NOUN
ejpam-7119	188	4	3	3	NUM
ejpam-7119	188	5	:	:	PUNCT
ejpam-7119	188	6	machine	machine	NOUN
ejpam-7119	188	7	learning	learning	NOUN
ejpam-7119	188	8	in	in	ADP
ejpam-7119	188	9	uncertain	uncertain	ADJ
ejpam-7119	188	10	environments	environment	NOUN
ejpam-7119	188	11	consider	consider	VERB
ejpam-7119	188	12	a	a	DET
ejpam-7119	188	13	clustering	clustering	ADJ
ejpam-7119	188	14	algorithm	algorithm	NOUN
ejpam-7119	188	15	in	in	ADP
ejpam-7119	188	16	a	a	DET
ejpam-7119	188	17	fonmr	fonmr	ADJ
ejpam-7119	188	18	-	-	PUNCT
ejpam-7119	188	19	ms	ms	PROPN
ejpam-7119	188	20	.	.	PROPN
ejpam-7119	188	21	data	data	PROPN
ejpam-7119	188	22	points	point	NOUN
ejpam-7119	188	23	reside	reside	VERB
ejpam-7119	188	24	in	in	ADP
ejpam-7119	188	25	z.	z.	PROPN
ejpam-7119	188	26	a	a	DET
ejpam-7119	188	27	clustering	cluster	VERB
ejpam-7119	188	28	operator	operator	NOUN
ejpam-7119	188	29	ψ	ψ	NOUN
ejpam-7119	188	30	assigns	assign	NOUN
ejpam-7119	188	31	each	each	DET
ejpam-7119	188	32	point	point	NOUN
ejpam-7119	188	33	to	to	ADP
ejpam-7119	188	34	a	a	DET
ejpam-7119	188	35	cluster	cluster	NOUN
ejpam-7119	188	36	centroid	centroid	NOUN
ejpam-7119	188	37	.	.	PUNCT
ejpam-7119	189	1	the	the	DET
ejpam-7119	189	2	fixed	fixed	ADJ
ejpam-7119	189	3	point	point	NOUN
ejpam-7119	189	4	v∗	v∗	NOUN
ejpam-7119	189	5	corresponds	correspond	NOUN
ejpam-7119	189	6	to	to	ADP
ejpam-7119	189	7	the	the	DET
ejpam-7119	189	8	optimal	optimal	ADJ
ejpam-7119	189	9	cluster	cluster	NOUN
ejpam-7119	189	10	centroid	centroid	NOUN
ejpam-7119	189	11	configuration	configuration	NOUN
ejpam-7119	189	12	.	.	PUNCT
ejpam-7119	190	1	the	the	DET
ejpam-7119	190	2	neutrosophic	neutrosophic	ADJ
ejpam-7119	190	3	framework	framework	NOUN
ejpam-7119	190	4	is	be	AUX
ejpam-7119	190	5	particularly	particularly	ADV
ejpam-7119	190	6	powerful	powerful	ADJ
ejpam-7119	190	7	here	here	ADV
ejpam-7119	190	8	:	:	PUNCT
ejpam-7119	190	9	•	•	NOUN
ejpam-7119	190	10	tα(v	tα(v	NUM
ejpam-7119	190	11	,	,	PUNCT
ejpam-7119	190	12	ξ	ξ	PROPN
ejpam-7119	190	13	,	,	PUNCT
ejpam-7119	190	14	γ	γ	X
ejpam-7119	190	15	):	):	PUNCT
ejpam-7119	190	16	confidence	confidence	NOUN
ejpam-7119	190	17	that	that	PRON
ejpam-7119	190	18	points	point	VERB
ejpam-7119	190	19	v	v	ADP
ejpam-7119	190	20	and	and	CCONJ
ejpam-7119	190	21	ξ	ξ	X
ejpam-7119	190	22	belong	belong	VERB
ejpam-7119	190	23	to	to	ADP
ejpam-7119	190	24	the	the	DET
ejpam-7119	190	25	same	same	ADJ
ejpam-7119	190	26	cluster	cluster	NOUN
ejpam-7119	190	27	.	.	PUNCT
ejpam-7119	191	1	•	•	NOUN
ejpam-7119	191	2	iα(v	iα(v	NUM
ejpam-7119	191	3	,	,	PUNCT
ejpam-7119	191	4	ξ	ξ	PROPN
ejpam-7119	191	5	,	,	PUNCT
ejpam-7119	191	6	γ	γ	NOUN
ejpam-7119	191	7	):	):	PUNCT
ejpam-7119	191	8	indeterminacy	indeterminacy	NOUN
ejpam-7119	191	9	in	in	ADP
ejpam-7119	191	10	cluster	cluster	NOUN
ejpam-7119	191	11	assignment	assignment	NOUN
ejpam-7119	191	12	(	(	PUNCT
ejpam-7119	191	13	e.g.	e.g.	ADV
ejpam-7119	191	14	,	,	PUNCT
ejpam-7119	191	15	points	point	VERB
ejpam-7119	191	16	lying	lie	VERB
ejpam-7119	191	17	on	on	ADP
ejpam-7119	191	18	the	the	DET
ejpam-7119	191	19	decision	decision	NOUN
ejpam-7119	191	20	boundary	boundary	NOUN
ejpam-7119	191	21	)	)	PUNCT
ejpam-7119	191	22	.	.	PUNCT
ejpam-7119	192	1	•	•	NUM
ejpam-7119	192	2	fα(v	fα(v	NUM
ejpam-7119	192	3	,	,	PUNCT
ejpam-7119	192	4	ξ	ξ	PROPN
ejpam-7119	192	5	,	,	PUNCT
ejpam-7119	192	6	γ	γ	X
ejpam-7119	192	7	):	):	PUNCT
ejpam-7119	192	8	confidence	confidence	NOUN
ejpam-7119	192	9	that	that	SCONJ
ejpam-7119	192	10	v	v	NOUN
ejpam-7119	192	11	and	and	CCONJ
ejpam-7119	192	12	ξ	ξ	PROPN
ejpam-7119	192	13	belong	belong	VERB
ejpam-7119	192	14	to	to	ADP
ejpam-7119	192	15	different	different	ADJ
ejpam-7119	192	16	clusters	cluster	NOUN
ejpam-7119	192	17	.	.	PUNCT
ejpam-7119	193	1	the	the	DET
ejpam-7119	193	2	contraction	contraction	NOUN
ejpam-7119	193	3	conditions	condition	NOUN
ejpam-7119	193	4	ensure	ensure	VERB
ejpam-7119	193	5	the	the	DET
ejpam-7119	193	6	clustering	cluster	VERB
ejpam-7119	193	7	algorithm	algorithm	NOUN
ejpam-7119	193	8	converges	converge	VERB
ejpam-7119	193	9	to	to	ADP
ejpam-7119	193	10	a	a	DET
ejpam-7119	193	11	unique	unique	ADJ
ejpam-7119	193	12	solution	solution	NOUN
ejpam-7119	193	13	,	,	PUNCT
ejpam-7119	193	14	while	while	SCONJ
ejpam-7119	193	15	the	the	DET
ejpam-7119	193	16	neutrosophic	neutrosophic	ADJ
ejpam-7119	193	17	properties	property	NOUN
ejpam-7119	193	18	provide	provide	VERB
ejpam-7119	193	19	a	a	DET
ejpam-7119	193	20	rich	rich	ADJ
ejpam-7119	193	21	,	,	PUNCT
ejpam-7119	193	22	interpretable	interpretable	ADJ
ejpam-7119	193	23	measure	measure	NOUN
ejpam-7119	193	24	of	of	ADP
ejpam-7119	193	25	the	the	DET
ejpam-7119	193	26	clustering	clustering	ADJ
ejpam-7119	193	27	quality	quality	NOUN
ejpam-7119	193	28	and	and	CCONJ
ejpam-7119	193	29	uncertainty	uncertainty	NOUN
ejpam-7119	193	30	at	at	ADP
ejpam-7119	193	31	each	each	DET
ejpam-7119	193	32	step	step	NOUN
ejpam-7119	193	33	.	.	PUNCT
ejpam-7119	194	1	a.	a.	PROPN
ejpam-7119	194	2	malkawi	malkawi	PROPN
ejpam-7119	194	3	,	,	PUNCT
ejpam-7119	194	4	a.	a.	PROPN
ejpam-7119	194	5	rabaiah	rabaiah	PROPN
ejpam-7119	194	6	/	/	SYM
ejpam-7119	194	7	eur	eur	PROPN
ejpam-7119	194	8	.	.	PUNCT
ejpam-7119	195	1	j.	j.	PROPN
ejpam-7119	195	2	pure	pure	PROPN
ejpam-7119	195	3	appl	appl	PROPN
ejpam-7119	195	4	.	.	PROPN
ejpam-7119	195	5	math	math	PROPN
ejpam-7119	195	6	,	,	PUNCT
ejpam-7119	195	7	18	18	NUM
ejpam-7119	195	8	(	(	PUNCT
ejpam-7119	195	9	4	4	NUM
ejpam-7119	195	10	)	)	PUNCT
ejpam-7119	195	11	(	(	PUNCT
ejpam-7119	195	12	2025	2025	NUM
ejpam-7119	195	13	)	)	PUNCT
ejpam-7119	195	14	,	,	PUNCT
ejpam-7119	195	15	7119	7119	NUM
ejpam-7119	195	16	10	10	NUM
ejpam-7119	195	17	of	of	ADP
ejpam-7119	195	18	13	13	NUM
ejpam-7119	195	19	3.5	3.5	NUM
ejpam-7119	195	20	.	.	PUNCT
ejpam-7119	196	1	numerical	numerical	PROPN
ejpam-7119	196	2	simulation	simulation	PROPN
ejpam-7119	196	3	snippet	snippet	VERB
ejpam-7119	196	4	the	the	DET
ejpam-7119	196	5	following	follow	VERB
ejpam-7119	196	6	python	python	NOUN
ejpam-7119	196	7	-	-	PUNCT
ejpam-7119	196	8	like	like	ADJ
ejpam-7119	196	9	pseudo	pseudo	NOUN
ejpam-7119	196	10	-	-	NOUN
ejpam-7119	196	11	code	code	NOUN
ejpam-7119	196	12	illustrates	illustrate	VERB
ejpam-7119	196	13	the	the	DET
ejpam-7119	196	14	core	core	NOUN
ejpam-7119	196	15	fixed	fix	VERB
ejpam-7119	196	16	point	point	NOUN
ejpam-7119	196	17	iteration	iteration	NOUN
ejpam-7119	196	18	from	from	ADP
ejpam-7119	196	19	theorem	theorem	ADJ
ejpam-7119	196	20	2.3	2.3	NUM
ejpam-7119	196	21	.	.	PUNCT
ejpam-7119	197	1	#	#	NOUN
ejpam-7119	197	2	pseudo	pseudo	NOUN
ejpam-7119	197	3	-	-	NOUN
ejpam-7119	197	4	code	code	NOUN
ejpam-7119	197	5	for	for	ADP
ejpam-7119	197	6	fixed	fix	VERB
ejpam-7119	197	7	point	point	NOUN
ejpam-7119	197	8	iteration	iteration	NOUN
ejpam-7119	197	9	in	in	ADP
ejpam-7119	197	10	fonmr	fonmr	ADJ
ejpam-7119	197	11	-	-	PUNCT
ejpam-7119	197	12	ms	ms	NOUN
ejpam-7119	197	13	def	def	PROPN
ejpam-7119	197	14	fractional_fixed_point_iteration(psi	fractional_fixed_point_iteration(psi	PROPN
ejpam-7119	197	15	,	,	PUNCT
ejpam-7119	197	16	v0	v0	PROPN
ejpam-7119	197	17	,	,	PUNCT
ejpam-7119	197	18	alpha	alpha	PROPN
ejpam-7119	197	19	,	,	PUNCT
ejpam-7119	197	20	kappa	kappa	PROPN
ejpam-7119	197	21	,	,	PUNCT
ejpam-7119	197	22	tolerance=1e-6	tolerance=1e-6	ADV
ejpam-7119	197	23	,	,	PUNCT
ejpam-7119	197	24	max_iter=1000	max_iter=1000	PROPN
ejpam-7119	197	25	):	):	PUNCT
ejpam-7119	197	26	v_old	v_old	PROPN
ejpam-7119	197	27	=	=	PROPN
ejpam-7119	197	28	v0	v0	PROPN
ejpam-7119	197	29	for	for	ADP
ejpam-7119	197	30	n	n	PROPN
ejpam-7119	197	31	in	in	ADP
ejpam-7119	197	32	range(max_iter	range(max_iter	NOUN
ejpam-7119	197	33	):	):	PUNCT
ejpam-7119	197	34	v_new	v_new	PROPN
ejpam-7119	197	35	=	=	SYM
ejpam-7119	197	36	psi(v_old	psi(v_old	ADJ
ejpam-7119	197	37	)	)	PUNCT
ejpam-7119	197	38	#	#	NOUN
ejpam-7119	197	39	apply	apply	VERB
ejpam-7119	197	40	the	the	DET
ejpam-7119	197	41	mapping	mapping	NOUN
ejpam-7119	197	42	#	#	NOUN
ejpam-7119	197	43	calculate	calculate	NOUN
ejpam-7119	197	44	the	the	DET
ejpam-7119	197	45	fractional	fractional	ADJ
ejpam-7119	197	46	metric	metric	ADJ
ejpam-7119	197	47	distance	distance	NOUN
ejpam-7119	197	48	(	(	PUNCT
ejpam-7119	197	49	simplified	simplified	ADJ
ejpam-7119	197	50	)	)	PUNCT
ejpam-7119	197	51	distance	distance	NOUN
ejpam-7119	197	52	=	=	SYM
ejpam-7119	197	53	m_alpha(v_new	m_alpha(v_new	PROPN
ejpam-7119	197	54	,	,	PUNCT
ejpam-7119	197	55	v_old	v_old	ADJ
ejpam-7119	197	56	,	,	PUNCT
ejpam-7119	197	57	v_old	v_old	ADJ
ejpam-7119	197	58	)	)	PUNCT
ejpam-7119	197	59	#	#	NOUN
ejpam-7119	197	60	check	check	NOUN
ejpam-7119	197	61	convergence	convergence	NOUN
ejpam-7119	197	62	(	(	PUNCT
ejpam-7119	197	63	using	use	VERB
ejpam-7119	197	64	metric	metric	NOUN
ejpam-7119	197	65	)	)	PUNCT
ejpam-7119	197	66	if	if	SCONJ
ejpam-7119	197	67	distance	distance	NOUN
ejpam-7119	197	68	<	<	X
ejpam-7119	197	69	tolerance	tolerance	NOUN
ejpam-7119	197	70	:	:	PUNCT
ejpam-7119	197	71	print(f"converged	print(f"converge	VERB
ejpam-7119	197	72	after	after	ADP
ejpam-7119	197	73	{	{	PUNCT
ejpam-7119	197	74	n	n	CCONJ
ejpam-7119	197	75	}	}	PUNCT
ejpam-7119	197	76	iterations	iteration	NOUN
ejpam-7119	197	77	.	.	PUNCT
ejpam-7119	197	78	"	"	PUNCT
ejpam-7119	197	79	)	)	PUNCT
ejpam-7119	197	80	return	return	VERB
ejpam-7119	197	81	v_new	v_new	PRON
ejpam-7119	197	82	#	#	NOUN
ejpam-7119	197	83	update	update	NOUN
ejpam-7119	197	84	neutrosophic	neutrosophic	ADJ
ejpam-7119	197	85	values	value	NOUN
ejpam-7119	197	86	(	(	PUNCT
ejpam-7119	197	87	conceptually	conceptually	ADV
ejpam-7119	197	88	)	)	PUNCT
ejpam-7119	197	89	t_alpha	t_alpha	NOUN
ejpam-7119	198	1	=	=	PUNCT
ejpam-7119	198	2	update_truth_membership(v_new	update_truth_membership(v_new	ADJ
ejpam-7119	198	3	,	,	PUNCT
ejpam-7119	198	4	v_old	v_old	ADJ
ejpam-7119	198	5	,	,	PUNCT
ejpam-7119	198	6	alpha	alpha	PROPN
ejpam-7119	198	7	,	,	PUNCT
ejpam-7119	198	8	kappa	kappa	ADJ
ejpam-7119	198	9	)	)	PUNCT
ejpam-7119	198	10	i_alpha	i_alpha	NOUN
ejpam-7119	199	1	=	=	SYM
ejpam-7119	199	2	update_indeterminacy(v_new	update_indeterminacy(v_new	ADJ
ejpam-7119	199	3	,	,	PUNCT
ejpam-7119	199	4	v_old	v_old	ADJ
ejpam-7119	199	5	,	,	PUNCT
ejpam-7119	199	6	alpha	alpha	NOUN
ejpam-7119	199	7	)	)	PUNCT
ejpam-7119	199	8	v_old	v_old	PROPN
ejpam-7119	200	1	=	=	PUNCT
ejpam-7119	200	2	v_new	v_new	ADJ
ejpam-7119	200	3	print("maximum	print("maximum	ADJ
ejpam-7119	200	4	iterations	iteration	NOUN
ejpam-7119	200	5	reached	reach	VERB
ejpam-7119	200	6	.	.	PUNCT
ejpam-7119	200	7	"	"	PUNCT
ejpam-7119	200	8	)	)	PUNCT
ejpam-7119	200	9	return	return	VERB
ejpam-7119	200	10	v_old	v_old	ADP
ejpam-7119	200	11	this	this	DET
ejpam-7119	200	12	framework	framework	NOUN
ejpam-7119	200	13	provides	provide	VERB
ejpam-7119	200	14	a	a	DET
ejpam-7119	200	15	robust	robust	ADJ
ejpam-7119	200	16	foundation	foundation	NOUN
ejpam-7119	200	17	for	for	ADP
ejpam-7119	200	18	modeling	model	VERB
ejpam-7119	200	19	complex	complex	ADJ
ejpam-7119	200	20	systems	system	NOUN
ejpam-7119	200	21	where	where	SCONJ
ejpam-7119	200	22	uncertainty	uncertainty	NOUN
ejpam-7119	200	23	,	,	PUNCT
ejpam-7119	200	24	fractional	fractional	ADJ
ejpam-7119	200	25	dynamics	dynamic	NOUN
ejpam-7119	200	26	,	,	PUNCT
ejpam-7119	200	27	and	and	CCONJ
ejpam-7119	200	28	convergence	convergence	NOUN
ejpam-7119	200	29	are	be	AUX
ejpam-7119	200	30	crucial	crucial	ADJ
ejpam-7119	200	31	.	.	PUNCT
ejpam-7119	201	1	references	reference	NOUN
ejpam-7119	201	2	[	[	X
ejpam-7119	201	3	1	1	NUM
ejpam-7119	201	4	]	]	X
ejpam-7119	201	5	i.a	i.a	PROPN
ejpam-7119	201	6	.	.	PROPN
ejpam-7119	201	7	bakhtin	bakhtin	PROPN
ejpam-7119	201	8	.	.	PUNCT
ejpam-7119	202	1	the	the	DET
ejpam-7119	202	2	contraction	contraction	NOUN
ejpam-7119	202	3	mapping	map	VERB
ejpam-7119	202	4	principle	principle	NOUN
ejpam-7119	202	5	in	in	ADP
ejpam-7119	202	6	almost	almost	ADV
ejpam-7119	202	7	metric	metric	ADJ
ejpam-7119	202	8	spaces	space	NOUN
ejpam-7119	202	9	.	.	PUNCT
ejpam-7119	203	1	funct	funct	ADJ
ejpam-7119	203	2	.	.	PUNCT
ejpam-7119	204	1	anal	anal	PROPN
ejpam-7119	204	2	.	.	PROPN
ejpam-7119	204	3	,	,	PUNCT
ejpam-7119	204	4	30:26–37	30:26–37	PROPN
ejpam-7119	204	5	,	,	PUNCT
ejpam-7119	204	6	1989	1989	NUM
ejpam-7119	204	7	.	.	PUNCT
ejpam-7119	205	1	[	[	X
ejpam-7119	205	2	2	2	X
ejpam-7119	205	3	]	]	PUNCT
ejpam-7119	205	4	s.	s.	PROPN
ejpam-7119	205	5	czerwik	czerwik	PROPN
ejpam-7119	205	6	.	.	PUNCT
ejpam-7119	206	1	contraction	contraction	NOUN
ejpam-7119	206	2	mappings	mapping	NOUN
ejpam-7119	206	3	in	in	ADP
ejpam-7119	206	4	b	b	NOUN
ejpam-7119	206	5	-	-	ADJ
ejpam-7119	206	6	metric	metric	ADJ
ejpam-7119	206	7	spaces	space	NOUN
ejpam-7119	206	8	.	.	PUNCT
ejpam-7119	207	1	acta	acta	PROPN
ejpam-7119	207	2	math	math	PROPN
ejpam-7119	207	3	.	.	PUNCT
ejpam-7119	208	1	inform	inform	NOUN
ejpam-7119	208	2	.	.	PUNCT
ejpam-7119	209	1	univ	univ	PROPN
ejpam-7119	209	2	.	.	PUNCT
ejpam-7119	209	3	ostra	ostra	PROPN
ejpam-7119	209	4	.	.	PROPN
ejpam-7119	209	5	,	,	PUNCT
ejpam-7119	209	6	1:5–11	1:5–11	NUM
ejpam-7119	209	7	,	,	PUNCT
ejpam-7119	209	8	1993	1993	NUM
ejpam-7119	209	9	.	.	PUNCT
ejpam-7119	210	1	[	[	X
ejpam-7119	210	2	3	3	NUM
ejpam-7119	210	3	]	]	X
ejpam-7119	210	4	a.	a.	NOUN
ejpam-7119	210	5	malkawi	malkawi	PROPN
ejpam-7119	210	6	,	,	PUNCT
ejpam-7119	210	7	a.	a.	PROPN
ejpam-7119	210	8	rabaiah	rabaiah	PROPN
ejpam-7119	210	9	,	,	PUNCT
ejpam-7119	210	10	w.	w.	PROPN
ejpam-7119	210	11	shatanawi	shatanawi	PROPN
ejpam-7119	210	12	,	,	PUNCT
ejpam-7119	210	13	and	and	CCONJ
ejpam-7119	210	14	a.	a.	NOUN
ejpam-7119	210	15	talafhah	talafhah	PROPN
ejpam-7119	210	16	.	.	PUNCT
ejpam-7119	211	1	mr	mr	PROPN
ejpam-7119	211	2	-	-	PUNCT
ejpam-7119	211	3	metric	metric	ADJ
ejpam-7119	211	4	spaces	space	NOUN
ejpam-7119	211	5	and	and	CCONJ
ejpam-7119	211	6	an	an	DET
ejpam-7119	211	7	application	application	NOUN
ejpam-7119	211	8	.	.	PUNCT
ejpam-7119	212	1	preprint	preprint	NOUN
ejpam-7119	212	2	,	,	PUNCT
ejpam-7119	212	3	2021	2021	NUM
ejpam-7119	212	4	.	.	PUNCT
ejpam-7119	213	1	[	[	X
ejpam-7119	213	2	4	4	NUM
ejpam-7119	213	3	]	]	PUNCT
ejpam-7119	213	4	a.	a.	NOUN
ejpam-7119	213	5	a.	a.	PROPN
ejpam-7119	213	6	r.	r.	PROPN
ejpam-7119	213	7	m.	m.	PROPN
ejpam-7119	213	8	malkawi	malkawi	PROPN
ejpam-7119	213	9	.	.	PROPN
ejpam-7119	213	10	existence	existence	NOUN
ejpam-7119	213	11	and	and	CCONJ
ejpam-7119	213	12	uniqueness	uniqueness	NOUN
ejpam-7119	213	13	of	of	ADP
ejpam-7119	213	14	fixed	fix	VERB
ejpam-7119	213	15	points	point	NOUN
ejpam-7119	213	16	in	in	ADP
ejpam-7119	213	17	mr	mr	PROPN
ejpam-7119	213	18	-	-	PUNCT
ejpam-7119	213	19	metric	metric	ADJ
ejpam-7119	213	20	spaces	space	NOUN
ejpam-7119	213	21	and	and	CCONJ
ejpam-7119	213	22	their	their	PRON
ejpam-7119	213	23	applications	application	NOUN
ejpam-7119	213	24	.	.	PUNCT
ejpam-7119	214	1	european	european	ADJ
ejpam-7119	214	2	journal	journal	PROPN
ejpam-7119	214	3	of	of	ADP
ejpam-7119	214	4	pure	pure	ADJ
ejpam-7119	214	5	and	and	CCONJ
ejpam-7119	214	6	applied	applied	ADJ
ejpam-7119	214	7	mathematics	mathematic	NOUN
ejpam-7119	214	8	,	,	PUNCT
ejpam-7119	214	9	18(2):id	18(2):id	NUM
ejpam-7119	214	10	:	:	PUNCT
ejpam-7119	214	11	6077	6077	NUM
ejpam-7119	214	12	,	,	PUNCT
ejpam-7119	214	13	2025	2025	NUM
ejpam-7119	214	14	.	.	PUNCT
ejpam-7119	215	1	[	[	X
ejpam-7119	215	2	5	5	NUM
ejpam-7119	215	3	]	]	PUNCT
ejpam-7119	215	4	a.	a.	NOUN
ejpam-7119	215	5	a.	a.	PROPN
ejpam-7119	215	6	r.	r.	PROPN
ejpam-7119	215	7	m.	m.	PROPN
ejpam-7119	215	8	malkawi	malkawi	PROPN
ejpam-7119	215	9	.	.	PROPN
ejpam-7119	215	10	convergence	convergence	NOUN
ejpam-7119	215	11	and	and	CCONJ
ejpam-7119	215	12	fixed	fix	VERB
ejpam-7119	215	13	points	point	NOUN
ejpam-7119	215	14	of	of	ADP
ejpam-7119	215	15	self	self	NOUN
ejpam-7119	215	16	-	-	PUNCT
ejpam-7119	215	17	mappings	mapping	NOUN
ejpam-7119	215	18	in	in	ADP
ejpam-7119	215	19	mr	mr	PROPN
ejpam-7119	215	20	-	-	PUNCT
ejpam-7119	215	21	metric	metric	ADJ
ejpam-7119	215	22	spaces	space	NOUN
ejpam-7119	215	23	:	:	PUNCT
ejpam-7119	215	24	theory	theory	NOUN
ejpam-7119	215	25	and	and	CCONJ
ejpam-7119	215	26	applications	application	NOUN
ejpam-7119	215	27	.	.	PUNCT
ejpam-7119	216	1	european	european	ADJ
ejpam-7119	216	2	journal	journal	PROPN
ejpam-7119	216	3	of	of	ADP
ejpam-7119	216	4	pure	pure	ADJ
ejpam-7119	216	5	and	and	CCONJ
ejpam-7119	216	6	applied	applied	ADJ
ejpam-7119	216	7	mathematics	mathematic	NOUN
ejpam-7119	216	8	,	,	PUNCT
ejpam-7119	216	9	18(2):id	18(2):id	NUM
ejpam-7119	216	10	:	:	SYM
ejpam-7119	216	11	5952	5952	NUM
ejpam-7119	216	12	,	,	PUNCT
ejpam-7119	216	13	2025	2025	NUM
ejpam-7119	216	14	.	.	PUNCT
ejpam-7119	217	1	[	[	X
ejpam-7119	217	2	6	6	NUM
ejpam-7119	217	3	]	]	PUNCT
ejpam-7119	217	4	a.	a.	NOUN
ejpam-7119	217	5	a.	a.	PROPN
ejpam-7119	217	6	r.	r.	PROPN
ejpam-7119	217	7	m.	m.	PROPN
ejpam-7119	217	8	malkawi	malkawi	PROPN
ejpam-7119	217	9	.	.	PUNCT
ejpam-7119	217	10	fixed	fix	VERB
ejpam-7119	217	11	point	point	NOUN
ejpam-7119	217	12	theorem	theorem	VERB
ejpam-7119	217	13	in	in	ADP
ejpam-7119	217	14	mr	mr	PROPN
ejpam-7119	217	15	-	-	PUNCT
ejpam-7119	217	16	metric	metric	ADJ
ejpam-7119	217	17	spaces	space	NOUN
ejpam-7119	217	18	via	via	ADP
ejpam-7119	217	19	integral	integral	ADJ
ejpam-7119	217	20	type	type	NOUN
ejpam-7119	217	21	contraction	contraction	NOUN
ejpam-7119	217	22	.	.	PUNCT
ejpam-7119	218	1	wseas	wseas	VERB
ejpam-7119	218	2	transactions	transaction	NOUN
ejpam-7119	218	3	on	on	ADP
ejpam-7119	218	4	mathematics	mathematic	NOUN
ejpam-7119	218	5	,	,	PUNCT
ejpam-7119	218	6	24:295–299	24:295–299	PROPN
ejpam-7119	218	7	,	,	PUNCT
ejpam-7119	218	8	2025	2025	NUM
ejpam-7119	218	9	.	.	PUNCT
ejpam-7119	219	1	[	[	X
ejpam-7119	219	2	7	7	NUM
ejpam-7119	219	3	]	]	PUNCT
ejpam-7119	219	4	a.	a.	NOUN
ejpam-7119	219	5	a.	a.	PROPN
ejpam-7119	219	6	r.	r.	PROPN
ejpam-7119	219	7	m.	m.	PROPN
ejpam-7119	219	8	malkawi	malkawi	PROPN
ejpam-7119	219	9	,	,	PUNCT
ejpam-7119	219	10	d.	d.	PROPN
ejpam-7119	219	11	mahmoud	mahmoud	PROPN
ejpam-7119	219	12	,	,	PUNCT
ejpam-7119	219	13	a.	a.	PROPN
ejpam-7119	219	14	m.	m.	PROPN
ejpam-7119	219	15	rabaiah	rabaiah	PROPN
ejpam-7119	219	16	,	,	PUNCT
ejpam-7119	219	17	r.	r.	PROPN
ejpam-7119	219	18	al	al	PROPN
ejpam-7119	219	19	-	-	PUNCT
ejpam-7119	219	20	deiakeh	deiakeh	PROPN
ejpam-7119	219	21	,	,	PUNCT
ejpam-7119	219	22	and	and	CCONJ
ejpam-7119	219	23	w.	w.	PROPN
ejpam-7119	219	24	shatanawi	shatanawi	PROPN
ejpam-7119	219	25	.	.	PUNCT
ejpam-7119	220	1	on	on	ADP
ejpam-7119	220	2	fixed	fix	VERB
ejpam-7119	220	3	point	point	NOUN
ejpam-7119	220	4	theorems	theorem	NOUN
ejpam-7119	220	5	in	in	ADP
ejpam-7119	220	6	mr	mr	PROPN
ejpam-7119	220	7	-	-	PUNCT
ejpam-7119	220	8	metric	metric	ADJ
ejpam-7119	220	9	spaces	space	NOUN
ejpam-7119	220	10	.	.	PUNCT
ejpam-7119	221	1	nonlinear	nonlinear	ADJ
ejpam-7119	221	2	functional	functional	ADJ
ejpam-7119	221	3	analysis	analysis	NOUN
ejpam-7119	221	4	and	and	CCONJ
ejpam-7119	221	5	applications	application	NOUN
ejpam-7119	221	6	,	,	PUNCT
ejpam-7119	221	7	29(4):1125–1136	29(4):1125–1136	NUM
ejpam-7119	221	8	,	,	PUNCT
ejpam-7119	221	9	2024	2024	NUM
ejpam-7119	221	10	.	.	PUNCT
ejpam-7119	222	1	[	[	X
ejpam-7119	222	2	8	8	NUM
ejpam-7119	222	3	]	]	PUNCT
ejpam-7119	222	4	s.	s.	PROPN
ejpam-7119	222	5	al	al	PROPN
ejpam-7119	222	6	-	-	PUNCT
ejpam-7119	222	7	sharif	sharif	PROPN
ejpam-7119	222	8	and	and	CCONJ
ejpam-7119	222	9	a.	a.	NOUN
ejpam-7119	222	10	malkawi	malkawi	PROPN
ejpam-7119	222	11	.	.	PUNCT
ejpam-7119	223	1	modification	modification	NOUN
ejpam-7119	223	2	of	of	ADP
ejpam-7119	223	3	conformable	conformable	ADJ
ejpam-7119	223	4	fractional	fractional	ADJ
ejpam-7119	223	5	derivative	derivative	NOUN
ejpam-7119	223	6	with	with	ADP
ejpam-7119	223	7	classical	classical	ADJ
ejpam-7119	223	8	properties	property	NOUN
ejpam-7119	223	9	.	.	PUNCT
ejpam-7119	224	1	ital	ital	PROPN
ejpam-7119	224	2	.	.	PUNCT
ejpam-7119	225	1	j.	j.	PROPN
ejpam-7119	225	2	pure	pure	PROPN
ejpam-7119	225	3	appl	appl	PROPN
ejpam-7119	225	4	.	.	PROPN
ejpam-7119	225	5	math	math	PROPN
ejpam-7119	225	6	,	,	PUNCT
ejpam-7119	225	7	44:30–39	44:30–39	PROPN
ejpam-7119	225	8	,	,	PUNCT
ejpam-7119	225	9	2020	2020	NUM
ejpam-7119	225	10	.	.	PUNCT
ejpam-7119	226	1	a.	a.	PROPN
ejpam-7119	226	2	malkawi	malkawi	PROPN
ejpam-7119	226	3	,	,	PUNCT
ejpam-7119	226	4	a.	a.	PROPN
ejpam-7119	226	5	rabaiah	rabaiah	PROPN
ejpam-7119	226	6	/	/	SYM
ejpam-7119	226	7	eur	eur	PROPN
ejpam-7119	226	8	.	.	PUNCT
ejpam-7119	227	1	j.	j.	PROPN
ejpam-7119	227	2	pure	pure	PROPN
ejpam-7119	227	3	appl	appl	PROPN
ejpam-7119	227	4	.	.	PROPN
ejpam-7119	227	5	math	math	PROPN
ejpam-7119	227	6	,	,	PUNCT
ejpam-7119	227	7	18	18	NUM
ejpam-7119	227	8	(	(	PUNCT
ejpam-7119	227	9	4	4	NUM
ejpam-7119	227	10	)	)	PUNCT
ejpam-7119	227	11	(	(	PUNCT
ejpam-7119	227	12	2025	2025	NUM
ejpam-7119	227	13	)	)	PUNCT
ejpam-7119	227	14	,	,	PUNCT
ejpam-7119	227	15	7119	7119	NUM
ejpam-7119	227	16	11	11	NUM
ejpam-7119	227	17	of	of	ADP
ejpam-7119	227	18	13	13	NUM
ejpam-7119	227	19	[	[	X
ejpam-7119	227	20	9	9	NUM
ejpam-7119	227	21	]	]	SYM
ejpam-7119	227	22	a.	a.	NOUN
ejpam-7119	227	23	malkawi	malkawi	PROPN
ejpam-7119	227	24	,	,	PUNCT
ejpam-7119	227	25	a.	a.	NOUN
ejpam-7119	227	26	talafhah	talafhah	PROPN
ejpam-7119	227	27	,	,	PUNCT
ejpam-7119	227	28	and	and	CCONJ
ejpam-7119	227	29	w.	w.	PROPN
ejpam-7119	227	30	shatanawi	shatanawi	PROPN
ejpam-7119	227	31	.	.	PUNCT
ejpam-7119	228	1	coincidence	coincidence	NOUN
ejpam-7119	228	2	and	and	CCONJ
ejpam-7119	228	3	fixed	fix	VERB
ejpam-7119	228	4	point	point	NOUN
ejpam-7119	228	5	results	result	NOUN
ejpam-7119	228	6	for	for	ADP
ejpam-7119	228	7	(	(	PUNCT
ejpam-7119	228	8	ψ	ψ	X
ejpam-7119	228	9	,	,	PUNCT
ejpam-7119	228	10	l)-mweak	l)-mweak	NOUN
ejpam-7119	228	11	contraction	contraction	NOUN
ejpam-7119	228	12	mapping	mapping	NOUN
ejpam-7119	228	13	on	on	ADP
ejpam-7119	228	14	mb	mb	ADJ
ejpam-7119	228	15	-	-	ADJ
ejpam-7119	228	16	metric	metric	ADJ
ejpam-7119	228	17	spaces	space	NOUN
ejpam-7119	228	18	.	.	PUNCT
ejpam-7119	229	1	italian	italian	ADJ
ejpam-7119	229	2	journal	journal	NOUN
ejpam-7119	229	3	of	of	ADP
ejpam-7119	229	4	pure	pure	ADJ
ejpam-7119	229	5	and	and	CCONJ
ejpam-7119	229	6	applied	applied	ADJ
ejpam-7119	229	7	mathematics	mathematic	NOUN
ejpam-7119	229	8	,	,	PUNCT
ejpam-7119	229	9	(	(	PUNCT
ejpam-7119	229	10	47):751–768	47):751–768	NOUN
ejpam-7119	229	11	,	,	PUNCT
ejpam-7119	229	12	2022	2022	NUM
ejpam-7119	229	13	.	.	PUNCT
ejpam-7119	230	1	[	[	X
ejpam-7119	230	2	10	10	NUM
ejpam-7119	230	3	]	]	PUNCT
ejpam-7119	230	4	t.	t.	NOUN
ejpam-7119	230	5	qawasmeh	qawasmeh	NOUN
ejpam-7119	230	6	and	and	CCONJ
ejpam-7119	230	7	a.	a.	NOUN
ejpam-7119	230	8	malkawi	malkawi	PROPN
ejpam-7119	230	9	.	.	PUNCT
ejpam-7119	230	10	fixed	fix	VERB
ejpam-7119	230	11	point	point	NOUN
ejpam-7119	230	12	theory	theory	NOUN
ejpam-7119	230	13	in	in	ADP
ejpam-7119	230	14	mr	mr	PROPN
ejpam-7119	230	15	-	-	PUNCT
ejpam-7119	230	16	metric	metric	ADJ
ejpam-7119	230	17	spaces	space	NOUN
ejpam-7119	230	18	:	:	PUNCT
ejpam-7119	230	19	fundamental	fundamental	ADJ
ejpam-7119	230	20	theorems	theorem	NOUN
ejpam-7119	230	21	and	and	CCONJ
ejpam-7119	230	22	applications	application	NOUN
ejpam-7119	230	23	to	to	ADP
ejpam-7119	230	24	integral	integral	ADJ
ejpam-7119	230	25	equations	equation	NOUN
ejpam-7119	230	26	and	and	CCONJ
ejpam-7119	230	27	neutron	neutron	NOUN
ejpam-7119	230	28	transport	transport	NOUN
ejpam-7119	230	29	.	.	PUNCT
ejpam-7119	231	1	european	european	ADJ
ejpam-7119	231	2	journal	journal	PROPN
ejpam-7119	231	3	of	of	ADP
ejpam-7119	231	4	pure	pure	ADJ
ejpam-7119	231	5	and	and	CCONJ
ejpam-7119	231	6	applied	applied	ADJ
ejpam-7119	231	7	mathematics	mathematic	NOUN
ejpam-7119	231	8	,	,	PUNCT
ejpam-7119	231	9	18(3):id	18(3):id	NUM
ejpam-7119	231	10	:	:	SYM
ejpam-7119	231	11	6440	6440	NUM
ejpam-7119	231	12	,	,	PUNCT
ejpam-7119	231	13	2025	2025	NUM
ejpam-7119	231	14	.	.	PUNCT
ejpam-7119	232	1	[	[	X
ejpam-7119	232	2	11	11	NUM
ejpam-7119	232	3	]	]	X
ejpam-7119	232	4	a.	a.	NOUN
ejpam-7119	232	5	malkawi	malkawi	NOUN
ejpam-7119	232	6	and	and	CCONJ
ejpam-7119	232	7	a.	a.	PROPN
ejpam-7119	232	8	rabaiah	rabaiah	PROPN
ejpam-7119	232	9	.	.	PUNCT
ejpam-7119	233	1	mr	mr	PROPN
ejpam-7119	233	2	-	-	PUNCT
ejpam-7119	233	3	metric	metric	ADJ
ejpam-7119	233	4	spaces	space	NOUN
ejpam-7119	233	5	:	:	PUNCT
ejpam-7119	233	6	theory	theory	NOUN
ejpam-7119	233	7	and	and	CCONJ
ejpam-7119	233	8	applications	application	NOUN
ejpam-7119	233	9	in	in	ADP
ejpam-7119	233	10	weighted	weighted	ADJ
ejpam-7119	233	11	graphs	graph	NOUN
ejpam-7119	233	12	,	,	PUNCT
ejpam-7119	233	13	expander	expander	NOUN
ejpam-7119	233	14	graphs	graph	NOUN
ejpam-7119	233	15	,	,	PUNCT
ejpam-7119	233	16	and	and	CCONJ
ejpam-7119	233	17	fixed	fix	VERB
ejpam-7119	233	18	-	-	PUNCT
ejpam-7119	233	19	point	point	NOUN
ejpam-7119	233	20	theorems	theorem	NOUN
ejpam-7119	233	21	.	.	PUNCT
ejpam-7119	234	1	european	european	PROPN
ejpam-7119	234	2	journal	journal	PROPN
ejpam-7119	234	3	of	of	ADP
ejpam-7119	234	4	pure	pure	ADJ
ejpam-7119	234	5	and	and	CCONJ
ejpam-7119	234	6	applied	applied	ADJ
ejpam-7119	234	7	mathematics	mathematic	NOUN
ejpam-7119	234	8	,	,	PUNCT
ejpam-7119	234	9	18(3):id	18(3):id	NUM
ejpam-7119	234	10	:	:	PUNCT
ejpam-7119	234	11	6525	6525	NUM
ejpam-7119	234	12	,	,	PUNCT
ejpam-7119	234	13	2025	2025	NUM
ejpam-7119	234	14	.	.	PUNCT
ejpam-7119	235	1	[	[	X
ejpam-7119	235	2	12	12	NUM
ejpam-7119	235	3	]	]	X
ejpam-7119	235	4	a.	a.	NOUN
ejpam-7119	235	5	malkawi	malkawi	NOUN
ejpam-7119	235	6	and	and	CCONJ
ejpam-7119	235	7	a.	a.	PROPN
ejpam-7119	235	8	rabaiah	rabaiah	PROPN
ejpam-7119	235	9	.	.	PUNCT
ejpam-7119	236	1	compactness	compactness	NOUN
ejpam-7119	236	2	and	and	CCONJ
ejpam-7119	236	3	separability	separability	NOUN
ejpam-7119	236	4	in	in	ADP
ejpam-7119	236	5	mr	mr	PROPN
ejpam-7119	236	6	-	-	PUNCT
ejpam-7119	236	7	metric	metric	ADJ
ejpam-7119	236	8	spaces	space	NOUN
ejpam-7119	236	9	with	with	ADP
ejpam-7119	236	10	applications	application	NOUN
ejpam-7119	236	11	to	to	ADP
ejpam-7119	236	12	deep	deep	ADJ
ejpam-7119	236	13	learning	learning	NOUN
ejpam-7119	236	14	.	.	PUNCT
ejpam-7119	237	1	european	european	ADJ
ejpam-7119	237	2	journal	journal	PROPN
ejpam-7119	237	3	of	of	ADP
ejpam-7119	237	4	pure	pure	ADJ
ejpam-7119	237	5	and	and	CCONJ
ejpam-7119	237	6	applied	applied	ADJ
ejpam-7119	237	7	mathematics	mathematic	NOUN
ejpam-7119	237	8	,	,	PUNCT
ejpam-7119	237	9	18(3):id	18(3):id	NUM
ejpam-7119	237	10	:	:	SYM
ejpam-7119	237	11	6592	6592	NUM
ejpam-7119	237	12	,	,	PUNCT
ejpam-7119	237	13	2025	2025	NUM
ejpam-7119	237	14	.	.	PUNCT
ejpam-7119	238	1	[	[	X
ejpam-7119	238	2	13	13	NUM
ejpam-7119	238	3	]	]	X
ejpam-7119	238	4	a.	a.	NOUN
ejpam-7119	238	5	malkawi	malkawi	PROPN
ejpam-7119	238	6	.	.	PUNCT
ejpam-7119	239	1	applications	application	NOUN
ejpam-7119	239	2	of	of	ADP
ejpam-7119	239	3	mr	mr	PROPN
ejpam-7119	239	4	-	-	PUNCT
ejpam-7119	239	5	metric	metric	ADJ
ejpam-7119	239	6	spaces	space	NOUN
ejpam-7119	239	7	in	in	ADP
ejpam-7119	239	8	measure	measure	NOUN
ejpam-7119	239	9	theory	theory	NOUN
ejpam-7119	239	10	and	and	CCONJ
ejpam-7119	239	11	convergence	convergence	NOUN
ejpam-7119	239	12	analysis	analysis	NOUN
ejpam-7119	239	13	.	.	PUNCT
ejpam-7119	240	1	european	european	ADJ
ejpam-7119	240	2	journal	journal	PROPN
ejpam-7119	240	3	of	of	ADP
ejpam-7119	240	4	pure	pure	ADJ
ejpam-7119	240	5	and	and	CCONJ
ejpam-7119	240	6	applied	applied	ADJ
ejpam-7119	240	7	mathematics	mathematic	NOUN
ejpam-7119	240	8	,	,	PUNCT
ejpam-7119	240	9	18(3):id	18(3):id	NUM
ejpam-7119	240	10	:	:	SYM
ejpam-7119	240	11	6528	6528	NUM
ejpam-7119	240	12	,	,	PUNCT
ejpam-7119	240	13	2025	2025	NUM
ejpam-7119	240	14	.	.	PUNCT
ejpam-7119	241	1	[	[	X
ejpam-7119	241	2	14	14	NUM
ejpam-7119	241	3	]	]	SYM
ejpam-7119	241	4	hazaymeh	hazaymeh	NOUN
ejpam-7119	241	5	ayman.a	ayman.a	PROPN
ejpam-7119	241	6	and	and	CCONJ
ejpam-7119	241	7	anwar	anwar	PROPN
ejpam-7119	241	8	bataihah	bataihah	PROPN
ejpam-7119	241	9	.	.	PUNCT
ejpam-7119	242	1	neutrosophic	neutrosophic	ADJ
ejpam-7119	242	2	fuzzy	fuzzy	ADJ
ejpam-7119	242	3	metric	metric	ADJ
ejpam-7119	242	4	spaces	space	NOUN
ejpam-7119	242	5	and	and	CCONJ
ejpam-7119	242	6	fixed	fix	VERB
ejpam-7119	242	7	points	point	NOUN
ejpam-7119	242	8	for	for	ADP
ejpam-7119	242	9	contractions	contraction	NOUN
ejpam-7119	242	10	of	of	ADP
ejpam-7119	242	11	nonlinear	nonlinear	ADJ
ejpam-7119	242	12	type	type	NOUN
ejpam-7119	242	13	.	.	PUNCT
ejpam-7119	243	1	neutrosophic	neutrosophic	ADJ
ejpam-7119	243	2	sets	set	NOUN
ejpam-7119	243	3	and	and	CCONJ
ejpam-7119	243	4	systems	system	NOUN
ejpam-7119	243	5	,	,	PUNCT
ejpam-7119	243	6	77(1):96–112	77(1):96–112	NUM
ejpam-7119	243	7	,	,	PUNCT
ejpam-7119	243	8	2025	2025	NUM
ejpam-7119	243	9	.	.	PUNCT
ejpam-7119	244	1	[	[	X
ejpam-7119	244	2	15	15	NUM
ejpam-7119	244	3	]	]	X
ejpam-7119	244	4	a.	a.	NOUN
ejpam-7119	244	5	bataihah	bataihah	PROPN
ejpam-7119	244	6	and	and	CCONJ
ejpam-7119	244	7	a.	a.	NOUN
ejpam-7119	244	8	hazaymeh	hazaymeh	NOUN
ejpam-7119	244	9	.	.	PUNCT
ejpam-7119	245	1	quasi	quasi	NOUN
ejpam-7119	245	2	contractions	contraction	NOUN
ejpam-7119	245	3	and	and	CCONJ
ejpam-7119	245	4	fixed	fix	VERB
ejpam-7119	245	5	point	point	NOUN
ejpam-7119	245	6	theorems	theorem	NOUN
ejpam-7119	245	7	in	in	ADP
ejpam-7119	245	8	the	the	DET
ejpam-7119	245	9	context	context	NOUN
ejpam-7119	245	10	of	of	ADP
ejpam-7119	245	11	neutrosophic	neutrosophic	ADJ
ejpam-7119	245	12	fuzzy	fuzzy	ADJ
ejpam-7119	245	13	metric	metric	ADJ
ejpam-7119	245	14	spaces	space	NOUN
ejpam-7119	245	15	.	.	PUNCT
ejpam-7119	246	1	european	european	ADJ
ejpam-7119	246	2	journal	journal	PROPN
ejpam-7119	246	3	of	of	ADP
ejpam-7119	246	4	pure	pure	ADJ
ejpam-7119	246	5	and	and	CCONJ
ejpam-7119	246	6	applied	applied	ADJ
ejpam-7119	246	7	mathematics	mathematic	NOUN
ejpam-7119	246	8	,	,	PUNCT
ejpam-7119	246	9	18(1):5785–5785	18(1):5785–5785	NUM
ejpam-7119	246	10	,	,	PUNCT
ejpam-7119	246	11	2025	2025	NUM
ejpam-7119	246	12	.	.	PUNCT
ejpam-7119	247	1	[	[	X
ejpam-7119	247	2	16	16	NUM
ejpam-7119	247	3	]	]	X
ejpam-7119	247	4	a.	a.	NOUN
ejpam-7119	247	5	malkawi	malkawi	PROPN
ejpam-7119	247	6	.	.	PUNCT
ejpam-7119	248	1	enhanced	enhance	VERB
ejpam-7119	248	2	uncertainty	uncertainty	NOUN
ejpam-7119	248	3	modeling	model	VERB
ejpam-7119	248	4	through	through	ADP
ejpam-7119	248	5	neutrosophic	neutrosophic	ADJ
ejpam-7119	248	6	mr	mr	PROPN
ejpam-7119	248	7	-	-	PUNCT
ejpam-7119	248	8	metrics	metric	NOUN
ejpam-7119	248	9	:	:	PUNCT
ejpam-7119	248	10	a	a	DET
ejpam-7119	248	11	unified	unified	ADJ
ejpam-7119	248	12	framework	framework	NOUN
ejpam-7119	248	13	with	with	ADP
ejpam-7119	248	14	fuzzy	fuzzy	ADJ
ejpam-7119	248	15	embedding	embedding	NOUN
ejpam-7119	248	16	and	and	CCONJ
ejpam-7119	248	17	contraction	contraction	NOUN
ejpam-7119	248	18	principles	principle	NOUN
ejpam-7119	248	19	.	.	PUNCT
ejpam-7119	249	1	european	european	ADJ
ejpam-7119	249	2	journal	journal	PROPN
ejpam-7119	249	3	of	of	ADP
ejpam-7119	249	4	pure	pure	ADJ
ejpam-7119	249	5	and	and	CCONJ
ejpam-7119	249	6	applied	applied	ADJ
ejpam-7119	249	7	mathematics	mathematic	NOUN
ejpam-7119	249	8	,	,	PUNCT
ejpam-7119	249	9	18(3):id	18(3):id	NUM
ejpam-7119	249	10	:	:	SYM
ejpam-7119	249	11	6475	6475	NUM
ejpam-7119	249	12	,	,	PUNCT
ejpam-7119	249	13	2025	2025	NUM
ejpam-7119	249	14	.	.	PUNCT
ejpam-7119	250	1	[	[	X
ejpam-7119	250	2	17	17	NUM
ejpam-7119	250	3	]	]	X
ejpam-7119	250	4	al	al	PROPN
ejpam-7119	250	5	deiakeh	deiakeh	PROPN
ejpam-7119	250	6	r.	r.	PROPN
ejpam-7119	250	7	,	,	PUNCT
ejpam-7119	250	8	m.	m.	NOUN
ejpam-7119	250	9	alquran	alquran	PROPN
ejpam-7119	250	10	,	,	PUNCT
ejpam-7119	250	11	m.	m.	PROPN
ejpam-7119	250	12	ali	ali	PROPN
ejpam-7119	250	13	,	,	PUNCT
ejpam-7119	250	14	s.	s.	PROPN
ejpam-7119	250	15	qureshi	qureshi	PROPN
ejpam-7119	250	16	,	,	PUNCT
ejpam-7119	250	17	s.	s.	PROPN
ejpam-7119	250	18	momani	momani	PROPN
ejpam-7119	250	19	,	,	PUNCT
ejpam-7119	250	20	and	and	CCONJ
ejpam-7119	251	1	a.	a.	NOUN
ejpam-7119	251	2	a.	a.	PROPN
ejpam-7119	251	3	r.	r.	PROPN
ejpam-7119	251	4	malkawi	malkawi	PROPN
ejpam-7119	251	5	.	.	PROPN
ejpam-7119	251	6	lie	lie	PROPN
ejpam-7119	251	7	symmetry	symmetry	NOUN
ejpam-7119	251	8	,	,	PUNCT
ejpam-7119	251	9	convergence	convergence	NOUN
ejpam-7119	251	10	analysis	analysis	NOUN
ejpam-7119	251	11	,	,	PUNCT
ejpam-7119	251	12	explicit	explicit	ADJ
ejpam-7119	251	13	solutions	solution	NOUN
ejpam-7119	251	14	,	,	PUNCT
ejpam-7119	251	15	and	and	CCONJ
ejpam-7119	251	16	conservation	conservation	NOUN
ejpam-7119	251	17	laws	law	NOUN
ejpam-7119	251	18	for	for	ADP
ejpam-7119	251	19	the	the	DET
ejpam-7119	251	20	timefractional	timefractional	ADJ
ejpam-7119	251	21	modified	modify	VERB
ejpam-7119	251	22	benjamin	benjamin	PROPN
ejpam-7119	251	23	-	-	PUNCT
ejpam-7119	251	24	bona	bona	ADJ
ejpam-7119	251	25	-	-	PUNCT
ejpam-7119	251	26	mahony	mahony	NOUN
ejpam-7119	251	27	equation	equation	NOUN
ejpam-7119	251	28	.	.	PUNCT
ejpam-7119	252	1	journal	journal	PROPN
ejpam-7119	252	2	of	of	ADP
ejpam-7119	252	3	applied	apply	VERB
ejpam-7119	252	4	mathematics	mathematic	NOUN
ejpam-7119	252	5	and	and	CCONJ
ejpam-7119	252	6	computational	computational	ADJ
ejpam-7119	252	7	mechanics	mechanic	NOUN
ejpam-7119	252	8	,	,	PUNCT
ejpam-7119	252	9	23(1):19–31	23(1):19–31	NUM
ejpam-7119	252	10	,	,	PUNCT
ejpam-7119	252	11	2024	2024	NUM
ejpam-7119	252	12	.	.	PUNCT
ejpam-7119	253	1	[	[	X
ejpam-7119	253	2	18	18	NUM
ejpam-7119	253	3	]	]	X
ejpam-7119	253	4	g.m	g.m	PROPN
ejpam-7119	253	5	.	.	PUNCT
ejpam-7119	253	6	gharib	gharib	PROPN
ejpam-7119	253	7	,	,	PUNCT
ejpam-7119	253	8	m.s	m.s	PROPN
ejpam-7119	253	9	.	.	PROPN
ejpam-7119	253	10	alsauodi	alsauodi	PROPN
ejpam-7119	253	11	,	,	PUNCT
ejpam-7119	253	12	a.	a.	NOUN
ejpam-7119	253	13	guiatni	guiatni	PROPN
ejpam-7119	253	14	,	,	PUNCT
ejpam-7119	253	15	m.a	m.a	PROPN
ejpam-7119	253	16	.	.	PROPN
ejpam-7119	253	17	al	al	PROPN
ejpam-7119	253	18	-	-	PUNCT
ejpam-7119	253	19	omari	omari	PROPN
ejpam-7119	253	20	,	,	PUNCT
ejpam-7119	253	21	and	and	CCONJ
ejpam-7119	253	22	a.a.-r.m	a.a.-r.m	PROPN
ejpam-7119	253	23	.	.	PUNCT
ejpam-7119	254	1	malkawi	malkawi	PROPN
ejpam-7119	254	2	.	.	PUNCT
ejpam-7119	255	1	using	use	VERB
ejpam-7119	255	2	atomic	atomic	ADJ
ejpam-7119	255	3	solution	solution	NOUN
ejpam-7119	255	4	method	method	NOUN
ejpam-7119	255	5	to	to	PART
ejpam-7119	255	6	solve	solve	VERB
ejpam-7119	255	7	the	the	DET
ejpam-7119	255	8	fractional	fractional	ADJ
ejpam-7119	255	9	equations	equation	NOUN
ejpam-7119	255	10	.	.	PUNCT
ejpam-7119	256	1	springer	springer	NOUN
ejpam-7119	256	2	proceedings	proceeding	NOUN
ejpam-7119	256	3	in	in	ADP
ejpam-7119	256	4	mathematics	mathematic	NOUN
ejpam-7119	256	5	and	and	CCONJ
ejpam-7119	256	6	statistics	statistic	NOUN
ejpam-7119	256	7	,	,	PUNCT
ejpam-7119	256	8	418:123–129	418:123–129	NUM
ejpam-7119	256	9	,	,	PUNCT
ejpam-7119	256	10	2023	2023	NUM
ejpam-7119	256	11	.	.	PUNCT
ejpam-7119	257	1	[	[	X
ejpam-7119	257	2	19	19	NUM
ejpam-7119	257	3	]	]	PUNCT
ejpam-7119	257	4	abed	abed	PROPN
ejpam-7119	257	5	al	al	PROPN
ejpam-7119	257	6	-	-	PUNCT
ejpam-7119	257	7	rahman	rahman	PROPN
ejpam-7119	257	8	m.	m.	NOUN
ejpam-7119	257	9	malkawi	malkawi	PROPN
ejpam-7119	257	10	and	and	CCONJ
ejpam-7119	257	11	ayat	ayat	PROPN
ejpam-7119	257	12	m.	m.	PROPN
ejpam-7119	257	13	rabaiah	rabaiah	PROPN
ejpam-7119	257	14	.	.	PUNCT
ejpam-7119	258	1	mr	mr	PROPN
ejpam-7119	258	2	-	-	PUNCT
ejpam-7119	258	3	metric	metric	ADJ
ejpam-7119	258	4	spaces	space	NOUN
ejpam-7119	258	5	:	:	PUNCT
ejpam-7119	258	6	theory	theory	NOUN
ejpam-7119	258	7	and	and	CCONJ
ejpam-7119	258	8	applications	application	NOUN
ejpam-7119	258	9	in	in	ADP
ejpam-7119	258	10	fractional	fractional	ADJ
ejpam-7119	258	11	calculus	calculus	NOUN
ejpam-7119	258	12	and	and	CCONJ
ejpam-7119	258	13	fixed	fix	VERB
ejpam-7119	258	14	-	-	PUNCT
ejpam-7119	258	15	point	point	NOUN
ejpam-7119	258	16	theorems	theorem	NOUN
ejpam-7119	258	17	.	.	PUNCT
ejpam-7119	258	18	neutrosophic	neutrosophic	ADJ
ejpam-7119	258	19	sets	set	NOUN
ejpam-7119	258	20	and	and	CCONJ
ejpam-7119	258	21	systems	system	NOUN
ejpam-7119	258	22	,	,	PUNCT
ejpam-7119	258	23	90:1103–1121	90:1103–1121	NUM
ejpam-7119	258	24	,	,	PUNCT
ejpam-7119	258	25	2025	2025	NUM
ejpam-7119	258	26	.	.	PUNCT
ejpam-7119	259	1	[	[	X
ejpam-7119	259	2	20	20	NUM
ejpam-7119	259	3	]	]	PUNCT
ejpam-7119	259	4	abed	abed	PROPN
ejpam-7119	259	5	al	al	PROPN
ejpam-7119	259	6	-	-	PUNCT
ejpam-7119	259	7	rahman	rahman	PROPN
ejpam-7119	259	8	m.	m.	NOUN
ejpam-7119	259	9	malkawi	malkawi	PROPN
ejpam-7119	259	10	and	and	CCONJ
ejpam-7119	259	11	ayat	ayat	PROPN
ejpam-7119	259	12	m.	m.	PROPN
ejpam-7119	259	13	rabaiah	rabaiah	PROPN
ejpam-7119	259	14	.	.	PUNCT
ejpam-7119	260	1	mr	mr	PROPN
ejpam-7119	260	2	-	-	PUNCT
ejpam-7119	260	3	metric	metric	ADJ
ejpam-7119	260	4	spaces	space	NOUN
ejpam-7119	260	5	:	:	PUNCT
ejpam-7119	260	6	theory	theory	NOUN
ejpam-7119	260	7	and	and	CCONJ
ejpam-7119	260	8	applications	application	NOUN
ejpam-7119	260	9	in	in	ADP
ejpam-7119	260	10	fractional	fractional	ADJ
ejpam-7119	260	11	calculus	calculus	NOUN
ejpam-7119	260	12	and	and	CCONJ
ejpam-7119	260	13	fixed	fix	VERB
ejpam-7119	260	14	-	-	PUNCT
ejpam-7119	260	15	point	point	NOUN
ejpam-7119	260	16	theorems	theorem	NOUN
ejpam-7119	260	17	.	.	PUNCT
ejpam-7119	260	18	neutrosophic	neutrosophic	ADJ
ejpam-7119	260	19	sets	set	NOUN
ejpam-7119	260	20	and	and	CCONJ
ejpam-7119	260	21	systems	system	NOUN
ejpam-7119	260	22	,	,	PUNCT
ejpam-7119	260	23	91:685–703	91:685–703	PROPN
ejpam-7119	260	24	,	,	PUNCT
ejpam-7119	260	25	2025	2025	NUM
ejpam-7119	260	26	.	.	PUNCT
ejpam-7119	261	1	[	[	X
ejpam-7119	261	2	21	21	NUM
ejpam-7119	261	3	]	]	PUNCT
ejpam-7119	261	4	t.	t.	NOUN
ejpam-7119	261	5	qawasmeh	qawasmeh	NOUN
ejpam-7119	261	6	.	.	PUNCT
ejpam-7119	262	1	(	(	PUNCT
ejpam-7119	262	2	h	h	NOUN
ejpam-7119	262	3	,	,	PUNCT
ejpam-7119	262	4	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-7119	262	5	contractions	contraction	NOUN
ejpam-7119	262	6	in	in	ADP
ejpam-7119	262	7	ωb	ωb	NOUN
ejpam-7119	262	8	-	-	PUNCT
ejpam-7119	262	9	distance	distance	NOUN
ejpam-7119	262	10	mappings	mapping	NOUN
ejpam-7119	262	11	with	with	ADP
ejpam-7119	262	12	applications	application	NOUN
ejpam-7119	262	13	.	.	PUNCT
ejpam-7119	263	1	european	european	ADJ
ejpam-7119	263	2	journal	journal	PROPN
ejpam-7119	263	3	of	of	ADP
ejpam-7119	263	4	pure	pure	ADJ
ejpam-7119	263	5	and	and	CCONJ
ejpam-7119	263	6	applied	applied	ADJ
ejpam-7119	263	7	mathematics	mathematic	NOUN
ejpam-7119	263	8	,	,	PUNCT
ejpam-7119	263	9	16(3):1717–1730	16(3):1717–1730	NUM
ejpam-7119	263	10	,	,	PUNCT
ejpam-7119	263	11	2023	2023	NUM
ejpam-7119	263	12	.	.	PUNCT
ejpam-7119	264	1	[	[	X
ejpam-7119	264	2	22	22	NUM
ejpam-7119	264	3	]	]	PUNCT
ejpam-7119	264	4	t.	t.	NOUN
ejpam-7119	264	5	qawasmeh	qawasmeh	NOUN
ejpam-7119	264	6	.	.	PUNCT
ejpam-7119	265	1	h	h	NOUN
ejpam-7119	265	2	-	-	PUNCT
ejpam-7119	265	3	simulation	simulation	NOUN
ejpam-7119	265	4	functions	function	NOUN
ejpam-7119	265	5	and	and	CCONJ
ejpam-7119	265	6	ωb	ωb	NOUN
ejpam-7119	265	7	-	-	PUNCT
ejpam-7119	265	8	distance	distance	NOUN
ejpam-7119	265	9	mappings	mapping	NOUN
ejpam-7119	265	10	in	in	ADP
ejpam-7119	265	11	the	the	DET
ejpam-7119	265	12	setting	setting	NOUN
ejpam-7119	265	13	of	of	ADP
ejpam-7119	265	14	gb	gb	ADV
ejpam-7119	265	15	-	-	PUNCT
ejpam-7119	265	16	metric	metric	ADJ
ejpam-7119	265	17	spaces	space	NOUN
ejpam-7119	265	18	and	and	CCONJ
ejpam-7119	265	19	application	application	NOUN
ejpam-7119	265	20	.	.	PUNCT
ejpam-7119	266	1	nonlinear	nonlinear	ADJ
ejpam-7119	266	2	functional	functional	ADJ
ejpam-7119	266	3	analysis	analysis	NOUN
ejpam-7119	266	4	and	and	CCONJ
ejpam-7119	266	5	applications	application	NOUN
ejpam-7119	266	6	,	,	PUNCT
ejpam-7119	266	7	28(2):557–570	28(2):557–570	NOUN
ejpam-7119	266	8	,	,	PUNCT
ejpam-7119	266	9	2023	2023	NUM
ejpam-7119	266	10	.	.	PUNCT
ejpam-7119	267	1	[	[	X
ejpam-7119	267	2	23	23	NUM
ejpam-7119	267	3	]	]	PUNCT
ejpam-7119	267	4	a.	a.	NOUN
ejpam-7119	267	5	bataihah	bataihah	PROPN
ejpam-7119	267	6	,	,	PUNCT
ejpam-7119	267	7	t.	t.	NOUN
ejpam-7119	267	8	qawasmeh	qawasmeh	NOUN
ejpam-7119	267	9	,	,	PUNCT
ejpam-7119	267	10	i.	i.	PROPN
ejpam-7119	267	11	batiha	batiha	PROPN
ejpam-7119	267	12	,	,	PUNCT
ejpam-7119	267	13	i.	i.	PROPN
ejpam-7119	267	14	m.	m.	PROPN
ejpam-7119	267	15	batiha	batiha	PROPN
ejpam-7119	267	16	,	,	PUNCT
ejpam-7119	267	17	and	and	CCONJ
ejpam-7119	267	18	t.	t.	PROPN
ejpam-7119	267	19	abdeljawad	abdeljawad	NOUN
ejpam-7119	267	20	.	.	PUNCT
ejpam-7119	268	1	gamma	gamma	NOUN
ejpam-7119	268	2	distance	distance	NOUN
ejpam-7119	268	3	mappings	mapping	NOUN
ejpam-7119	268	4	with	with	ADP
ejpam-7119	268	5	application	application	NOUN
ejpam-7119	268	6	to	to	ADP
ejpam-7119	268	7	fractional	fractional	ADJ
ejpam-7119	268	8	boundary	boundary	ADJ
ejpam-7119	268	9	differential	differential	NOUN
ejpam-7119	268	10	equation	equation	NOUN
ejpam-7119	268	11	.	.	PUNCT
ejpam-7119	269	1	journal	journal	PROPN
ejpam-7119	269	2	of	of	ADP
ejpam-7119	269	3	mathematical	mathematical	ADJ
ejpam-7119	269	4	analysis	analysis	NOUN
ejpam-7119	269	5	,	,	PUNCT
ejpam-7119	269	6	15(5):99–106	15(5):99–106	NUM
ejpam-7119	269	7	,	,	PUNCT
ejpam-7119	269	8	2024	2024	NUM
ejpam-7119	269	9	.	.	PUNCT
ejpam-7119	270	1	[	[	X
ejpam-7119	270	2	24	24	NUM
ejpam-7119	270	3	]	]	PUNCT
ejpam-7119	270	4	a.	a.	NOUN
ejpam-7119	270	5	bataihah	bataihah	PROPN
ejpam-7119	270	6	,	,	PUNCT
ejpam-7119	270	7	a.	a.	NOUN
ejpam-7119	270	8	tallafha	tallafha	NOUN
ejpam-7119	270	9	,	,	PUNCT
ejpam-7119	270	10	and	and	CCONJ
ejpam-7119	270	11	w.	w.	PROPN
ejpam-7119	270	12	shatanawi	shatanawi	PROPN
ejpam-7119	270	13	.	.	PUNCT
ejpam-7119	271	1	fixed	fix	VERB
ejpam-7119	271	2	point	point	NOUN
ejpam-7119	271	3	results	result	NOUN
ejpam-7119	271	4	with	with	ADP
ejpam-7119	271	5	ω	ω	NOUN
ejpam-7119	271	6	-	-	PUNCT
ejpam-7119	271	7	distance	distance	NOUN
ejpam-7119	271	8	by	by	ADP
ejpam-7119	271	9	utilizing	utilize	VERB
ejpam-7119	271	10	simulation	simulation	NOUN
ejpam-7119	271	11	functions	function	NOUN
ejpam-7119	271	12	.	.	PUNCT
ejpam-7119	272	1	ital	ital	PROPN
ejpam-7119	272	2	.	.	PUNCT
ejpam-7119	273	1	j.	j.	PROPN
ejpam-7119	273	2	pure	pure	PROPN
ejpam-7119	273	3	appl	appl	PROPN
ejpam-7119	273	4	.	.	PROPN
ejpam-7119	273	5	math	math	PROPN
ejpam-7119	273	6	,	,	PUNCT
ejpam-7119	273	7	(	(	PUNCT
ejpam-7119	273	8	43):185–196	43):185–196	NUM
ejpam-7119	273	9	,	,	PUNCT
ejpam-7119	273	10	2017	2017	NUM
ejpam-7119	273	11	.	.	PUNCT
ejpam-7119	274	1	[	[	X
ejpam-7119	274	2	25	25	NUM
ejpam-7119	274	3	]	]	PUNCT
ejpam-7119	274	4	wasfi	wasfi	NOUN
ejpam-7119	274	5	shatanawi	shatanawi	PROPN
ejpam-7119	274	6	,	,	PUNCT
ejpam-7119	274	7	georgeta	georgeta	PROPN
ejpam-7119	274	8	maniu	maniu	PROPN
ejpam-7119	274	9	,	,	PUNCT
ejpam-7119	274	10	anwar	anwar	PROPN
ejpam-7119	274	11	bataihah	bataihah	PROPN
ejpam-7119	274	12	,	,	PUNCT
ejpam-7119	274	13	and	and	CCONJ
ejpam-7119	274	14	f.b	f.b	PROPN
ejpam-7119	274	15	ahmad	ahmad	PROPN
ejpam-7119	274	16	.	.	PUNCT
ejpam-7119	275	1	common	common	ADJ
ejpam-7119	275	2	fixed	fix	VERB
ejpam-7119	275	3	points	point	NOUN
ejpam-7119	275	4	for	for	ADP
ejpam-7119	275	5	mappings	mapping	NOUN
ejpam-7119	275	6	of	of	ADP
ejpam-7119	275	7	cyclic	cyclic	ADJ
ejpam-7119	275	8	form	form	NOUN
ejpam-7119	275	9	satisfying	satisfy	VERB
ejpam-7119	275	10	linear	linear	PROPN
ejpam-7119	275	11	contractive	contractive	ADJ
ejpam-7119	275	12	conditions	condition	NOUN
ejpam-7119	275	13	with	with	ADP
ejpam-7119	275	14	omegadistance	omegadistance	NOUN
ejpam-7119	275	15	.	.	PUNCT
ejpam-7119	276	1	upb	upb	ADJ
ejpam-7119	276	2	scientific	scientific	ADJ
ejpam-7119	276	3	bulletin	bulletin	NOUN
ejpam-7119	276	4	,	,	PUNCT
ejpam-7119	276	5	series	series	PROPN
ejpam-7119	276	6	a	a	PRON
ejpam-7119	276	7	:	:	PUNCT
ejpam-7119	276	8	applied	apply	VERB
ejpam-7119	276	9	mathematics	mathematic	NOUN
ejpam-7119	276	10	and	and	CCONJ
ejpam-7119	276	11	physics	physics	NOUN
ejpam-7119	276	12	,	,	PUNCT
ejpam-7119	276	13	79:11–20	79:11–20	NUM
ejpam-7119	276	14	,	,	PUNCT
ejpam-7119	276	15	2017	2017	NUM
ejpam-7119	276	16	.	.	PUNCT
ejpam-7119	277	1	[	[	X
ejpam-7119	277	2	26	26	NUM
ejpam-7119	277	3	]	]	PUNCT
ejpam-7119	277	4	t.	t.	NOUN
ejpam-7119	277	5	qawasmeh	qawasmeh	NOUN
ejpam-7119	277	6	,	,	PUNCT
ejpam-7119	277	7	w.	w.	PROPN
ejpam-7119	277	8	shatanawi	shatanawi	PROPN
ejpam-7119	277	9	,	,	PUNCT
ejpam-7119	277	10	a.	a.	NOUN
ejpam-7119	277	11	bataihah	bataihah	PROPN
ejpam-7119	277	12	,	,	PUNCT
ejpam-7119	277	13	and	and	CCONJ
ejpam-7119	277	14	a.	a.	NOUN
ejpam-7119	277	15	tallafha	tallafha	NOUN
ejpam-7119	277	16	.	.	PUNCT
ejpam-7119	278	1	common	common	ADJ
ejpam-7119	278	2	fixed	fix	VERB
ejpam-7119	278	3	point	point	NOUN
ejpam-7119	278	4	results	result	NOUN
ejpam-7119	278	5	for	for	ADP
ejpam-7119	278	6	a.	a.	NOUN
ejpam-7119	278	7	malkawi	malkawi	PROPN
ejpam-7119	278	8	,	,	PUNCT
ejpam-7119	278	9	a.	a.	PROPN
ejpam-7119	278	10	rabaiah	rabaiah	PROPN
ejpam-7119	278	11	/	/	SYM
ejpam-7119	278	12	eur	eur	PROPN
ejpam-7119	278	13	.	.	PUNCT
ejpam-7119	279	1	j.	j.	PROPN
ejpam-7119	279	2	pure	pure	PROPN
ejpam-7119	279	3	appl	appl	PROPN
ejpam-7119	279	4	.	.	PROPN
ejpam-7119	279	5	math	math	PROPN
ejpam-7119	279	6	,	,	PUNCT
ejpam-7119	279	7	18	18	NUM
ejpam-7119	279	8	(	(	PUNCT
ejpam-7119	279	9	4	4	NUM
ejpam-7119	279	10	)	)	PUNCT
ejpam-7119	279	11	(	(	PUNCT
ejpam-7119	279	12	2025	2025	NUM
ejpam-7119	279	13	)	)	PUNCT
ejpam-7119	279	14	,	,	PUNCT
ejpam-7119	279	15	7119	7119	NUM
ejpam-7119	279	16	12	12	NUM
ejpam-7119	279	17	of	of	ADP
ejpam-7119	279	18	13	13	NUM
ejpam-7119	279	19	rational	rational	ADJ
ejpam-7119	279	20	(	(	PUNCT
ejpam-7119	279	21	α	α	NOUN
ejpam-7119	279	22	,	,	PUNCT
ejpam-7119	279	23	β)ϕ-mω	β)ϕ-mω	NOUN
ejpam-7119	279	24	contractions	contraction	NOUN
ejpam-7119	279	25	in	in	ADP
ejpam-7119	279	26	complete	complete	ADJ
ejpam-7119	279	27	quasi	quasi	ADJ
ejpam-7119	279	28	metric	metric	ADJ
ejpam-7119	279	29	spaces	space	NOUN
ejpam-7119	279	30	.	.	PUNCT
ejpam-7119	280	1	mathematics	mathematic	NOUN
ejpam-7119	280	2	,	,	PUNCT
ejpam-7119	280	3	7(5):392	7(5):392	NUM
ejpam-7119	280	4	,	,	PUNCT
ejpam-7119	280	5	2019	2019	NUM
ejpam-7119	280	6	.	.	PUNCT
ejpam-7119	281	1	[	[	X
ejpam-7119	281	2	27	27	NUM
ejpam-7119	281	3	]	]	PUNCT
ejpam-7119	281	4	wasfi	wasfi	NOUN
ejpam-7119	281	5	shatanawi	shatanawi	PROPN
ejpam-7119	281	6	,	,	PUNCT
ejpam-7119	281	7	anwar	anwar	PROPN
ejpam-7119	281	8	bataihah	bataihah	PROPN
ejpam-7119	281	9	,	,	PUNCT
ejpam-7119	281	10	and	and	CCONJ
ejpam-7119	281	11	ariana	ariana	PROPN
ejpam-7119	281	12	pitea	pitea	NOUN
ejpam-7119	281	13	.	.	PUNCT
ejpam-7119	282	1	fixed	fix	VERB
ejpam-7119	282	2	and	and	CCONJ
ejpam-7119	282	3	common	common	ADJ
ejpam-7119	282	4	fixed	fix	VERB
ejpam-7119	282	5	point	point	NOUN
ejpam-7119	282	6	results	result	NOUN
ejpam-7119	282	7	for	for	ADP
ejpam-7119	282	8	cyclic	cyclic	ADJ
ejpam-7119	282	9	mappings	mapping	NOUN
ejpam-7119	282	10	of	of	ADP
ejpam-7119	282	11	ω	ω	NOUN
ejpam-7119	282	12	-	-	PUNCT
ejpam-7119	282	13	distance	distance	NOUN
ejpam-7119	282	14	.	.	PUNCT
ejpam-7119	283	1	journal	journal	PROPN
ejpam-7119	283	2	of	of	ADP
ejpam-7119	283	3	nonlinear	nonlinear	ADJ
ejpam-7119	283	4	science	science	NOUN
ejpam-7119	283	5	and	and	CCONJ
ejpam-7119	283	6	applications	application	NOUN
ejpam-7119	283	7	,	,	PUNCT
ejpam-7119	283	8	9:727–735	9:727–735	NUM
ejpam-7119	283	9	,	,	PUNCT
ejpam-7119	283	10	2016	2016	NUM
ejpam-7119	283	11	.	.	PUNCT
ejpam-7119	284	1	[	[	X
ejpam-7119	284	2	28	28	NUM
ejpam-7119	284	3	]	]	PUNCT
ejpam-7119	284	4	a.	a.	NOUN
ejpam-7119	284	5	rabaiah	rabaiah	PROPN
ejpam-7119	284	6	,	,	PUNCT
ejpam-7119	284	7	a.	a.	NOUN
ejpam-7119	284	8	tallafha	tallafha	NOUN
ejpam-7119	284	9	,	,	PUNCT
ejpam-7119	284	10	and	and	CCONJ
ejpam-7119	284	11	w.	w.	PROPN
ejpam-7119	284	12	shatanawi	shatanawi	PROPN
ejpam-7119	284	13	.	.	PUNCT
ejpam-7119	285	1	common	common	ADJ
ejpam-7119	285	2	fixed	fix	VERB
ejpam-7119	285	3	point	point	NOUN
ejpam-7119	285	4	results	result	NOUN
ejpam-7119	285	5	for	for	ADP
ejpam-7119	285	6	mappings	mapping	NOUN
ejpam-7119	285	7	under	under	ADP
ejpam-7119	285	8	nonlinear	nonlinear	ADJ
ejpam-7119	285	9	contraction	contraction	NOUN
ejpam-7119	285	10	of	of	ADP
ejpam-7119	285	11	cyclic	cyclic	ADJ
ejpam-7119	285	12	form	form	NOUN
ejpam-7119	285	13	in	in	ADP
ejpam-7119	285	14	b	b	NOUN
ejpam-7119	285	15	-	-	ADJ
ejpam-7119	285	16	metric	metric	ADJ
ejpam-7119	285	17	spaces	space	NOUN
ejpam-7119	285	18	.	.	PUNCT
ejpam-7119	286	1	advances	advance	NOUN
ejpam-7119	286	2	in	in	ADP
ejpam-7119	286	3	mathematics	mathematics	NOUN
ejpam-7119	286	4	scientific	scientific	ADJ
ejpam-7119	286	5	journal	journal	NOUN
ejpam-7119	286	6	,	,	PUNCT
ejpam-7119	286	7	26(2):289–301	26(2):289–301	PROPN
ejpam-7119	286	8	,	,	PUNCT
ejpam-7119	286	9	2021	2021	NUM
ejpam-7119	286	10	.	.	PUNCT
ejpam-7119	287	1	[	[	X
ejpam-7119	287	2	29	29	NUM
ejpam-7119	287	3	]	]	X
ejpam-7119	287	4	i.	i.	PROPN
ejpam-7119	287	5	abu	abu	PROPN
ejpam-7119	287	6	-	-	PUNCT
ejpam-7119	287	7	irwaq	irwaq	PROPN
ejpam-7119	287	8	,	,	PUNCT
ejpam-7119	287	9	w.	w.	PROPN
ejpam-7119	287	10	shatanawi	shatanawi	PROPN
ejpam-7119	287	11	,	,	PUNCT
ejpam-7119	287	12	a.	a.	NOUN
ejpam-7119	287	13	bataihah	bataihah	PROPN
ejpam-7119	287	14	,	,	PUNCT
ejpam-7119	287	15	and	and	CCONJ
ejpam-7119	287	16	i.	i.	PROPN
ejpam-7119	287	17	nuseir	nuseir	PROPN
ejpam-7119	287	18	.	.	PUNCT
ejpam-7119	288	1	fixed	fix	VERB
ejpam-7119	288	2	point	point	NOUN
ejpam-7119	288	3	results	result	NOUN
ejpam-7119	288	4	for	for	ADP
ejpam-7119	288	5	nonlinear	nonlinear	ADJ
ejpam-7119	288	6	contractions	contraction	NOUN
ejpam-7119	288	7	with	with	ADP
ejpam-7119	288	8	generalized	generalized	ADJ
ejpam-7119	288	9	ω	ω	NUM
ejpam-7119	288	10	-	-	PUNCT
ejpam-7119	288	11	distance	distance	NOUN
ejpam-7119	288	12	mappings	mapping	NOUN
ejpam-7119	288	13	.	.	PUNCT
ejpam-7119	289	1	upb	upb	PROPN
ejpam-7119	289	2	sci	sci	PROPN
ejpam-7119	289	3	.	.	PUNCT
ejpam-7119	289	4	bull	bull	PROPN
ejpam-7119	289	5	.	.	PUNCT
ejpam-7119	290	1	ser	ser	PROPN
ejpam-7119	290	2	.	.	PUNCT
ejpam-7119	291	1	a	a	DET
ejpam-7119	291	2	,	,	PUNCT
ejpam-7119	291	3	81(1):57–64	81(1):57–64	NUM
ejpam-7119	291	4	,	,	PUNCT
ejpam-7119	291	5	2019	2019	NUM
ejpam-7119	291	6	.	.	PUNCT
ejpam-7119	292	1	[	[	X
ejpam-7119	292	2	30	30	NUM
ejpam-7119	292	3	]	]	X
ejpam-7119	292	4	g.	g.	PROPN
ejpam-7119	292	5	gharib	gharib	PROPN
ejpam-7119	292	6	,	,	PUNCT
ejpam-7119	292	7	a.	a.	PROPN
ejpam-7119	292	8	malkawi	malkawi	PROPN
ejpam-7119	292	9	,	,	PUNCT
ejpam-7119	292	10	a.	a.	PROPN
ejpam-7119	292	11	rabaiah	rabaiah	PROPN
ejpam-7119	292	12	,	,	PUNCT
ejpam-7119	292	13	w.	w.	PROPN
ejpam-7119	292	14	shatanawi	shatanawi	PROPN
ejpam-7119	292	15	,	,	PUNCT
ejpam-7119	292	16	and	and	CCONJ
ejpam-7119	292	17	m.	m.	NOUN
ejpam-7119	292	18	alsauodi	alsauodi	PROPN
ejpam-7119	292	19	.	.	PUNCT
ejpam-7119	293	1	a	a	DET
ejpam-7119	293	2	common	common	ADJ
ejpam-7119	293	3	fixed	fix	VERB
ejpam-7119	293	4	point	point	NOUN
ejpam-7119	293	5	theorem	theorem	VERB
ejpam-7119	293	6	in	in	ADP
ejpam-7119	293	7	m*-metric	m*-metric	ADV
ejpam-7119	293	8	space	space	NOUN
ejpam-7119	293	9	and	and	CCONJ
ejpam-7119	293	10	an	an	DET
ejpam-7119	293	11	application	application	NOUN
ejpam-7119	293	12	.	.	PUNCT
ejpam-7119	294	1	nonlinear	nonlinear	ADJ
ejpam-7119	294	2	functional	functional	ADJ
ejpam-7119	294	3	analysis	analysis	NOUN
ejpam-7119	294	4	and	and	CCONJ
ejpam-7119	294	5	applications	application	NOUN
ejpam-7119	294	6	,	,	PUNCT
ejpam-7119	294	7	27(2):289–308	27(2):289–308	NUM
ejpam-7119	294	8	,	,	PUNCT
ejpam-7119	294	9	2022	2022	NUM
ejpam-7119	294	10	.	.	PUNCT
ejpam-7119	295	1	[	[	X
ejpam-7119	295	2	31	31	NUM
ejpam-7119	295	3	]	]	X
ejpam-7119	295	4	a.	a.	NOUN
ejpam-7119	295	5	malkawi	malkawi	PROPN
ejpam-7119	295	6	,	,	PUNCT
ejpam-7119	295	7	a.	a.	NOUN
ejpam-7119	295	8	tallafha	tallafha	NOUN
ejpam-7119	295	9	,	,	PUNCT
ejpam-7119	295	10	and	and	CCONJ
ejpam-7119	295	11	w.	w.	PROPN
ejpam-7119	295	12	shatanawi	shatanawi	PROPN
ejpam-7119	295	13	.	.	PUNCT
ejpam-7119	296	1	coincidence	coincidence	NOUN
ejpam-7119	296	2	and	and	CCONJ
ejpam-7119	296	3	fixed	fix	VERB
ejpam-7119	296	4	point	point	NOUN
ejpam-7119	296	5	results	result	NOUN
ejpam-7119	296	6	for	for	ADP
ejpam-7119	296	7	generalized	generalized	ADJ
ejpam-7119	296	8	weak	weak	ADJ
ejpam-7119	296	9	contraction	contraction	NOUN
ejpam-7119	296	10	mapping	mapping	NOUN
ejpam-7119	296	11	on	on	ADP
ejpam-7119	296	12	b	b	NOUN
ejpam-7119	296	13	-	-	PUNCT
ejpam-7119	296	14	metric	metric	ADJ
ejpam-7119	296	15	spaces	space	NOUN
ejpam-7119	296	16	.	.	PUNCT
ejpam-7119	297	1	nonlinear	nonlinear	ADJ
ejpam-7119	297	2	functional	functional	ADJ
ejpam-7119	297	3	analysis	analysis	NOUN
ejpam-7119	297	4	and	and	CCONJ
ejpam-7119	297	5	applications	application	NOUN
ejpam-7119	297	6	,	,	PUNCT
ejpam-7119	297	7	26(1):177–195	26(1):177–195	NOUN
ejpam-7119	297	8	,	,	PUNCT
ejpam-7119	297	9	2021	2021	NUM
ejpam-7119	297	10	.	.	PUNCT
ejpam-7119	298	1	[	[	X
ejpam-7119	298	2	32	32	NUM
ejpam-7119	298	3	]	]	PUNCT
ejpam-7119	298	4	abed	abed	PROPN
ejpam-7119	298	5	al	al	PROPN
ejpam-7119	298	6	-	-	PUNCT
ejpam-7119	298	7	rahman	rahman	PROPN
ejpam-7119	298	8	m.	m.	PROPN
ejpam-7119	298	9	malkawi	malkawi	PROPN
ejpam-7119	298	10	.	.	PUNCT
ejpam-7119	298	11	fixed	fix	VERB
ejpam-7119	298	12	point	point	NOUN
ejpam-7119	298	13	theorems	theorem	NOUN
ejpam-7119	298	14	for	for	ADP
ejpam-7119	298	15	fuzzy	fuzzy	ADJ
ejpam-7119	298	16	mappings	mapping	NOUN
ejpam-7119	298	17	in	in	ADP
ejpam-7119	298	18	neutrosophic	neutrosophic	ADJ
ejpam-7119	298	19	mr	mr	PROPN
ejpam-7119	298	20	-	-	PUNCT
ejpam-7119	298	21	metric	metric	ADJ
ejpam-7119	298	22	spaces	space	NOUN
ejpam-7119	298	23	.	.	PUNCT
ejpam-7119	299	1	journal	journal	PROPN
ejpam-7119	299	2	of	of	ADP
ejpam-7119	299	3	nonlinear	nonlinear	ADJ
ejpam-7119	299	4	modeling	modeling	NOUN
ejpam-7119	299	5	and	and	CCONJ
ejpam-7119	299	6	analysis	analysis	NOUN
ejpam-7119	299	7	,	,	PUNCT
ejpam-7119	299	8	acceptance	acceptance	NOUN
ejpam-7119	299	9	,	,	PUNCT
ejpam-7119	299	10	2025	2025	NUM
ejpam-7119	299	11	.	.	PUNCT
ejpam-7119	300	1	[	[	X
ejpam-7119	300	2	33	33	NUM
ejpam-7119	300	3	]	]	X
ejpam-7119	300	4	anwar	anwar	PROPN
ejpam-7119	300	5	bataihah	bataihah	PROPN
ejpam-7119	300	6	,	,	PUNCT
ejpam-7119	300	7	tariq	tariq	NOUN
ejpam-7119	300	8	qawasmeh	qawasmeh	NOUN
ejpam-7119	300	9	,	,	PUNCT
ejpam-7119	300	10	and	and	CCONJ
ejpam-7119	300	11	mutaz	mutaz	NOUN
ejpam-7119	300	12	shatnawi	shatnawi	ADJ
ejpam-7119	300	13	.	.	PUNCT
ejpam-7119	301	1	discussion	discussion	NOUN
ejpam-7119	301	2	on	on	ADP
ejpam-7119	301	3	b	b	X
ejpam-7119	301	4	-	-	ADJ
ejpam-7119	301	5	metric	metric	ADJ
ejpam-7119	301	6	spaces	space	NOUN
ejpam-7119	301	7	and	and	CCONJ
ejpam-7119	301	8	related	relate	VERB
ejpam-7119	301	9	results	result	NOUN
ejpam-7119	301	10	in	in	ADP
ejpam-7119	301	11	metric	metric	ADJ
ejpam-7119	301	12	and	and	CCONJ
ejpam-7119	301	13	g	g	NOUN
ejpam-7119	301	14	-	-	PUNCT
ejpam-7119	301	15	metric	metric	ADJ
ejpam-7119	301	16	spaces	space	NOUN
ejpam-7119	301	17	.	.	PUNCT
ejpam-7119	302	1	nonlinear	nonlinear	ADJ
ejpam-7119	302	2	functional	functional	ADJ
ejpam-7119	302	3	analysis	analysis	NOUN
ejpam-7119	302	4	and	and	CCONJ
ejpam-7119	302	5	applications	application	NOUN
ejpam-7119	302	6	,	,	PUNCT
ejpam-7119	302	7	27:233–247	27:233–247	NUM
ejpam-7119	302	8	,	,	PUNCT
ejpam-7119	302	9	2022	2022	NUM
ejpam-7119	302	10	.	.	PUNCT
ejpam-7119	303	1	[	[	X
ejpam-7119	303	2	34	34	NUM
ejpam-7119	303	3	]	]	SYM
ejpam-7119	303	4	a.	a.	NOUN
ejpam-7119	303	5	bataihah	bataihah	PROPN
ejpam-7119	303	6	and	and	CCONJ
ejpam-7119	303	7	t.	t.	NOUN
ejpam-7119	303	8	qawasmeh	qawasmeh	NOUN
ejpam-7119	303	9	.	.	PUNCT
ejpam-7119	304	1	a	a	DET
ejpam-7119	304	2	new	new	ADJ
ejpam-7119	304	3	type	type	NOUN
ejpam-7119	304	4	of	of	ADP
ejpam-7119	304	5	distance	distance	NOUN
ejpam-7119	304	6	spaces	space	NOUN
ejpam-7119	304	7	and	and	CCONJ
ejpam-7119	304	8	fixed	fix	VERB
ejpam-7119	304	9	point	point	NOUN
ejpam-7119	304	10	results	result	NOUN
ejpam-7119	304	11	.	.	PUNCT
ejpam-7119	305	1	journal	journal	NOUN
ejpam-7119	305	2	of	of	ADP
ejpam-7119	305	3	mathematical	mathematical	ADJ
ejpam-7119	305	4	analysis	analysis	NOUN
ejpam-7119	305	5	,	,	PUNCT
ejpam-7119	305	6	15(4):81–90	15(4):81–90	NUM
ejpam-7119	305	7	,	,	PUNCT
ejpam-7119	305	8	2024	2024	NUM
ejpam-7119	305	9	.	.	PUNCT
ejpam-7119	306	1	[	[	X
ejpam-7119	306	2	35	35	NUM
ejpam-7119	306	3	]	]	PUNCT
ejpam-7119	306	4	a.	a.	NOUN
ejpam-7119	306	5	bataihah	bataihah	PROPN
ejpam-7119	306	6	.	.	PUNCT
ejpam-7119	307	1	some	some	DET
ejpam-7119	307	2	fixed	fix	VERB
ejpam-7119	307	3	point	point	NOUN
ejpam-7119	307	4	results	result	NOUN
ejpam-7119	307	5	with	with	ADP
ejpam-7119	307	6	application	application	NOUN
ejpam-7119	307	7	to	to	ADP
ejpam-7119	307	8	fractional	fractional	ADJ
ejpam-7119	307	9	differential	differential	ADJ
ejpam-7119	307	10	equation	equation	NOUN
ejpam-7119	307	11	via	via	ADP
ejpam-7119	307	12	new	new	ADJ
ejpam-7119	307	13	type	type	NOUN
ejpam-7119	307	14	of	of	ADP
ejpam-7119	307	15	distance	distance	NOUN
ejpam-7119	307	16	spaces	space	NOUN
ejpam-7119	307	17	.	.	PUNCT
ejpam-7119	308	1	results	result	NOUN
ejpam-7119	308	2	in	in	ADP
ejpam-7119	308	3	nonlinear	nonlinear	ADJ
ejpam-7119	308	4	analysis	analysis	NOUN
ejpam-7119	308	5	,	,	PUNCT
ejpam-7119	308	6	7:202–208	7:202–208	NUM
ejpam-7119	308	7	,	,	PUNCT
ejpam-7119	308	8	2024	2024	NUM
ejpam-7119	308	9	.	.	PUNCT
ejpam-7119	309	1	[	[	X
ejpam-7119	309	2	36	36	NUM
ejpam-7119	309	3	]	]	X
ejpam-7119	309	4	bataihah	bataihah	PROPN
ejpam-7119	309	5	,	,	PUNCT
ejpam-7119	309	6	t.	t.	NOUN
ejpam-7119	309	7	qawasmeh	qawasmeh	NOUN
ejpam-7119	309	8	,	,	PUNCT
ejpam-7119	309	9	i.	i.	PROPN
ejpam-7119	309	10	batiha	batiha	PROPN
ejpam-7119	309	11	,	,	PUNCT
ejpam-7119	309	12	i.	i.	PROPN
ejpam-7119	309	13	m.	m.	PROPN
ejpam-7119	309	14	batiha	batiha	PROPN
ejpam-7119	309	15	,	,	PUNCT
ejpam-7119	309	16	and	and	CCONJ
ejpam-7119	309	17	t.	t.	PROPN
ejpam-7119	309	18	abdeljawad	abdeljawad	NOUN
ejpam-7119	309	19	.	.	PUNCT
ejpam-7119	310	1	gamma	gamma	NOUN
ejpam-7119	310	2	distance	distance	NOUN
ejpam-7119	310	3	mappings	mapping	NOUN
ejpam-7119	310	4	with	with	ADP
ejpam-7119	310	5	application	application	NOUN
ejpam-7119	310	6	to	to	ADP
ejpam-7119	310	7	fractional	fractional	ADJ
ejpam-7119	310	8	boundary	boundary	ADJ
ejpam-7119	310	9	differential	differential	NOUN
ejpam-7119	310	10	equation	equation	NOUN
ejpam-7119	310	11	.	.	PUNCT
ejpam-7119	311	1	journal	journal	PROPN
ejpam-7119	311	2	of	of	ADP
ejpam-7119	311	3	mathematical	mathematical	ADJ
ejpam-7119	311	4	analysis	analysis	NOUN
ejpam-7119	311	5	,	,	PUNCT
ejpam-7119	311	6	15(5):99–106	15(5):99–106	NUM
ejpam-7119	311	7	,	,	PUNCT
ejpam-7119	311	8	2024	2024	NUM
ejpam-7119	311	9	.	.	PUNCT
ejpam-7119	312	1	[	[	X
ejpam-7119	312	2	37	37	NUM
ejpam-7119	312	3	]	]	PUNCT
ejpam-7119	312	4	a.	a.	PROPN
ejpam-7119	312	5	al	al	PROPN
ejpam-7119	312	6	-	-	PUNCT
ejpam-7119	312	7	zghoul	zghoul	PROPN
ejpam-7119	312	8	,	,	PUNCT
ejpam-7119	312	9	t.	t.	NOUN
ejpam-7119	312	10	qawasmeh	qawasmeh	NOUN
ejpam-7119	312	11	,	,	PUNCT
ejpam-7119	312	12	r.	r.	PROPN
ejpam-7119	312	13	hatamleh	hatamleh	PROPN
ejpam-7119	312	14	,	,	PUNCT
ejpam-7119	312	15	and	and	CCONJ
ejpam-7119	312	16	a.	a.	NOUN
ejpam-7119	312	17	alhazimeh	alhazimeh	NOUN
ejpam-7119	312	18	.	.	PUNCT
ejpam-7119	313	1	a	a	DET
ejpam-7119	313	2	new	new	ADJ
ejpam-7119	313	3	contraction	contraction	NOUN
ejpam-7119	313	4	by	by	ADP
ejpam-7119	313	5	utilizing	utilize	VERB
ejpam-7119	313	6	h	h	NOUN
ejpam-7119	313	7	-	-	PUNCT
ejpam-7119	313	8	simulition	simulition	NOUN
ejpam-7119	313	9	functions	function	NOUN
ejpam-7119	313	10	and	and	CCONJ
ejpam-7119	313	11	ω	ω	NUM
ejpam-7119	313	12	-	-	PUNCT
ejpam-7119	313	13	distance	distance	NOUN
ejpam-7119	313	14	mappings	mapping	NOUN
ejpam-7119	313	15	in	in	ADP
ejpam-7119	313	16	the	the	DET
ejpam-7119	313	17	frame	frame	NOUN
ejpam-7119	313	18	of	of	ADP
ejpam-7119	313	19	complete	complete	ADJ
ejpam-7119	313	20	g	g	NOUN
ejpam-7119	313	21	-	-	PUNCT
ejpam-7119	313	22	metric	metric	ADJ
ejpam-7119	313	23	spaces	space	NOUN
ejpam-7119	313	24	.	.	PUNCT
ejpam-7119	314	1	j.	j.	PROPN
ejpam-7119	314	2	appl	appl	PROPN
ejpam-7119	314	3	.	.	PROPN
ejpam-7119	314	4	math	math	PROPN
ejpam-7119	314	5	.	.	PUNCT
ejpam-7119	314	6	&	&	CCONJ
ejpam-7119	314	7	informatics	informatics	PROPN
ejpam-7119	314	8	,	,	PUNCT
ejpam-7119	314	9	42(4):749–759	42(4):749–759	PROPN
ejpam-7119	314	10	,	,	PUNCT
ejpam-7119	314	11	2024	2024	NUM
ejpam-7119	314	12	.	.	PUNCT
ejpam-7119	315	1	[	[	X
ejpam-7119	315	2	38	38	NUM
ejpam-7119	315	3	]	]	PUNCT
ejpam-7119	315	4	t.	t.	NOUN
ejpam-7119	315	5	qawasmeh	qawasmeh	NOUN
ejpam-7119	315	6	,	,	PUNCT
ejpam-7119	315	7	a.	a.	NOUN
ejpam-7119	315	8	tallafha	tallafha	NOUN
ejpam-7119	315	9	,	,	PUNCT
ejpam-7119	315	10	and	and	CCONJ
ejpam-7119	315	11	w.	w.	PROPN
ejpam-7119	315	12	shatanawi	shatanawi	PROPN
ejpam-7119	315	13	.	.	PUNCT
ejpam-7119	316	1	fixed	fix	VERB
ejpam-7119	316	2	and	and	CCONJ
ejpam-7119	316	3	common	common	ADJ
ejpam-7119	316	4	fixed	fix	VERB
ejpam-7119	316	5	point	point	NOUN
ejpam-7119	316	6	theorems	theorem	NOUN
ejpam-7119	316	7	through	through	ADP
ejpam-7119	316	8	modified	modify	VERB
ejpam-7119	316	9	ω	ω	NUM
ejpam-7119	316	10	-	-	PUNCT
ejpam-7119	316	11	distance	distance	NOUN
ejpam-7119	316	12	mappings	mapping	NOUN
ejpam-7119	316	13	.	.	PUNCT
ejpam-7119	317	1	nonlinear	nonlinear	ADJ
ejpam-7119	317	2	funct	funct	NOUN
ejpam-7119	317	3	.	.	PUNCT
ejpam-7119	318	1	anal	anal	PROPN
ejpam-7119	318	2	.	.	PUNCT
ejpam-7119	319	1	and	and	CCONJ
ejpam-7119	319	2	appl	appl	PROPN
ejpam-7119	319	3	.	.	PROPN
ejpam-7119	319	4	,	,	PUNCT
ejpam-7119	319	5	24(2):221–239	24(2):221–239	NUM
ejpam-7119	319	6	,	,	PUNCT
ejpam-7119	319	7	2021	2021	NUM
ejpam-7119	319	8	.	.	PUNCT
ejpam-7119	320	1	[	[	X
ejpam-7119	320	2	39	39	NUM
ejpam-7119	320	3	]	]	PUNCT
ejpam-7119	320	4	k.	k.	PROPN
ejpam-7119	320	5	abodayeh	abodayeh	PROPN
ejpam-7119	320	6	,	,	PUNCT
ejpam-7119	320	7	t.	t.	NOUN
ejpam-7119	320	8	qawasmeh	qawasmeh	NOUN
ejpam-7119	320	9	,	,	PUNCT
ejpam-7119	320	10	w.	w.	PROPN
ejpam-7119	320	11	shatanawi	shatanawi	PROPN
ejpam-7119	320	12	,	,	PUNCT
ejpam-7119	320	13	and	and	CCONJ
ejpam-7119	320	14	a.	a.	NOUN
ejpam-7119	320	15	tallafha	tallafha	NOUN
ejpam-7119	320	16	.	.	PUNCT
ejpam-7119	321	1	ϵφ	ϵφ	NOUN
ejpam-7119	321	2	-	-	NOUN
ejpam-7119	321	3	contraction	contraction	NOUN
ejpam-7119	321	4	and	and	CCONJ
ejpam-7119	321	5	some	some	DET
ejpam-7119	321	6	fixed	fix	VERB
ejpam-7119	321	7	point	point	NOUN
ejpam-7119	321	8	results	result	NOUN
ejpam-7119	321	9	via	via	ADP
ejpam-7119	321	10	modified	modify	VERB
ejpam-7119	321	11	ω	ω	VERB
ejpam-7119	321	12	-	-	PUNCT
ejpam-7119	321	13	distance	distance	NOUN
ejpam-7119	321	14	mappings	mapping	NOUN
ejpam-7119	321	15	in	in	ADP
ejpam-7119	321	16	the	the	DET
ejpam-7119	321	17	frame	frame	NOUN
ejpam-7119	321	18	of	of	ADP
ejpam-7119	321	19	complete	complete	ADJ
ejpam-7119	321	20	quasi	quasi	ADJ
ejpam-7119	321	21	metric	metric	ADJ
ejpam-7119	321	22	spaces	space	NOUN
ejpam-7119	321	23	and	and	CCONJ
ejpam-7119	321	24	applications	application	NOUN
ejpam-7119	321	25	.	.	PUNCT
ejpam-7119	322	1	inter	inter	PROPN
ejpam-7119	322	2	.	.	PUNCT
ejpam-7119	323	1	j.	j.	PROPN
ejpam-7119	323	2	electrical	electrical	ADJ
ejpam-7119	323	3	comp	comp	PROPN
ejpam-7119	323	4	.	.	PUNCT
ejpam-7119	324	1	eng	eng	PROPN
ejpam-7119	324	2	.	.	PROPN
ejpam-7119	324	3	,	,	PUNCT
ejpam-7119	324	4	10(4):3839–3853	10(4):3839–3853	NUM
ejpam-7119	324	5	,	,	PUNCT
ejpam-7119	324	6	2020	2020	NUM
ejpam-7119	324	7	.	.	PUNCT
ejpam-7119	325	1	[	[	X
ejpam-7119	325	2	40	40	NUM
ejpam-7119	325	3	]	]	PUNCT
ejpam-7119	325	4	t.	t.	NOUN
ejpam-7119	325	5	qawasmeh	qawasmeh	NOUN
ejpam-7119	325	6	,	,	PUNCT
ejpam-7119	325	7	a.	a.	NOUN
ejpam-7119	325	8	bataihah	bataihah	PROPN
ejpam-7119	325	9	,	,	PUNCT
ejpam-7119	325	10	a.	a.	NOUN
ejpam-7119	325	11	a.	a.	NOUN
ejpam-7119	325	12	hazaymeh	hazaymeh	PROPN
ejpam-7119	325	13	,	,	PUNCT
ejpam-7119	325	14	r.	r.	PROPN
ejpam-7119	325	15	hatamleh	hatamleh	PROPN
ejpam-7119	325	16	,	,	PUNCT
ejpam-7119	325	17	r.	r.	PROPN
ejpam-7119	325	18	abdelrahim	abdelrahim	PROPN
ejpam-7119	325	19	,	,	PUNCT
ejpam-7119	325	20	and	and	CCONJ
ejpam-7119	325	21	a.	a.	NOUN
ejpam-7119	325	22	a.	a.	PROPN
ejpam-7119	325	23	hassan	hassan	PROPN
ejpam-7119	325	24	.	.	PUNCT
ejpam-7119	326	1	new	new	ADJ
ejpam-7119	326	2	fixed	fix	VERB
ejpam-7119	326	3	point	point	NOUN
ejpam-7119	326	4	results	result	NOUN
ejpam-7119	326	5	for	for	ADP
ejpam-7119	326	6	gamma	gamma	NOUN
ejpam-7119	326	7	interpolative	interpolative	ADJ
ejpam-7119	326	8	contractions	contraction	NOUN
ejpam-7119	326	9	through	through	ADP
ejpam-7119	326	10	gamma	gamma	NOUN
ejpam-7119	326	11	distance	distance	NOUN
ejpam-7119	326	12	mappings	mapping	NOUN
ejpam-7119	326	13	.	.	PUNCT
ejpam-7119	327	1	wseas	wseas	NOUN
ejpam-7119	327	2	transactions	transaction	NOUN
ejpam-7119	327	3	on	on	ADP
ejpam-7119	327	4	mathematics	mathematic	NOUN
ejpam-7119	327	5	,	,	PUNCT
ejpam-7119	327	6	24:424–430	24:424–430	PROPN
ejpam-7119	327	7	,	,	PUNCT
ejpam-7119	327	8	2025	2025	NUM
ejpam-7119	327	9	.	.	PUNCT
ejpam-7119	328	1	[	[	X
ejpam-7119	328	2	41	41	NUM
ejpam-7119	328	3	]	]	PUNCT
ejpam-7119	328	4	a.	a.	PROPN
ejpam-7119	328	5	h.	h.	PROPN
ejpam-7119	328	6	ganie	ganie	PROPN
ejpam-7119	328	7	,	,	PUNCT
ejpam-7119	328	8	n.	n.	PROPN
ejpam-7119	328	9	e.	e.	PROPN
ejpam-7119	328	10	m.	m.	PROPN
ejpam-7119	328	11	gheith	gheith	PROPN
ejpam-7119	328	12	,	,	PUNCT
ejpam-7119	328	13	y.	y.	PROPN
ejpam-7119	328	14	al	al	PROPN
ejpam-7119	328	15	-	-	PUNCT
ejpam-7119	328	16	qudah	qudah	PROPN
ejpam-7119	328	17	,	,	PUNCT
ejpam-7119	328	18	a.	a.	PROPN
ejpam-7119	328	19	h.	h.	PROPN
ejpam-7119	328	20	ganie	ganie	PROPN
ejpam-7119	328	21	,	,	PUNCT
ejpam-7119	328	22	s.	s.	PROPN
ejpam-7119	328	23	k.	k.	PROPN
ejpam-7119	328	24	sharma	sharma	PROPN
ejpam-7119	328	25	,	,	PUNCT
ejpam-7119	328	26	a.	a.	PROPN
ejpam-7119	328	27	m.	m.	PROPN
ejpam-7119	328	28	aqlan	aqlan	PROPN
ejpam-7119	328	29	,	,	PUNCT
ejpam-7119	328	30	and	and	CCONJ
ejpam-7119	328	31	m.	m.	NOUN
ejpam-7119	328	32	m.	m.	PROPN
ejpam-7119	328	33	khalaf	khalaf	PROPN
ejpam-7119	328	34	.	.	PUNCT
ejpam-7119	329	1	an	an	DET
ejpam-7119	329	2	innovative	innovative	ADJ
ejpam-7119	329	3	fermatean	fermatean	NOUN
ejpam-7119	329	4	fuzzy	fuzzy	ADJ
ejpam-7119	329	5	distance	distance	NOUN
ejpam-7119	329	6	metric	metric	ADJ
ejpam-7119	329	7	with	with	ADP
ejpam-7119	329	8	its	its	PRON
ejpam-7119	329	9	application	application	NOUN
ejpam-7119	329	10	in	in	ADP
ejpam-7119	329	11	classification	classification	NOUN
ejpam-7119	329	12	and	and	CCONJ
ejpam-7119	329	13	bidirectional	bidirectional	ADJ
ejpam-7119	329	14	approximate	approximate	ADJ
ejpam-7119	329	15	reasoning	reasoning	NOUN
ejpam-7119	329	16	.	.	PUNCT
ejpam-7119	330	1	ieee	ieee	NOUN
ejpam-7119	330	2	access	access	NOUN
ejpam-7119	330	3	,	,	PUNCT
ejpam-7119	330	4	12:4780–4791	12:4780–4791	NUM
ejpam-7119	330	5	,	,	PUNCT
ejpam-7119	330	6	2024	2024	NUM
ejpam-7119	330	7	.	.	PUNCT
ejpam-7119	331	1	[	[	X
ejpam-7119	331	2	42	42	NUM
ejpam-7119	331	3	]	]	X
ejpam-7119	331	4	n.	n.	PROPN
ejpam-7119	331	5	hassan	hassan	PROPN
ejpam-7119	331	6	and	and	CCONJ
ejpam-7119	331	7	y.	y.	PROPN
ejpam-7119	331	8	al	al	PROPN
ejpam-7119	331	9	-	-	PUNCT
ejpam-7119	331	10	qudah	qudah	PROPN
ejpam-7119	331	11	.	.	PUNCT
ejpam-7119	332	1	fuzzy	fuzzy	ADJ
ejpam-7119	332	2	parameterized	parameterized	ADJ
ejpam-7119	332	3	complex	complex	ADJ
ejpam-7119	332	4	multi	multi	ADJ
ejpam-7119	332	5	-	-	ADJ
ejpam-7119	332	6	fuzzy	fuzzy	ADJ
ejpam-7119	332	7	soft	soft	ADJ
ejpam-7119	332	8	set	set	NOUN
ejpam-7119	332	9	.	.	PUNCT
ejpam-7119	333	1	journal	journal	PROPN
ejpam-7119	333	2	of	of	ADP
ejpam-7119	333	3	physics	physics	PROPN
ejpam-7119	333	4	:	:	PUNCT
ejpam-7119	333	5	conference	conference	NOUN
ejpam-7119	333	6	series	series	NOUN
ejpam-7119	333	7	,	,	PUNCT
ejpam-7119	333	8	1212(1):012016	1212(1):012016	NUM
ejpam-7119	333	9	,	,	PUNCT
ejpam-7119	333	10	2019	2019	NUM
ejpam-7119	333	11	.	.	PUNCT
ejpam-7119	334	1	[	[	X
ejpam-7119	334	2	43	43	NUM
ejpam-7119	334	3	]	]	X
ejpam-7119	334	4	y.	y.	PROPN
ejpam-7119	334	5	al	al	PROPN
ejpam-7119	334	6	-	-	PUNCT
ejpam-7119	334	7	qudah	qudah	PROPN
ejpam-7119	334	8	,	,	PUNCT
ejpam-7119	334	9	a.	a.	PROPN
ejpam-7119	334	10	jaradat	jaradat	PROPN
ejpam-7119	334	11	,	,	PUNCT
ejpam-7119	334	12	s.	s.	PROPN
ejpam-7119	334	13	k.	k.	PROPN
ejpam-7119	334	14	sharma	sharma	PROPN
ejpam-7119	334	15	,	,	PUNCT
ejpam-7119	334	16	and	and	CCONJ
ejpam-7119	334	17	v.	v.	PROPN
ejpam-7119	334	18	k.	k.	PROPN
ejpam-7119	334	19	bhat	bhat	PROPN
ejpam-7119	334	20	.	.	PUNCT
ejpam-7119	335	1	mathematical	mathematical	ADJ
ejpam-7119	335	2	analysis	analysis	NOUN
ejpam-7119	335	3	of	of	ADP
ejpam-7119	335	4	the	the	DET
ejpam-7119	335	5	structure	structure	NOUN
ejpam-7119	335	6	of	of	ADP
ejpam-7119	335	7	one	one	NUM
ejpam-7119	335	8	-	-	PUNCT
ejpam-7119	335	9	heptagonal	heptagonal	ADJ
ejpam-7119	335	10	carbon	carbon	NOUN
ejpam-7119	335	11	nanocone	nanocone	NOUN
ejpam-7119	335	12	in	in	ADP
ejpam-7119	335	13	terms	term	NOUN
ejpam-7119	335	14	of	of	ADP
ejpam-7119	335	15	its	its	PRON
ejpam-7119	335	16	basis	basis	NOUN
ejpam-7119	335	17	and	and	CCONJ
ejpam-7119	335	18	dimension	dimension	NOUN
ejpam-7119	335	19	.	.	PUNCT
ejpam-7119	336	1	physica	physica	PROPN
ejpam-7119	336	2	scripta	scripta	PROPN
ejpam-7119	336	3	,	,	PUNCT
ejpam-7119	336	4	99(5):055252	99(5):055252	NUM
ejpam-7119	336	5	,	,	PUNCT
ejpam-7119	336	6	2024	2024	NUM
ejpam-7119	336	7	.	.	PUNCT
ejpam-7119	337	1	[	[	X
ejpam-7119	337	2	44	44	NUM
ejpam-7119	337	3	]	]	X
ejpam-7119	337	4	y.	y.	PROPN
ejpam-7119	337	5	al	al	PROPN
ejpam-7119	337	6	-	-	PUNCT
ejpam-7119	337	7	qudah	qudah	PROPN
ejpam-7119	337	8	,	,	PUNCT
ejpam-7119	337	9	a.	a.	NOUN
ejpam-7119	337	10	o.	o.	PROPN
ejpam-7119	337	11	kh	kh	PROPN
ejpam-7119	337	12	hamadameen	hamadameen	PROPN
ejpam-7119	337	13	,	,	PUNCT
ejpam-7119	337	14	n.	n.	PROPN
ejpam-7119	337	15	a.	a.	PROPN
ejpam-7119	337	16	,	,	PUNCT
ejpam-7119	337	17	and	and	CCONJ
ejpam-7119	337	18	f.	f.	PROPN
ejpam-7119	337	19	al	al	PROPN
ejpam-7119	337	20	-	-	PUNCT
ejpam-7119	337	21	sharqi	sharqi	PROPN
ejpam-7119	337	22	.	.	PUNCT
ejpam-7119	338	1	a	a	DET
ejpam-7119	338	2	new	new	ADJ
ejpam-7119	338	3	generalization	generalization	NOUN
ejpam-7119	338	4	of	of	ADP
ejpam-7119	338	5	interval	interval	NOUN
ejpam-7119	338	6	-	-	PUNCT
ejpam-7119	338	7	valued	value	VERB
ejpam-7119	338	8	q	q	ADJ
ejpam-7119	338	9	-	-	ADJ
ejpam-7119	338	10	neutrosophic	neutrosophic	ADJ
ejpam-7119	338	11	soft	soft	ADJ
ejpam-7119	338	12	matrix	matrix	NOUN
ejpam-7119	338	13	and	and	CCONJ
ejpam-7119	338	14	its	its	PRON
ejpam-7119	338	15	applications	application	NOUN
ejpam-7119	338	16	.	.	PUNCT
ejpam-7119	339	1	international	international	ADJ
ejpam-7119	339	2	journal	journal	PROPN
ejpam-7119	339	3	of	of	ADP
ejpam-7119	339	4	a.	a.	PROPN
ejpam-7119	339	5	malkawi	malkawi	PROPN
ejpam-7119	339	6	,	,	PUNCT
ejpam-7119	339	7	a.	a.	PROPN
ejpam-7119	339	8	rabaiah	rabaiah	PROPN
ejpam-7119	339	9	/	/	SYM
ejpam-7119	339	10	eur	eur	PROPN
ejpam-7119	339	11	.	.	PUNCT
ejpam-7119	340	1	j.	j.	PROPN
ejpam-7119	340	2	pure	pure	PROPN
ejpam-7119	340	3	appl	appl	PROPN
ejpam-7119	340	4	.	.	PROPN
ejpam-7119	340	5	math	math	PROPN
ejpam-7119	340	6	,	,	PUNCT
ejpam-7119	340	7	18	18	NUM
ejpam-7119	340	8	(	(	PUNCT
ejpam-7119	340	9	4	4	NUM
ejpam-7119	340	10	)	)	PUNCT
ejpam-7119	340	11	(	(	PUNCT
ejpam-7119	340	12	2025	2025	NUM
ejpam-7119	340	13	)	)	PUNCT
ejpam-7119	340	14	,	,	PUNCT
ejpam-7119	340	15	7119	7119	NUM
ejpam-7119	340	16	13	13	NUM
ejpam-7119	340	17	of	of	ADP
ejpam-7119	340	18	13	13	NUM
ejpam-7119	340	19	neutrosophic	neutrosophic	ADJ
ejpam-7119	340	20	science	science	NOUN
ejpam-7119	340	21	(	(	PUNCT
ejpam-7119	340	22	ijns	ijns	PROPN
ejpam-7119	340	23	)	)	PUNCT
ejpam-7119	340	24	,	,	PUNCT
ejpam-7119	340	25	25(3):242–257	25(3):242–257	NOUN
ejpam-7119	340	26	,	,	PUNCT
ejpam-7119	340	27	2025	2025	NUM
ejpam-7119	340	28	.	.	PUNCT
ejpam-7119	341	1	[	[	X
ejpam-7119	341	2	45	45	NUM
ejpam-7119	341	3	]	]	X
ejpam-7119	341	4	y.	y.	PROPN
ejpam-7119	341	5	al	al	PROPN
ejpam-7119	341	6	-	-	PUNCT
ejpam-7119	341	7	qudah	qudah	PROPN
ejpam-7119	341	8	,	,	PUNCT
ejpam-7119	341	9	f.	f.	PROPN
ejpam-7119	341	10	al	al	PROPN
ejpam-7119	341	11	-	-	PUNCT
ejpam-7119	341	12	sharqi	sharqi	PROPN
ejpam-7119	341	13	,	,	PUNCT
ejpam-7119	341	14	m.	m.	NOUN
ejpam-7119	341	15	mishlish	mishlish	NOUN
ejpam-7119	341	16	,	,	PUNCT
ejpam-7119	341	17	and	and	CCONJ
ejpam-7119	341	18	m.	m.	NOUN
ejpam-7119	341	19	m.	m.	PROPN
ejpam-7119	341	20	rasheed	rasheed	PROPN
ejpam-7119	341	21	.	.	PUNCT
ejpam-7119	341	22	hybrid	hybrid	ADJ
ejpam-7119	341	23	integrated	integrate	VERB
ejpam-7119	341	24	decisionmaking	decisionmake	VERB
ejpam-7119	341	25	algorithm	algorithm	NOUN
ejpam-7119	341	26	based	base	VERB
ejpam-7119	341	27	on	on	ADP
ejpam-7119	341	28	ao	ao	PROPN
ejpam-7119	341	29	of	of	ADP
ejpam-7119	341	30	possibility	possibility	NOUN
ejpam-7119	341	31	interval	interval	NOUN
ejpam-7119	341	32	-	-	PUNCT
ejpam-7119	341	33	valued	value	VERB
ejpam-7119	341	34	neutrosophic	neutrosophic	ADJ
ejpam-7119	341	35	soft	soft	ADJ
ejpam-7119	341	36	settings	setting	NOUN
ejpam-7119	341	37	.	.	PUNCT
ejpam-7119	342	1	international	international	ADJ
ejpam-7119	342	2	journal	journal	PROPN
ejpam-7119	342	3	of	of	ADP
ejpam-7119	342	4	neutrosophic	neutrosophic	ADJ
ejpam-7119	342	5	science	science	NOUN
ejpam-7119	342	6	,	,	PUNCT
ejpam-7119	342	7	22(3):84–98	22(3):84–98	NUM
ejpam-7119	342	8	,	,	PUNCT
ejpam-7119	342	9	2023	2023	NUM
ejpam-7119	342	10	.	.	PUNCT
ejpam-7119	343	1	[	[	X
ejpam-7119	343	2	46	46	NUM
ejpam-7119	343	3	]	]	X
ejpam-7119	343	4	y.	y.	PROPN
ejpam-7119	343	5	al	al	PROPN
ejpam-7119	343	6	-	-	PUNCT
ejpam-7119	343	7	qudah	qudah	PROPN
ejpam-7119	343	8	,	,	PUNCT
ejpam-7119	343	9	k.	k.	PROPN
ejpam-7119	343	10	alhazaymeh	alhazaymeh	PROPN
ejpam-7119	343	11	,	,	PUNCT
ejpam-7119	343	12	n.	n.	PROPN
ejpam-7119	343	13	hassan	hassan	PROPN
ejpam-7119	343	14	,	,	PUNCT
ejpam-7119	343	15	m.	m.	NOUN
ejpam-7119	343	16	almousa	almousa	NOUN
ejpam-7119	343	17	,	,	PUNCT
ejpam-7119	343	18	and	and	CCONJ
ejpam-7119	343	19	m.	m.	NOUN
ejpam-7119	343	20	alaroud	alaroud	PROPN
ejpam-7119	343	21	.	.	PUNCT
ejpam-7119	344	1	transitive	transitive	ADJ
ejpam-7119	344	2	closure	closure	NOUN
ejpam-7119	344	3	of	of	ADP
ejpam-7119	344	4	vague	vague	ADJ
ejpam-7119	344	5	soft	soft	ADJ
ejpam-7119	344	6	set	set	NOUN
ejpam-7119	344	7	relations	relation	NOUN
ejpam-7119	344	8	and	and	CCONJ
ejpam-7119	344	9	its	its	PRON
ejpam-7119	344	10	operators	operator	NOUN
ejpam-7119	344	11	.	.	PUNCT
ejpam-7119	345	1	international	international	ADJ
ejpam-7119	345	2	journal	journal	NOUN
ejpam-7119	345	3	of	of	ADP
ejpam-7119	345	4	fuzzy	fuzzy	ADJ
ejpam-7119	345	5	logic	logic	NOUN
ejpam-7119	345	6	and	and	CCONJ
ejpam-7119	345	7	intelligent	intelligent	ADJ
ejpam-7119	345	8	systems	system	NOUN
ejpam-7119	345	9	,	,	PUNCT
ejpam-7119	345	10	22(1):59–68	22(1):59–68	NUM
ejpam-7119	345	11	,	,	PUNCT
ejpam-7119	345	12	2022	2022	NUM
ejpam-7119	345	13	.	.	PUNCT
ejpam-7119	346	1	[	[	X
ejpam-7119	346	2	47	47	NUM
ejpam-7119	346	3	]	]	X
ejpam-7119	346	4	h.	h.	PROPN
ejpam-7119	346	5	qoqazeh	qoqazeh	PROPN
ejpam-7119	346	6	,	,	PUNCT
ejpam-7119	346	7	y.	y.	PROPN
ejpam-7119	346	8	al	al	PROPN
ejpam-7119	346	9	-	-	PUNCT
ejpam-7119	346	10	qudah	qudah	PROPN
ejpam-7119	346	11	,	,	PUNCT
ejpam-7119	346	12	m.	m.	NOUN
ejpam-7119	346	13	almousa	almousa	NOUN
ejpam-7119	346	14	,	,	PUNCT
ejpam-7119	346	15	and	and	CCONJ
ejpam-7119	346	16	a.	a.	NOUN
ejpam-7119	346	17	jaradat	jaradat	PROPN
ejpam-7119	346	18	.	.	PUNCT
ejpam-7119	347	1	on	on	ADP
ejpam-7119	347	2	d	d	ADJ
ejpam-7119	347	3	-	-	ADJ
ejpam-7119	347	4	compact	compact	ADJ
ejpam-7119	347	5	topological	topological	ADJ
ejpam-7119	347	6	spaces	space	NOUN
ejpam-7119	347	7	.	.	PUNCT
ejpam-7119	348	1	journal	journal	NOUN
ejpam-7119	348	2	of	of	ADP
ejpam-7119	348	3	applied	apply	VERB
ejpam-7119	348	4	mathematics	mathematic	NOUN
ejpam-7119	348	5	and	and	CCONJ
ejpam-7119	348	6	informatics	informatic	NOUN
ejpam-7119	348	7	,	,	PUNCT
ejpam-7119	348	8	39(5	39(5	PROPN
ejpam-7119	348	9	-	-	SYM
ejpam-7119	348	10	6):883–894	6):883–894	NUM
ejpam-7119	348	11	,	,	PUNCT
ejpam-7119	348	12	2021	2021	NUM
ejpam-7119	348	13	.	.	PUNCT
ejpam-7119	349	1	[	[	X
ejpam-7119	349	2	48	48	NUM
ejpam-7119	349	3	]	]	PUNCT
ejpam-7119	349	4	y.	y.	PROPN
ejpam-7119	349	5	al	al	PROPN
ejpam-7119	349	6	-	-	PUNCT
ejpam-7119	349	7	qudah	qudah	PROPN
ejpam-7119	349	8	.	.	PUNCT
ejpam-7119	350	1	a	a	DET
ejpam-7119	350	2	robust	robust	ADJ
ejpam-7119	350	3	framework	framework	NOUN
ejpam-7119	350	4	for	for	ADP
ejpam-7119	350	5	the	the	DET
ejpam-7119	350	6	decision	decision	NOUN
ejpam-7119	350	7	-	-	PUNCT
ejpam-7119	350	8	making	making	NOUN
ejpam-7119	350	9	based	base	VERB
ejpam-7119	350	10	on	on	ADP
ejpam-7119	350	11	single	single	ADJ
ejpam-7119	350	12	-	-	PUNCT
ejpam-7119	350	13	valued	value	VERB
ejpam-7119	350	14	neutrosophic	neutrosophic	ADJ
ejpam-7119	350	15	fuzzy	fuzzy	ADJ
ejpam-7119	350	16	soft	soft	ADJ
ejpam-7119	350	17	expert	expert	NOUN
ejpam-7119	350	18	setting	setting	NOUN
ejpam-7119	350	19	.	.	PUNCT
ejpam-7119	351	1	international	international	ADJ
ejpam-7119	351	2	journal	journal	PROPN
ejpam-7119	351	3	of	of	ADP
ejpam-7119	351	4	neutrosophic	neutrosophic	ADJ
ejpam-7119	351	5	science	science	NOUN
ejpam-7119	351	6	,	,	PUNCT
ejpam-7119	351	7	23(2):195	23(2):195	PROPN
ejpam-7119	351	8	–	–	PUNCT
ejpam-7119	351	9	210	210	NUM
ejpam-7119	351	10	,	,	PUNCT
ejpam-7119	351	11	2024	2024	NUM
ejpam-7119	351	12	.	.	PUNCT
ejpam-7119	352	1	[	[	X
ejpam-7119	352	2	49	49	X
ejpam-7119	352	3	]	]	X
ejpam-7119	352	4	y.	y.	PROPN
ejpam-7119	352	5	al	al	PROPN
ejpam-7119	352	6	-	-	PUNCT
ejpam-7119	352	7	qudah	qudah	PROPN
ejpam-7119	352	8	,	,	PUNCT
ejpam-7119	352	9	m.	m.	NOUN
ejpam-7119	352	10	alaroud	alaroud	PROPN
ejpam-7119	352	11	,	,	PUNCT
ejpam-7119	352	12	h.	h.	PROPN
ejpam-7119	352	13	qoqazeh	qoqazeh	PROPN
ejpam-7119	352	14	,	,	PUNCT
ejpam-7119	352	15	s.e	s.e	PROPN
ejpam-7119	352	16	.	.	PROPN
ejpam-7119	352	17	alhazmi	alhazmi	PROPN
ejpam-7119	352	18	,	,	PUNCT
ejpam-7119	352	19	and	and	CCONJ
ejpam-7119	352	20	s.	s.	PROPN
ejpam-7119	352	21	al	al	PROPN
ejpam-7119	352	22	-	-	PUNCT
ejpam-7119	352	23	omari	omari	PROPN
ejpam-7119	352	24	.	.	PUNCT
ejpam-7119	352	25	approximate	approximate	ADJ
ejpam-7119	352	26	analytic	analytic	ADJ
ejpam-7119	352	27	–	–	PUNCT
ejpam-7119	352	28	numeric	numeric	ADJ
ejpam-7119	352	29	fuzzy	fuzzy	ADJ
ejpam-7119	352	30	solutions	solution	NOUN
ejpam-7119	352	31	of	of	ADP
ejpam-7119	352	32	fuzzy	fuzzy	ADJ
ejpam-7119	352	33	fractional	fractional	ADJ
ejpam-7119	352	34	equations	equation	NOUN
ejpam-7119	352	35	using	use	VERB
ejpam-7119	352	36	a	a	DET
ejpam-7119	352	37	residual	residual	ADJ
ejpam-7119	352	38	power	power	NOUN
ejpam-7119	352	39	series	series	NOUN
ejpam-7119	352	40	approach	approach	NOUN
ejpam-7119	352	41	.	.	PUNCT
ejpam-7119	353	1	symmetry	symmetry	NOUN
ejpam-7119	353	2	,	,	PUNCT
ejpam-7119	353	3	14(4):804	14(4):804	NOUN
ejpam-7119	353	4	,	,	PUNCT
ejpam-7119	353	5	2022	2022	NUM
ejpam-7119	353	6	.	.	PUNCT