id	sid	tid	token	lemma	pos
ejpam-5864	1	1	european	european	PROPN
ejpam-5864	1	2	journal	journal	PROPN
ejpam-5864	1	3	of	of	ADP
ejpam-5864	1	4	pure	pure	ADJ
ejpam-5864	1	5	and	and	CCONJ
ejpam-5864	1	6	applied	applied	ADJ
ejpam-5864	1	7	mathematics	mathematic	NOUN
ejpam-5864	1	8	2025	2025	NUM
ejpam-5864	1	9	,	,	PUNCT
ejpam-5864	1	10	vol	vol	NOUN
ejpam-5864	1	11	.	.	PROPN
ejpam-5864	1	12	18	18	NUM
ejpam-5864	1	13	,	,	PUNCT
ejpam-5864	1	14	issue	issue	NOUN
ejpam-5864	1	15	2	2	NUM
ejpam-5864	1	16	,	,	PUNCT
ejpam-5864	1	17	article	article	NOUN
ejpam-5864	1	18	number	number	NOUN
ejpam-5864	1	19	5864	5864	NUM
ejpam-5864	1	20	issn	issn	PROPN
ejpam-5864	1	21	1307	1307	NUM
ejpam-5864	1	22	-	-	SYM
ejpam-5864	1	23	5543	5543	NUM
ejpam-5864	1	24	–	–	PUNCT
ejpam-5864	1	25	ejpam.com	ejpam.com	X
ejpam-5864	1	26	published	publish	VERB
ejpam-5864	1	27	by	by	ADP
ejpam-5864	1	28	new	new	PROPN
ejpam-5864	1	29	york	york	PROPN
ejpam-5864	1	30	business	business	PROPN
ejpam-5864	1	31	global	global	PROPN
ejpam-5864	1	32	cα	cα	NOUN
ejpam-5864	1	33	-	-	PUNCT
ejpam-5864	1	34	rectifying	rectifying	NOUN
ejpam-5864	1	35	curves	curve	NOUN
ejpam-5864	1	36	in	in	ADP
ejpam-5864	1	37	a	a	DET
ejpam-5864	1	38	new	new	ADJ
ejpam-5864	1	39	conformable	conformable	ADJ
ejpam-5864	1	40	differential	differential	NOUN
ejpam-5864	1	41	geometry	geometry	NOUN
ejpam-5864	1	42	aykut	aykut	PROPN
ejpam-5864	1	43	has1,∗	has1,∗	PROPN
ejpam-5864	1	44	,	,	PUNCT
ejpam-5864	1	45	beyhan	beyhan	PROPN
ejpam-5864	1	46	yılmaz1	yılmaz1	PROPN
ejpam-5864	1	47	,	,	PUNCT
ejpam-5864	1	48	thabet	thabet	ADJ
ejpam-5864	1	49	abdeljawad2	abdeljawad2	PROPN
ejpam-5864	1	50	1	1	NUM
ejpam-5864	1	51	department	department	NOUN
ejpam-5864	1	52	of	of	ADP
ejpam-5864	1	53	mathematics	mathematic	NOUN
ejpam-5864	1	54	,	,	PUNCT
ejpam-5864	1	55	faculty	faculty	NOUN
ejpam-5864	1	56	of	of	ADP
ejpam-5864	1	57	science	science	NOUN
ejpam-5864	1	58	,	,	PUNCT
ejpam-5864	1	59	kahramanmaras	kahramanmaras	PROPN
ejpam-5864	1	60	sutcu	sutcu	PROPN
ejpam-5864	1	61	imam	imam	PROPN
ejpam-5864	1	62	university	university	PROPN
ejpam-5864	1	63	,	,	PUNCT
ejpam-5864	1	64	46100	46100	NUM
ejpam-5864	1	65	,	,	PUNCT
ejpam-5864	1	66	kahramanmaras	kahramanmaras	PROPN
ejpam-5864	1	67	,	,	PUNCT
ejpam-5864	1	68	turkey	turkey	PROPN
ejpam-5864	1	69	2	2	NUM
ejpam-5864	1	70	department	department	NOUN
ejpam-5864	1	71	of	of	ADP
ejpam-5864	1	72	mathematics	mathematic	NOUN
ejpam-5864	1	73	and	and	CCONJ
ejpam-5864	1	74	sciences	science	NOUN
ejpam-5864	1	75	,	,	PUNCT
ejpam-5864	1	76	prince	prince	PROPN
ejpam-5864	1	77	sultan	sultan	PROPN
ejpam-5864	1	78	university	university	PROPN
ejpam-5864	1	79	,	,	PUNCT
ejpam-5864	1	80	66833	66833	NUM
ejpam-5864	1	81	,	,	PUNCT
ejpam-5864	1	82	11586	11586	NUM
ejpam-5864	1	83	riyadh	riyadh	NOUN
ejpam-5864	1	84	,	,	PUNCT
ejpam-5864	1	85	saudi	saudi	PROPN
ejpam-5864	1	86	arabia	arabia	PROPN
ejpam-5864	1	87	abstract	abstract	NOUN
ejpam-5864	1	88	.	.	PUNCT
ejpam-5864	2	1	in	in	ADP
ejpam-5864	2	2	this	this	DET
ejpam-5864	2	3	study	study	NOUN
ejpam-5864	2	4	,	,	PUNCT
ejpam-5864	2	5	we	we	PRON
ejpam-5864	2	6	reintroduce	reintroduce	VERB
ejpam-5864	2	7	the	the	DET
ejpam-5864	2	8	theory	theory	NOUN
ejpam-5864	2	9	of	of	ADP
ejpam-5864	2	10	curves	curve	NOUN
ejpam-5864	2	11	by	by	ADP
ejpam-5864	2	12	incorporating	incorporate	VERB
ejpam-5864	2	13	local	local	ADJ
ejpam-5864	2	14	fractional	fractional	ADJ
ejpam-5864	2	15	calculus	calculus	NOUN
ejpam-5864	2	16	.	.	PUNCT
ejpam-5864	3	1	we	we	PRON
ejpam-5864	3	2	elucidate	elucidate	VERB
ejpam-5864	3	3	the	the	DET
ejpam-5864	3	4	condition	condition	NOUN
ejpam-5864	3	5	for	for	ADP
ejpam-5864	3	6	a	a	DET
ejpam-5864	3	7	naturally	naturally	ADV
ejpam-5864	3	8	parametrized	parametrized	ADJ
ejpam-5864	3	9	curve	curve	NOUN
ejpam-5864	3	10	to	to	PART
ejpam-5864	3	11	be	be	AUX
ejpam-5864	3	12	conformable	conformable	ADJ
ejpam-5864	3	13	,	,	PUNCT
ejpam-5864	3	14	and	and	CCONJ
ejpam-5864	3	15	we	we	PRON
ejpam-5864	3	16	define	define	VERB
ejpam-5864	3	17	the	the	DET
ejpam-5864	3	18	orthonormal	orthonormal	ADJ
ejpam-5864	3	19	conformable	conformable	ADJ
ejpam-5864	3	20	frame	frame	NOUN
ejpam-5864	3	21	of	of	ADP
ejpam-5864	3	22	such	such	DET
ejpam-5864	3	23	a	a	DET
ejpam-5864	3	24	curve	curve	NOUN
ejpam-5864	3	25	at	at	ADP
ejpam-5864	3	26	any	any	DET
ejpam-5864	3	27	given	give	VERB
ejpam-5864	3	28	point	point	NOUN
ejpam-5864	3	29	.	.	PUNCT
ejpam-5864	4	1	then	then	ADV
ejpam-5864	4	2	,	,	PUNCT
ejpam-5864	4	3	we	we	PRON
ejpam-5864	4	4	provide	provide	VERB
ejpam-5864	4	5	a	a	DET
ejpam-5864	4	6	comprehensive	comprehensive	ADJ
ejpam-5864	4	7	explanation	explanation	NOUN
ejpam-5864	4	8	of	of	ADP
ejpam-5864	4	9	how	how	SCONJ
ejpam-5864	4	10	these	these	DET
ejpam-5864	4	11	newly	newly	ADV
ejpam-5864	4	12	derived	derive	VERB
ejpam-5864	4	13	conformable	conformable	ADJ
ejpam-5864	4	14	geometric	geometric	ADJ
ejpam-5864	4	15	concepts	concept	NOUN
ejpam-5864	4	16	are	be	AUX
ejpam-5864	4	17	related	relate	VERB
ejpam-5864	4	18	to	to	ADP
ejpam-5864	4	19	their	their	PRON
ejpam-5864	4	20	classical	classical	ADJ
ejpam-5864	4	21	counterparts	counterpart	NOUN
ejpam-5864	4	22	.	.	PUNCT
ejpam-5864	5	1	furthermore	furthermore	ADV
ejpam-5864	5	2	,	,	PUNCT
ejpam-5864	5	3	we	we	PRON
ejpam-5864	5	4	introduce	introduce	VERB
ejpam-5864	5	5	the	the	DET
ejpam-5864	5	6	concept	concept	NOUN
ejpam-5864	5	7	of	of	ADP
ejpam-5864	5	8	a	a	DET
ejpam-5864	5	9	conformable	conformable	ADJ
ejpam-5864	5	10	rectifying	rectifying	NOUN
ejpam-5864	5	11	curve	curve	NOUN
ejpam-5864	5	12	and	and	CCONJ
ejpam-5864	5	13	provide	provide	VERB
ejpam-5864	5	14	its	its	PRON
ejpam-5864	5	15	characterizations	characterization	NOUN
ejpam-5864	5	16	in	in	ADP
ejpam-5864	5	17	terms	term	NOUN
ejpam-5864	5	18	of	of	ADP
ejpam-5864	5	19	this	this	DET
ejpam-5864	5	20	differentiation	differentiation	NOUN
ejpam-5864	5	21	with	with	ADP
ejpam-5864	5	22	respect	respect	NOUN
ejpam-5864	5	23	to	to	ADP
ejpam-5864	5	24	arbitrary	arbitrary	ADJ
ejpam-5864	5	25	order	order	NOUN
ejpam-5864	5	26	.	.	PUNCT
ejpam-5864	6	1	some	some	DET
ejpam-5864	6	2	illustrative	illustrative	ADJ
ejpam-5864	6	3	graphs	graph	NOUN
ejpam-5864	6	4	are	be	AUX
ejpam-5864	6	5	provided	provide	VERB
ejpam-5864	6	6	.	.	PUNCT
ejpam-5864	7	1	2020	2020	NUM
ejpam-5864	7	2	mathematics	mathematic	NOUN
ejpam-5864	7	3	subject	subject	NOUN
ejpam-5864	7	4	classifications	classification	NOUN
ejpam-5864	7	5	:	:	PUNCT
ejpam-5864	7	6	53a04	53a04	NUM
ejpam-5864	7	7	,	,	PUNCT
ejpam-5864	7	8	26a33	26a33	NUM
ejpam-5864	7	9	key	key	ADJ
ejpam-5864	7	10	words	word	NOUN
ejpam-5864	7	11	and	and	CCONJ
ejpam-5864	7	12	phrases	phrase	NOUN
ejpam-5864	7	13	:	:	PUNCT
ejpam-5864	7	14	fractional	fractional	ADJ
ejpam-5864	7	15	calculus	calculus	NOUN
ejpam-5864	7	16	,	,	PUNCT
ejpam-5864	7	17	conformable	conformable	ADJ
ejpam-5864	7	18	fractional	fractional	ADJ
ejpam-5864	7	19	calculus	calculus	NOUN
ejpam-5864	7	20	,	,	PUNCT
ejpam-5864	7	21	frenet	frenet	NOUN
ejpam-5864	7	22	frame	frame	NOUN
ejpam-5864	7	23	,	,	PUNCT
ejpam-5864	7	24	rectifying	rectifying	NOUN
ejpam-5864	7	25	curve	curve	NOUN
ejpam-5864	7	26	,	,	PUNCT
ejpam-5864	7	27	spherical	spherical	ADJ
ejpam-5864	7	28	curve	curve	NOUN
ejpam-5864	7	29	1	1	NUM
ejpam-5864	7	30	.	.	PUNCT
ejpam-5864	7	31	introduction	introduction	NOUN
ejpam-5864	7	32	one	one	NUM
ejpam-5864	7	33	of	of	ADP
ejpam-5864	7	34	the	the	DET
ejpam-5864	7	35	most	most	ADV
ejpam-5864	7	36	interesting	interesting	ADJ
ejpam-5864	7	37	topics	topic	NOUN
ejpam-5864	7	38	in	in	ADP
ejpam-5864	7	39	differential	differential	ADJ
ejpam-5864	7	40	geometry	geometry	NOUN
ejpam-5864	7	41	is	be	AUX
ejpam-5864	7	42	the	the	DET
ejpam-5864	7	43	theory	theory	NOUN
ejpam-5864	7	44	of	of	ADP
ejpam-5864	7	45	curves	curve	NOUN
ejpam-5864	7	46	.	.	PUNCT
ejpam-5864	8	1	the	the	DET
ejpam-5864	8	2	reason	reason	NOUN
ejpam-5864	8	3	for	for	ADP
ejpam-5864	8	4	this	this	PRON
ejpam-5864	8	5	is	be	AUX
ejpam-5864	8	6	that	that	SCONJ
ejpam-5864	8	7	curves	curve	NOUN
ejpam-5864	8	8	are	be	AUX
ejpam-5864	8	9	used	use	VERB
ejpam-5864	8	10	in	in	ADP
ejpam-5864	8	11	modeling	model	VERB
ejpam-5864	8	12	many	many	ADJ
ejpam-5864	8	13	problems	problem	NOUN
ejpam-5864	8	14	that	that	PRON
ejpam-5864	8	15	we	we	PRON
ejpam-5864	8	16	encounter	encounter	VERB
ejpam-5864	8	17	in	in	ADP
ejpam-5864	8	18	real	real	ADJ
ejpam-5864	8	19	life	life	NOUN
ejpam-5864	8	20	.	.	PUNCT
ejpam-5864	9	1	for	for	ADP
ejpam-5864	9	2	example	example	NOUN
ejpam-5864	9	3	,	,	PUNCT
ejpam-5864	9	4	curves	curve	NOUN
ejpam-5864	9	5	are	be	AUX
ejpam-5864	9	6	used	use	VERB
ejpam-5864	9	7	when	when	SCONJ
ejpam-5864	9	8	observing	observe	VERB
ejpam-5864	9	9	the	the	DET
ejpam-5864	9	10	motion	motion	NOUN
ejpam-5864	9	11	of	of	ADP
ejpam-5864	9	12	a	a	DET
ejpam-5864	9	13	charged	charge	VERB
ejpam-5864	9	14	particle	particle	NOUN
ejpam-5864	9	15	in	in	ADP
ejpam-5864	9	16	a	a	DET
ejpam-5864	9	17	magnetic	magnetic	ADJ
ejpam-5864	9	18	field	field	NOUN
ejpam-5864	9	19	[	[	X
ejpam-5864	9	20	1	1	NUM
ejpam-5864	9	21	,	,	PUNCT
ejpam-5864	9	22	2	2	NUM
ejpam-5864	9	23	]	]	PUNCT
ejpam-5864	9	24	.	.	PUNCT
ejpam-5864	10	1	in	in	ADP
ejpam-5864	10	2	addition	addition	NOUN
ejpam-5864	10	3	,	,	PUNCT
ejpam-5864	10	4	many	many	ADJ
ejpam-5864	10	5	operations	operation	NOUN
ejpam-5864	10	6	are	be	AUX
ejpam-5864	10	7	performed	perform	VERB
ejpam-5864	10	8	using	use	VERB
ejpam-5864	10	9	curves	curve	NOUN
ejpam-5864	10	10	in	in	ADP
ejpam-5864	10	11	computeraided	computeraide	VERB
ejpam-5864	10	12	geometric	geometric	ADJ
ejpam-5864	10	13	designs	design	NOUN
ejpam-5864	10	14	[	[	X
ejpam-5864	10	15	3	3	NUM
ejpam-5864	10	16	,	,	PUNCT
ejpam-5864	10	17	4	4	NUM
ejpam-5864	10	18	]	]	PUNCT
ejpam-5864	10	19	.	.	PUNCT
ejpam-5864	11	1	the	the	DET
ejpam-5864	11	2	first	first	ADJ
ejpam-5864	11	3	thing	thing	NOUN
ejpam-5864	11	4	to	to	PART
ejpam-5864	11	5	do	do	VERB
ejpam-5864	11	6	when	when	SCONJ
ejpam-5864	11	7	designing	design	VERB
ejpam-5864	11	8	these	these	DET
ejpam-5864	11	9	geometric	geometric	ADJ
ejpam-5864	11	10	models	model	NOUN
ejpam-5864	11	11	is	be	AUX
ejpam-5864	11	12	to	to	PART
ejpam-5864	11	13	characterize	characterize	VERB
ejpam-5864	11	14	the	the	DET
ejpam-5864	11	15	curve	curve	NOUN
ejpam-5864	11	16	.	.	PUNCT
ejpam-5864	12	1	because	because	SCONJ
ejpam-5864	12	2	curves	curve	NOUN
ejpam-5864	12	3	are	be	AUX
ejpam-5864	12	4	concepts	concept	NOUN
ejpam-5864	12	5	that	that	PRON
ejpam-5864	12	6	are	be	AUX
ejpam-5864	12	7	characterized	characterize	VERB
ejpam-5864	12	8	and	and	CCONJ
ejpam-5864	12	9	studied	study	VERB
ejpam-5864	12	10	.	.	PUNCT
ejpam-5864	13	1	there	there	PRON
ejpam-5864	13	2	are	be	VERB
ejpam-5864	13	3	some	some	DET
ejpam-5864	13	4	methods	method	NOUN
ejpam-5864	13	5	used	use	VERB
ejpam-5864	13	6	when	when	SCONJ
ejpam-5864	13	7	characterizing	characterize	VERB
ejpam-5864	13	8	curves	curve	NOUN
ejpam-5864	13	9	.	.	PUNCT
ejpam-5864	14	1	the	the	DET
ejpam-5864	14	2	most	most	ADV
ejpam-5864	14	3	important	important	ADJ
ejpam-5864	14	4	of	of	ADP
ejpam-5864	14	5	these	these	PRON
ejpam-5864	14	6	are	be	AUX
ejpam-5864	14	7	that	that	SCONJ
ejpam-5864	14	8	the	the	DET
ejpam-5864	14	9	curve	curve	NOUN
ejpam-5864	14	10	is	be	AUX
ejpam-5864	14	11	characterized	characterize	VERB
ejpam-5864	14	12	by	by	ADP
ejpam-5864	14	13	its	its	PRON
ejpam-5864	14	14	curvatures	curvature	NOUN
ejpam-5864	14	15	and	and	CCONJ
ejpam-5864	14	16	frenet	frenet	ADJ
ejpam-5864	14	17	vectors	vector	NOUN
ejpam-5864	14	18	.	.	PUNCT
ejpam-5864	15	1	the	the	DET
ejpam-5864	15	2	rectifying	rectifying	NOUN
ejpam-5864	15	3	curves	curve	NOUN
ejpam-5864	15	4	that	that	PRON
ejpam-5864	15	5	are	be	AUX
ejpam-5864	15	6	the	the	DET
ejpam-5864	15	7	subject	subject	NOUN
ejpam-5864	15	8	of	of	ADP
ejpam-5864	15	9	the	the	DET
ejpam-5864	15	10	article	article	NOUN
ejpam-5864	15	11	are	be	AUX
ejpam-5864	15	12	characterized	characterize	VERB
ejpam-5864	15	13	by	by	ADP
ejpam-5864	15	14	both	both	DET
ejpam-5864	15	15	frenet	frenet	ADJ
ejpam-5864	15	16	vectors	vector	NOUN
ejpam-5864	15	17	and	and	CCONJ
ejpam-5864	15	18	curvatures	curvature	NOUN
ejpam-5864	15	19	by	by	ADP
ejpam-5864	15	20	b.y	b.y	PROPN
ejpam-5864	15	21	.	.	PROPN
ejpam-5864	15	22	chen	chen	PROPN
ejpam-5864	16	1	[	[	X
ejpam-5864	16	2	5	5	NUM
ejpam-5864	16	3	]	]	PUNCT
ejpam-5864	16	4	.	.	PUNCT
ejpam-5864	17	1	a	a	DET
ejpam-5864	17	2	naturally	naturally	ADV
ejpam-5864	17	3	parametrized	parametrized	ADJ
ejpam-5864	17	4	curve	curve	NOUN
ejpam-5864	17	5	is	be	AUX
ejpam-5864	17	6	called	call	VERB
ejpam-5864	17	7	a	a	DET
ejpam-5864	17	8	rectifying	rectifying	NOUN
ejpam-5864	17	9	curve	curve	NOUN
ejpam-5864	17	10	if	if	SCONJ
ejpam-5864	17	11	it	it	PRON
ejpam-5864	17	12	lies	lie	VERB
ejpam-5864	17	13	in	in	ADP
ejpam-5864	17	14	the	the	DET
ejpam-5864	17	15	plane	plane	NOUN
ejpam-5864	17	16	formed	form	VERB
ejpam-5864	17	17	by	by	ADP
ejpam-5864	17	18	its	its	PRON
ejpam-5864	17	19	tangent	tangent	NOUN
ejpam-5864	17	20	and	and	CCONJ
ejpam-5864	17	21	binormal	binormal	NOUN
ejpam-5864	17	22	at	at	ADP
ejpam-5864	17	23	a	a	DET
ejpam-5864	17	24	point	point	NOUN
ejpam-5864	17	25	.	.	PUNCT
ejpam-5864	18	1	also	also	ADV
ejpam-5864	18	2	,	,	PUNCT
ejpam-5864	18	3	the	the	DET
ejpam-5864	18	4	ratio	ratio	NOUN
ejpam-5864	18	5	of	of	ADP
ejpam-5864	18	6	∗corresponding	∗corresponde	VERB
ejpam-5864	18	7	author	author	NOUN
ejpam-5864	18	8	.	.	PUNCT
ejpam-5864	19	1	doi	doi	NOUN
ejpam-5864	19	2	:	:	PUNCT
ejpam-5864	19	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5864	https://doi.org/10.29020/nybg.ejpam.v18i2.5864	ADJ
ejpam-5864	19	4	email	email	NOUN
ejpam-5864	19	5	addresses	address	NOUN
ejpam-5864	19	6	:	:	PUNCT
ejpam-5864	19	7	ahas@ksu.edu.tr	ahas@ksu.edu.tr	PROPN
ejpam-5864	19	8	(	(	PUNCT
ejpam-5864	19	9	a.	a.	NOUN
ejpam-5864	19	10	has	have	VERB
ejpam-5864	19	11	)	)	PUNCT
ejpam-5864	19	12	,	,	PUNCT
ejpam-5864	19	13	beyhanyilmaz@ksu.edu.tr	beyhanyilmaz@ksu.edu.tr	PROPN
ejpam-5864	19	14	(	(	PUNCT
ejpam-5864	19	15	b.	b.	PROPN
ejpam-5864	19	16	yılmaz	yılmaz	PROPN
ejpam-5864	19	17	)	)	PUNCT
ejpam-5864	19	18	,	,	PUNCT
ejpam-5864	19	19	tabdeljawad@psu.edu.sa	tabdeljawad@psu.edu.sa	PROPN
ejpam-5864	19	20	(	(	PUNCT
ejpam-5864	19	21	t.	t.	NOUN
ejpam-5864	19	22	abdeljawad	abdeljawad	PROPN
ejpam-5864	19	23	)	)	PUNCT
ejpam-5864	19	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5864	19	25	1	1	NUM
ejpam-5864	19	26	copyright	copyright	NOUN
ejpam-5864	19	27	:	:	PUNCT
ejpam-5864	20	1	©	©	PROPN
ejpam-5864	20	2	2025	2025	NUM
ejpam-5864	20	3	the	the	DET
ejpam-5864	20	4	author(s	author(s	NOUN
ejpam-5864	20	5	)	)	PUNCT
ejpam-5864	20	6	.	.	PUNCT
ejpam-5864	21	1	(	(	PUNCT
ejpam-5864	21	2	cc	cc	NOUN
ejpam-5864	21	3	by	by	ADP
ejpam-5864	21	4	-	-	PUNCT
ejpam-5864	21	5	nc	nc	PROPN
ejpam-5864	21	6	4.0	4.0	NUM
ejpam-5864	21	7	)	)	PUNCT
ejpam-5864	21	8	a.	a.	NOUN
ejpam-5864	21	9	has	have	AUX
ejpam-5864	21	10	,	,	PUNCT
ejpam-5864	21	11	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	21	12	,	,	PUNCT
ejpam-5864	21	13	t.	t.	PROPN
ejpam-5864	21	14	abdeljawad	abdeljawad	PROPN
ejpam-5864	21	15	/	/	SYM
ejpam-5864	21	16	eur	eur	PROPN
ejpam-5864	21	17	.	.	PUNCT
ejpam-5864	22	1	j.	j.	PROPN
ejpam-5864	22	2	pure	pure	PROPN
ejpam-5864	22	3	appl	appl	PROPN
ejpam-5864	22	4	.	.	PROPN
ejpam-5864	22	5	math	math	PROPN
ejpam-5864	22	6	,	,	PUNCT
ejpam-5864	22	7	18	18	NUM
ejpam-5864	22	8	(	(	PUNCT
ejpam-5864	22	9	2	2	NUM
ejpam-5864	22	10	)	)	PUNCT
ejpam-5864	22	11	(	(	PUNCT
ejpam-5864	22	12	2025	2025	NUM
ejpam-5864	22	13	)	)	PUNCT
ejpam-5864	22	14	,	,	PUNCT
ejpam-5864	22	15	5864	5864	NUM
ejpam-5864	22	16	2	2	NUM
ejpam-5864	22	17	of	of	ADP
ejpam-5864	22	18	14	14	NUM
ejpam-5864	22	19	torsion	torsion	NOUN
ejpam-5864	22	20	to	to	PART
ejpam-5864	22	21	curvature	curvature	VERB
ejpam-5864	22	22	of	of	ADP
ejpam-5864	22	23	rectifying	rectify	VERB
ejpam-5864	22	24	curves	curve	NOUN
ejpam-5864	22	25	results	result	NOUN
ejpam-5864	22	26	in	in	ADP
ejpam-5864	22	27	a	a	DET
ejpam-5864	22	28	linear	linear	ADJ
ejpam-5864	22	29	equation	equation	NOUN
ejpam-5864	22	30	.	.	PUNCT
ejpam-5864	23	1	moreover	moreover	ADV
ejpam-5864	23	2	,	,	PUNCT
ejpam-5864	23	3	it	it	PRON
ejpam-5864	23	4	is	be	AUX
ejpam-5864	23	5	known	know	VERB
ejpam-5864	23	6	that	that	SCONJ
ejpam-5864	23	7	centrodes	centrode	VERB
ejpam-5864	23	8	(	(	PUNCT
ejpam-5864	23	9	i.e.	i.e.	X
ejpam-5864	23	10	angular	angular	ADJ
ejpam-5864	23	11	velocity	velocity	NOUN
ejpam-5864	23	12	vectors	vector	NOUN
ejpam-5864	23	13	)	)	PUNCT
ejpam-5864	23	14	play	play	VERB
ejpam-5864	23	15	some	some	DET
ejpam-5864	23	16	important	important	ADJ
ejpam-5864	23	17	roles	role	NOUN
ejpam-5864	23	18	in	in	ADP
ejpam-5864	23	19	mechanics	mechanic	NOUN
ejpam-5864	23	20	and	and	CCONJ
ejpam-5864	23	21	joint	joint	ADJ
ejpam-5864	23	22	kinematics	kinematic	NOUN
ejpam-5864	24	1	[	[	X
ejpam-5864	24	2	6	6	NUM
ejpam-5864	24	3	,	,	PUNCT
ejpam-5864	24	4	7	7	NUM
ejpam-5864	24	5	]	]	PUNCT
ejpam-5864	24	6	.	.	PUNCT
ejpam-5864	25	1	in	in	ADP
ejpam-5864	25	2	this	this	DET
ejpam-5864	25	3	direction	direction	NOUN
ejpam-5864	25	4	b.y	b.y	PROPN
ejpam-5864	25	5	.	.	PROPN
ejpam-5864	25	6	chen	chen	PROPN
ejpam-5864	25	7	and	and	CCONJ
ejpam-5864	25	8	f.	f.	PROPN
ejpam-5864	25	9	dillen	dillen	PROPN
ejpam-5864	25	10	observed	observe	VERB
ejpam-5864	25	11	that	that	SCONJ
ejpam-5864	25	12	rectifying	rectifying	NOUN
ejpam-5864	25	13	curves	curve	NOUN
ejpam-5864	25	14	can	can	AUX
ejpam-5864	25	15	be	be	AUX
ejpam-5864	25	16	viewed	view	VERB
ejpam-5864	25	17	as	as	ADP
ejpam-5864	25	18	centrodes	centrode	NOUN
ejpam-5864	25	19	and	and	CCONJ
ejpam-5864	25	20	extremal	extremal	ADJ
ejpam-5864	25	21	curves	curve	NOUN
ejpam-5864	25	22	in	in	ADP
ejpam-5864	25	23	e3	e3	NOUN
ejpam-5864	25	24	[	[	X
ejpam-5864	25	25	8	8	NUM
ejpam-5864	25	26	]	]	PUNCT
ejpam-5864	25	27	.	.	PUNCT
ejpam-5864	26	1	in	in	ADP
ejpam-5864	26	2	addition	addition	NOUN
ejpam-5864	26	3	,	,	PUNCT
ejpam-5864	26	4	rectifying	rectifying	NOUN
ejpam-5864	26	5	curves	curve	NOUN
ejpam-5864	26	6	are	be	AUX
ejpam-5864	26	7	studied	study	VERB
ejpam-5864	26	8	by	by	ADP
ejpam-5864	26	9	many	many	ADJ
ejpam-5864	26	10	researchers	researcher	NOUN
ejpam-5864	26	11	in	in	ADP
ejpam-5864	26	12	different	different	ADJ
ejpam-5864	26	13	spaces	space	NOUN
ejpam-5864	26	14	and	and	CCONJ
ejpam-5864	26	15	different	different	ADJ
ejpam-5864	26	16	dimensions	dimension	NOUN
ejpam-5864	26	17	[	[	X
ejpam-5864	26	18	9–13	9–13	NOUN
ejpam-5864	26	19	]	]	PUNCT
ejpam-5864	26	20	.	.	PUNCT
ejpam-5864	27	1	fractional	fractional	ADJ
ejpam-5864	27	2	calculus	calculus	NOUN
ejpam-5864	27	3	represents	represent	VERB
ejpam-5864	27	4	a	a	DET
ejpam-5864	27	5	generalization	generalization	NOUN
ejpam-5864	27	6	of	of	ADP
ejpam-5864	27	7	classical	classical	ADJ
ejpam-5864	27	8	derivative	derivative	ADJ
ejpam-5864	27	9	and	and	CCONJ
ejpam-5864	27	10	integral	integral	ADJ
ejpam-5864	27	11	concepts	concept	NOUN
ejpam-5864	27	12	,	,	PUNCT
ejpam-5864	27	13	extensively	extensively	ADV
ejpam-5864	27	14	explored	explore	VERB
ejpam-5864	27	15	by	by	ADP
ejpam-5864	27	16	contemporary	contemporary	ADJ
ejpam-5864	27	17	researchers	researcher	NOUN
ejpam-5864	27	18	.	.	PUNCT
ejpam-5864	28	1	the	the	DET
ejpam-5864	28	2	notion	notion	NOUN
ejpam-5864	28	3	of	of	ADP
ejpam-5864	28	4	fractional	fractional	ADJ
ejpam-5864	28	5	derivative	derivative	NOUN
ejpam-5864	28	6	essentially	essentially	ADV
ejpam-5864	28	7	refers	refer	VERB
ejpam-5864	28	8	to	to	ADP
ejpam-5864	28	9	derivatives	derivative	NOUN
ejpam-5864	28	10	of	of	ADP
ejpam-5864	28	11	non	non	ADJ
ejpam-5864	28	12	-	-	ADJ
ejpam-5864	28	13	integer	integer	ADJ
ejpam-5864	28	14	order	order	NOUN
ejpam-5864	28	15	.	.	PUNCT
ejpam-5864	29	1	remarkably	remarkably	ADV
ejpam-5864	29	2	,	,	PUNCT
ejpam-5864	29	3	the	the	DET
ejpam-5864	29	4	concepts	concept	NOUN
ejpam-5864	29	5	of	of	ADP
ejpam-5864	29	6	fractional	fractional	ADJ
ejpam-5864	29	7	derivatives	derivative	NOUN
ejpam-5864	29	8	and	and	CCONJ
ejpam-5864	29	9	integrals	integral	NOUN
ejpam-5864	29	10	have	have	VERB
ejpam-5864	29	11	an	an	DET
ejpam-5864	29	12	age	age	NOUN
ejpam-5864	29	13	parallel	parallel	NOUN
ejpam-5864	29	14	to	to	ADP
ejpam-5864	29	15	that	that	PRON
ejpam-5864	29	16	of	of	ADP
ejpam-5864	29	17	integer	integer	NOUN
ejpam-5864	29	18	derivatives	derivative	NOUN
ejpam-5864	29	19	and	and	CCONJ
ejpam-5864	29	20	integrals	integral	NOUN
ejpam-5864	29	21	,	,	PUNCT
ejpam-5864	29	22	with	with	ADP
ejpam-5864	29	23	the	the	DET
ejpam-5864	29	24	term	term	NOUN
ejpam-5864	29	25	”	"	PUNCT
ejpam-5864	29	26	fractional	fractional	ADJ
ejpam-5864	29	27	derivative	derivative	NOUN
ejpam-5864	29	28	”	"	PUNCT
ejpam-5864	29	29	first	first	ADV
ejpam-5864	29	30	mentioned	mention	VERB
ejpam-5864	29	31	in	in	ADP
ejpam-5864	29	32	leibniz	leibniz	PROPN
ejpam-5864	29	33	’s	’s	PART
ejpam-5864	29	34	1695	1695	NUM
ejpam-5864	29	35	letter	letter	NOUN
ejpam-5864	29	36	to	to	ADP
ejpam-5864	29	37	l’hospital	l’hospital	PROPN
ejpam-5864	29	38	,	,	PUNCT
ejpam-5864	29	39	as	as	SCONJ
ejpam-5864	29	40	documented	document	VERB
ejpam-5864	29	41	in	in	ADP
ejpam-5864	29	42	various	various	ADJ
ejpam-5864	29	43	sources	source	NOUN
ejpam-5864	29	44	.	.	PUNCT
ejpam-5864	30	1	in	in	ADP
ejpam-5864	30	2	this	this	DET
ejpam-5864	30	3	letter	letter	NOUN
ejpam-5864	30	4	,	,	PUNCT
ejpam-5864	30	5	leibniz	leibniz	PROPN
ejpam-5864	30	6	posed	pose	VERB
ejpam-5864	30	7	the	the	DET
ejpam-5864	30	8	query	query	NOUN
ejpam-5864	30	9	,	,	PUNCT
ejpam-5864	30	10	”	"	PUNCT
ejpam-5864	30	11	can	can	AUX
ejpam-5864	30	12	the	the	DET
ejpam-5864	30	13	notion	notion	NOUN
ejpam-5864	30	14	of	of	ADP
ejpam-5864	30	15	integer	integer	NOUN
ejpam-5864	30	16	derivatives	derivative	NOUN
ejpam-5864	30	17	be	be	AUX
ejpam-5864	30	18	extended	extend	VERB
ejpam-5864	30	19	to	to	ADP
ejpam-5864	30	20	fractional	fractional	ADJ
ejpam-5864	30	21	derivatives	derivative	NOUN
ejpam-5864	30	22	?	?	PUNCT
ejpam-5864	30	23	”	"	PUNCT
ejpam-5864	31	1	the	the	DET
ejpam-5864	31	2	concept	concept	NOUN
ejpam-5864	31	3	of	of	ADP
ejpam-5864	31	4	fractional	fractional	ADJ
ejpam-5864	31	5	calculus	calculus	NOUN
ejpam-5864	31	6	has	have	AUX
ejpam-5864	31	7	captivated	captivate	VERB
ejpam-5864	31	8	the	the	DET
ejpam-5864	31	9	interest	interest	NOUN
ejpam-5864	31	10	of	of	ADP
ejpam-5864	31	11	numerous	numerous	ADJ
ejpam-5864	31	12	mathematicians	mathematician	NOUN
ejpam-5864	31	13	,	,	PUNCT
ejpam-5864	31	14	becoming	become	VERB
ejpam-5864	31	15	a	a	DET
ejpam-5864	31	16	broad	broad	ADJ
ejpam-5864	31	17	area	area	NOUN
ejpam-5864	31	18	of	of	ADP
ejpam-5864	31	19	study	study	NOUN
ejpam-5864	31	20	.	.	PUNCT
ejpam-5864	32	1	it	it	PRON
ejpam-5864	32	2	has	have	AUX
ejpam-5864	32	3	emerged	emerge	VERB
ejpam-5864	32	4	as	as	ADP
ejpam-5864	32	5	an	an	DET
ejpam-5864	32	6	indispensable	indispensable	ADJ
ejpam-5864	32	7	cornerstone	cornerstone	NOUN
ejpam-5864	32	8	across	across	ADP
ejpam-5864	32	9	various	various	ADJ
ejpam-5864	32	10	domains	domain	NOUN
ejpam-5864	32	11	within	within	ADP
ejpam-5864	32	12	basic	basic	ADJ
ejpam-5864	32	13	sciences	science	NOUN
ejpam-5864	32	14	and	and	CCONJ
ejpam-5864	32	15	engineering	engineering	NOUN
ejpam-5864	32	16	,	,	PUNCT
ejpam-5864	32	17	purportedly	purportedly	ADV
ejpam-5864	32	18	offering	offer	VERB
ejpam-5864	32	19	more	more	ADV
ejpam-5864	32	20	nuanced	nuanced	ADJ
ejpam-5864	32	21	numerical	numerical	ADJ
ejpam-5864	32	22	results	result	NOUN
ejpam-5864	32	23	,	,	PUNCT
ejpam-5864	32	24	particularly	particularly	ADV
ejpam-5864	32	25	in	in	ADP
ejpam-5864	32	26	the	the	DET
ejpam-5864	32	27	realm	realm	NOUN
ejpam-5864	32	28	of	of	ADP
ejpam-5864	32	29	differential	differential	ADJ
ejpam-5864	32	30	equation	equation	NOUN
ejpam-5864	32	31	solutions	solution	NOUN
ejpam-5864	32	32	.	.	PUNCT
ejpam-5864	33	1	fractional	fractional	ADJ
ejpam-5864	33	2	calculus	calculus	NOUN
ejpam-5864	33	3	has	have	AUX
ejpam-5864	33	4	gained	gain	VERB
ejpam-5864	33	5	widespread	widespread	ADJ
ejpam-5864	33	6	popularity	popularity	NOUN
ejpam-5864	33	7	,	,	PUNCT
ejpam-5864	33	8	leading	lead	VERB
ejpam-5864	33	9	to	to	ADP
ejpam-5864	33	10	diverse	diverse	ADJ
ejpam-5864	33	11	definitions	definition	NOUN
ejpam-5864	33	12	and	and	CCONJ
ejpam-5864	33	13	features	feature	NOUN
ejpam-5864	33	14	proposed	propose	VERB
ejpam-5864	33	15	by	by	ADP
ejpam-5864	33	16	numerous	numerous	ADJ
ejpam-5864	33	17	researchers	researcher	NOUN
ejpam-5864	33	18	.	.	PUNCT
ejpam-5864	34	1	notable	notable	ADJ
ejpam-5864	34	2	among	among	ADP
ejpam-5864	34	3	these	these	PRON
ejpam-5864	34	4	are	be	AUX
ejpam-5864	34	5	the	the	DET
ejpam-5864	34	6	riemann	riemann	PROPN
ejpam-5864	34	7	-	-	PUNCT
ejpam-5864	34	8	liouville	liouville	NOUN
ejpam-5864	34	9	(	(	PUNCT
ejpam-5864	34	10	r	r	NOUN
ejpam-5864	34	11	-	-	PUNCT
ejpam-5864	34	12	l	l	NOUN
ejpam-5864	34	13	)	)	PUNCT
ejpam-5864	34	14	,	,	PUNCT
ejpam-5864	34	15	caputo	caputo	PROPN
ejpam-5864	34	16	,	,	PUNCT
ejpam-5864	34	17	grünwald	grünwald	NOUN
ejpam-5864	34	18	-	-	PUNCT
ejpam-5864	34	19	letnikov	letnikov	ADJ
ejpam-5864	34	20	,	,	PUNCT
ejpam-5864	34	21	wely	wely	ADV
ejpam-5864	34	22	,	,	PUNCT
ejpam-5864	34	23	and	and	CCONJ
ejpam-5864	34	24	riesz	riesz	VERB
ejpam-5864	34	25	fractional	fractional	ADJ
ejpam-5864	34	26	derivatives	derivative	NOUN
ejpam-5864	34	27	[	[	X
ejpam-5864	34	28	14–16	14–16	NUM
ejpam-5864	34	29	]	]	PUNCT
ejpam-5864	34	30	.	.	PUNCT
ejpam-5864	35	1	while	while	SCONJ
ejpam-5864	35	2	they	they	PRON
ejpam-5864	35	3	share	share	VERB
ejpam-5864	35	4	common	common	ADJ
ejpam-5864	35	5	features	feature	NOUN
ejpam-5864	35	6	,	,	PUNCT
ejpam-5864	35	7	each	each	DET
ejpam-5864	35	8	fractional	fractional	ADJ
ejpam-5864	35	9	calculus	calculus	NOUN
ejpam-5864	35	10	possesses	possess	VERB
ejpam-5864	35	11	unique	unique	ADJ
ejpam-5864	35	12	rules	rule	NOUN
ejpam-5864	35	13	.	.	PUNCT
ejpam-5864	36	1	for	for	ADP
ejpam-5864	36	2	instance	instance	NOUN
ejpam-5864	36	3	,	,	PUNCT
ejpam-5864	36	4	nonlocal	nonlocal	ADJ
ejpam-5864	36	5	fractional	fractional	ADJ
ejpam-5864	36	6	derivative	derivative	ADJ
ejpam-5864	36	7	types	type	NOUN
ejpam-5864	36	8	diverge	diverge	VERB
ejpam-5864	36	9	from	from	ADP
ejpam-5864	36	10	satisfying	satisfy	VERB
ejpam-5864	36	11	the	the	DET
ejpam-5864	36	12	classical	classical	ADJ
ejpam-5864	36	13	leibniz	leibniz	NOUN
ejpam-5864	36	14	and	and	CCONJ
ejpam-5864	36	15	chain	chain	NOUN
ejpam-5864	36	16	rules	rule	NOUN
ejpam-5864	36	17	.	.	PUNCT
ejpam-5864	37	1	notably	notably	ADV
ejpam-5864	37	2	,	,	PUNCT
ejpam-5864	37	3	except	except	SCONJ
ejpam-5864	37	4	for	for	ADP
ejpam-5864	37	5	the	the	DET
ejpam-5864	37	6	caputo	caputo	PROPN
ejpam-5864	37	7	fractional	fractional	PROPN
ejpam-5864	37	8	derivative	derivative	PROPN
ejpam-5864	37	9	,	,	PUNCT
ejpam-5864	37	10	the	the	DET
ejpam-5864	37	11	derivative	derivative	NOUN
ejpam-5864	37	12	of	of	ADP
ejpam-5864	37	13	a	a	DET
ejpam-5864	37	14	constant	constant	ADJ
ejpam-5864	37	15	is	be	AUX
ejpam-5864	37	16	non	non	ADJ
ejpam-5864	37	17	-	-	ADJ
ejpam-5864	37	18	zero	zero	NUM
ejpam-5864	37	19	in	in	ADP
ejpam-5864	37	20	non	non	ADJ
ejpam-5864	37	21	-	-	ADJ
ejpam-5864	37	22	local	local	ADJ
ejpam-5864	37	23	fractional	fractional	ADJ
ejpam-5864	37	24	derivatives	derivative	NOUN
ejpam-5864	37	25	[	[	X
ejpam-5864	37	26	17	17	NUM
ejpam-5864	37	27	]	]	PUNCT
ejpam-5864	37	28	.	.	PUNCT
ejpam-5864	38	1	on	on	ADP
ejpam-5864	38	2	the	the	DET
ejpam-5864	38	3	other	other	ADJ
ejpam-5864	38	4	hand	hand	NOUN
ejpam-5864	38	5	,	,	PUNCT
ejpam-5864	38	6	local	local	ADJ
ejpam-5864	38	7	fractional	fractional	ADJ
ejpam-5864	38	8	derivatives	derivative	NOUN
ejpam-5864	38	9	such	such	ADJ
ejpam-5864	38	10	as	as	ADP
ejpam-5864	38	11	conformable	conformable	ADJ
ejpam-5864	38	12	,	,	PUNCT
ejpam-5864	38	13	alternative	alternative	ADJ
ejpam-5864	38	14	,	,	PUNCT
ejpam-5864	38	15	m	m	NOUN
ejpam-5864	38	16	-fractional	-fractional	ADJ
ejpam-5864	38	17	,	,	PUNCT
ejpam-5864	38	18	and	and	CCONJ
ejpam-5864	38	19	v	v	ADP
ejpam-5864	38	20	-fractional	-fractional	ADJ
ejpam-5864	38	21	adhere	adhere	NOUN
ejpam-5864	38	22	to	to	ADP
ejpam-5864	38	23	satisfying	satisfy	VERB
ejpam-5864	38	24	leibniz	leibniz	PROPN
ejpam-5864	38	25	’s	’s	PART
ejpam-5864	38	26	and	and	CCONJ
ejpam-5864	38	27	the	the	DET
ejpam-5864	38	28	chain	chain	NOUN
ejpam-5864	38	29	rule	rule	NOUN
ejpam-5864	38	30	.	.	PUNCT
ejpam-5864	39	1	hence	hence	ADV
ejpam-5864	39	2	,	,	PUNCT
ejpam-5864	39	3	local	local	ADJ
ejpam-5864	39	4	fractional	fractional	ADJ
ejpam-5864	39	5	derivatives	derivative	NOUN
ejpam-5864	39	6	hold	hold	VERB
ejpam-5864	39	7	an	an	DET
ejpam-5864	39	8	advantageous	advantageous	ADJ
ejpam-5864	39	9	position	position	NOUN
ejpam-5864	39	10	in	in	ADP
ejpam-5864	39	11	algebraically	algebraically	ADV
ejpam-5864	39	12	constructed	construct	VERB
ejpam-5864	39	13	subjects	subject	NOUN
ejpam-5864	39	14	due	due	ADJ
ejpam-5864	39	15	to	to	ADP
ejpam-5864	39	16	their	their	PRON
ejpam-5864	39	17	adherence	adherence	NOUN
ejpam-5864	39	18	to	to	ADP
ejpam-5864	39	19	these	these	DET
ejpam-5864	39	20	classical	classical	ADJ
ejpam-5864	39	21	rules	rule	NOUN
ejpam-5864	39	22	[	[	X
ejpam-5864	39	23	18–22	18–22	NUM
ejpam-5864	39	24	]	]	PUNCT
ejpam-5864	39	25	.	.	PUNCT
ejpam-5864	40	1	the	the	DET
ejpam-5864	40	2	author	author	NOUN
ejpam-5864	40	3	in	in	ADP
ejpam-5864	40	4	[	[	X
ejpam-5864	40	5	23	23	NUM
ejpam-5864	40	6	]	]	PUNCT
ejpam-5864	40	7	studied	study	VERB
ejpam-5864	40	8	more	more	ADJ
ejpam-5864	40	9	features	feature	NOUN
ejpam-5864	40	10	of	of	ADP
ejpam-5864	40	11	conformable	conformable	ADJ
ejpam-5864	40	12	fractional	fractional	ADJ
ejpam-5864	40	13	derivatives	derivative	NOUN
ejpam-5864	40	14	where	where	SCONJ
ejpam-5864	40	15	the	the	DET
ejpam-5864	40	16	endpoints	endpoint	NOUN
ejpam-5864	40	17	are	be	AUX
ejpam-5864	40	18	allowed	allow	VERB
ejpam-5864	40	19	to	to	PART
ejpam-5864	40	20	appear	appear	VERB
ejpam-5864	40	21	in	in	ADP
ejpam-5864	40	22	the	the	DET
ejpam-5864	40	23	weight	weight	NOUN
ejpam-5864	40	24	of	of	ADP
ejpam-5864	40	25	the	the	DET
ejpam-5864	40	26	conformable	conformable	ADJ
ejpam-5864	40	27	integral	integral	ADJ
ejpam-5864	40	28	to	to	PART
ejpam-5864	40	29	define	define	VERB
ejpam-5864	40	30	the	the	DET
ejpam-5864	40	31	concepts	concept	NOUN
ejpam-5864	40	32	of	of	ADP
ejpam-5864	40	33	left	left	ADJ
ejpam-5864	40	34	and	and	CCONJ
ejpam-5864	40	35	right	right	ADJ
ejpam-5864	40	36	conformable	conformable	ADJ
ejpam-5864	40	37	derivatives	derivative	NOUN
ejpam-5864	40	38	.	.	PUNCT
ejpam-5864	41	1	recalling	recall	VERB
ejpam-5864	41	2	that	that	SCONJ
ejpam-5864	41	3	,	,	PUNCT
ejpam-5864	41	4	if	if	SCONJ
ejpam-5864	41	5	a	a	DET
ejpam-5864	41	6	function	function	NOUN
ejpam-5864	41	7	f	f	PROPN
ejpam-5864	41	8	is	be	AUX
ejpam-5864	41	9	differentiable	differentiable	ADJ
ejpam-5864	41	10	then	then	ADV
ejpam-5864	41	11	its	its	PRON
ejpam-5864	41	12	conformable	conformable	ADJ
ejpam-5864	41	13	derivative	derivative	ADJ
ejpam-5864	41	14	dαf(t	dαf(t	NOUN
ejpam-5864	41	15	)	)	PUNCT
ejpam-5864	41	16	of	of	ADP
ejpam-5864	41	17	order	order	NOUN
ejpam-5864	41	18	α	α	X
ejpam-5864	41	19	∈	∈	PROPN
ejpam-5864	41	20	(	(	PUNCT
ejpam-5864	41	21	0	0	NUM
ejpam-5864	41	22	,	,	PUNCT
ejpam-5864	41	23	1	1	NUM
ejpam-5864	41	24	]	]	PUNCT
ejpam-5864	41	25	will	will	AUX
ejpam-5864	41	26	equal	equal	VERB
ejpam-5864	41	27	to	to	ADP
ejpam-5864	41	28	t1−αf	t1−αf	NUM
ejpam-5864	41	29	′(t	′(t	NOUN
ejpam-5864	41	30	)	)	PUNCT
ejpam-5864	41	31	,	,	PUNCT
ejpam-5864	41	32	we	we	PRON
ejpam-5864	41	33	can	can	AUX
ejpam-5864	41	34	relate	relate	VERB
ejpam-5864	41	35	conformable	conformable	ADJ
ejpam-5864	41	36	derivatives	derivative	NOUN
ejpam-5864	41	37	to	to	ADP
ejpam-5864	41	38	a	a	DET
ejpam-5864	41	39	fractal	fractal	ADJ
ejpam-5864	41	40	type	type	NOUN
ejpam-5864	41	41	.	.	PUNCT
ejpam-5864	42	1	indeed	indeed	ADV
ejpam-5864	42	2	,	,	PUNCT
ejpam-5864	42	3	we	we	PRON
ejpam-5864	42	4	have	have	VERB
ejpam-5864	42	5	lim	lim	PROPN
ejpam-5864	42	6	t→s	t→s	NUM
ejpam-5864	42	7	f(t)−	f(t)−	PROPN
ejpam-5864	42	8	f(s	f(	NOUN
ejpam-5864	42	9	)	)	PUNCT
ejpam-5864	43	1	tα	tα	VERB
ejpam-5864	43	2	−	−	PROPN
ejpam-5864	43	3	sα	sα	PROPN
ejpam-5864	43	4	=	=	PROPN
ejpam-5864	43	5	lim	lim	PROPN
ejpam-5864	43	6	t→s	t→s	NUM
ejpam-5864	43	7	f(t)−	f(t)−	PROPN
ejpam-5864	43	8	f(s	f(	NOUN
ejpam-5864	43	9	)	)	PUNCT
ejpam-5864	43	10	tα	tα	VERB
ejpam-5864	43	11	−	−	PROPN
ejpam-5864	44	1	sα	sα	ADV
ejpam-5864	44	2	.	.	PUNCT
ejpam-5864	45	1	t−	t−	PROPN
ejpam-5864	45	2	s	s	VERB
ejpam-5864	45	3	t−	t−	PROPN
ejpam-5864	45	4	s	s	PART
ejpam-5864	45	5	.	.	PUNCT
ejpam-5864	46	1	(	(	PUNCT
ejpam-5864	46	2	1	1	X
ejpam-5864	46	3	)	)	PUNCT
ejpam-5864	46	4	then	then	ADV
ejpam-5864	46	5	,	,	PUNCT
ejpam-5864	46	6	we	we	PRON
ejpam-5864	46	7	have	have	VERB
ejpam-5864	46	8	lim	lim	PROPN
ejpam-5864	46	9	t→s	t→s	NUM
ejpam-5864	46	10	f(t)−	f(t)−	PROPN
ejpam-5864	46	11	f(s	f(	NOUN
ejpam-5864	46	12	)	)	PUNCT
ejpam-5864	47	1	tα	tα	VERB
ejpam-5864	47	2	−	−	PROPN
ejpam-5864	47	3	sα	sα	PROPN
ejpam-5864	47	4	=	=	PROPN
ejpam-5864	47	5	lim	lim	PROPN
ejpam-5864	47	6	t→s	t→s	NUM
ejpam-5864	47	7	t−	t−	PROPN
ejpam-5864	47	8	s	s	PART
ejpam-5864	47	9	tα	tα	PROPN
ejpam-5864	47	10	−	−	PROPN
ejpam-5864	47	11	sα	sα	PROPN
ejpam-5864	47	12	f	f	PROPN
ejpam-5864	47	13	′(t	′(t	PROPN
ejpam-5864	47	14	)	)	PUNCT
ejpam-5864	47	15	=	=	SYM
ejpam-5864	48	1	1	1	NUM
ejpam-5864	48	2	α	α	NOUN
ejpam-5864	48	3	t1−αf	t1−αf	NUM
ejpam-5864	48	4	′(t	′(t	NOUN
ejpam-5864	48	5	)	)	PUNCT
ejpam-5864	48	6	.	.	PUNCT
ejpam-5864	49	1	(	(	PUNCT
ejpam-5864	49	2	2	2	X
ejpam-5864	49	3	)	)	PUNCT
ejpam-5864	49	4	that	that	PRON
ejpam-5864	49	5	is	be	AUX
ejpam-5864	49	6	lim	lim	PROPN
ejpam-5864	49	7	t→s	t→s	NUM
ejpam-5864	49	8	f(t)−	f(t)−	PROPN
ejpam-5864	49	9	f(s	f(	NOUN
ejpam-5864	49	10	)	)	PUNCT
ejpam-5864	50	1	tα	tα	VERB
ejpam-5864	50	2	−	−	PROPN
ejpam-5864	50	3	sα	sα	ADJ
ejpam-5864	50	4	=	=	SYM
ejpam-5864	50	5	1	1	NUM
ejpam-5864	50	6	α	α	NOUN
ejpam-5864	50	7	dαf(t	dαf(t	PROPN
ejpam-5864	50	8	)	)	PUNCT
ejpam-5864	50	9	.	.	PUNCT
ejpam-5864	51	1	(	(	PUNCT
ejpam-5864	51	2	3	3	X
ejpam-5864	51	3	)	)	PUNCT
ejpam-5864	51	4	the	the	DET
ejpam-5864	51	5	theory	theory	NOUN
ejpam-5864	51	6	of	of	ADP
ejpam-5864	51	7	curves	curve	NOUN
ejpam-5864	51	8	involves	involve	VERB
ejpam-5864	51	9	examining	examine	VERB
ejpam-5864	51	10	the	the	DET
ejpam-5864	51	11	movement	movement	NOUN
ejpam-5864	51	12	of	of	ADP
ejpam-5864	51	13	a	a	DET
ejpam-5864	51	14	point	point	NOUN
ejpam-5864	51	15	within	within	ADP
ejpam-5864	51	16	a	a	DET
ejpam-5864	51	17	plane	plane	NOUN
ejpam-5864	51	18	or	or	CCONJ
ejpam-5864	51	19	a.	a.	NOUN
ejpam-5864	51	20	has	have	VERB
ejpam-5864	51	21	,	,	PUNCT
ejpam-5864	51	22	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	51	23	,	,	PUNCT
ejpam-5864	51	24	t.	t.	PROPN
ejpam-5864	51	25	abdeljawad	abdeljawad	PROPN
ejpam-5864	51	26	/	/	SYM
ejpam-5864	51	27	eur	eur	PROPN
ejpam-5864	51	28	.	.	PUNCT
ejpam-5864	52	1	j.	j.	PROPN
ejpam-5864	52	2	pure	pure	PROPN
ejpam-5864	52	3	appl	appl	PROPN
ejpam-5864	52	4	.	.	PROPN
ejpam-5864	52	5	math	math	PROPN
ejpam-5864	52	6	,	,	PUNCT
ejpam-5864	52	7	18	18	NUM
ejpam-5864	52	8	(	(	PUNCT
ejpam-5864	52	9	2	2	NUM
ejpam-5864	52	10	)	)	PUNCT
ejpam-5864	52	11	(	(	PUNCT
ejpam-5864	52	12	2025	2025	NUM
ejpam-5864	52	13	)	)	PUNCT
ejpam-5864	52	14	,	,	PUNCT
ejpam-5864	52	15	5864	5864	NUM
ejpam-5864	52	16	3	3	NUM
ejpam-5864	52	17	of	of	ADP
ejpam-5864	52	18	14	14	NUM
ejpam-5864	52	19	space	space	NOUN
ejpam-5864	52	20	using	use	VERB
ejpam-5864	52	21	tools	tool	NOUN
ejpam-5864	52	22	from	from	ADP
ejpam-5864	52	23	linear	linear	ADJ
ejpam-5864	52	24	algebra	algebra	NOUN
ejpam-5864	52	25	and	and	CCONJ
ejpam-5864	52	26	calculus	calculus	NOUN
ejpam-5864	52	27	.	.	PUNCT
ejpam-5864	53	1	in	in	ADP
ejpam-5864	53	2	recent	recent	ADJ
ejpam-5864	53	3	research	research	NOUN
ejpam-5864	53	4	,	,	PUNCT
ejpam-5864	53	5	there	there	PRON
ejpam-5864	53	6	’s	’	VERB
ejpam-5864	53	7	a	a	DET
ejpam-5864	53	8	notable	notable	ADJ
ejpam-5864	53	9	trend	trend	NOUN
ejpam-5864	53	10	where	where	SCONJ
ejpam-5864	53	11	fractional	fractional	ADJ
ejpam-5864	53	12	calculus	calculus	NOUN
ejpam-5864	53	13	has	have	AUX
ejpam-5864	53	14	begun	begin	VERB
ejpam-5864	53	15	to	to	PART
ejpam-5864	53	16	be	be	AUX
ejpam-5864	53	17	applied	apply	VERB
ejpam-5864	53	18	to	to	ADP
ejpam-5864	53	19	the	the	DET
ejpam-5864	53	20	study	study	NOUN
ejpam-5864	53	21	of	of	ADP
ejpam-5864	53	22	curves	curve	NOUN
ejpam-5864	53	23	and	and	CCONJ
ejpam-5864	53	24	surfaces	surface	NOUN
ejpam-5864	53	25	within	within	ADP
ejpam-5864	53	26	differential	differential	ADJ
ejpam-5864	53	27	geometry	geometry	NOUN
ejpam-5864	53	28	.	.	PUNCT
ejpam-5864	54	1	this	this	DET
ejpam-5864	54	2	trend	trend	NOUN
ejpam-5864	54	3	was	be	AUX
ejpam-5864	54	4	initiated	initiate	VERB
ejpam-5864	54	5	with	with	ADP
ejpam-5864	54	6	the	the	DET
ejpam-5864	54	7	pioneering	pioneering	ADJ
ejpam-5864	54	8	work	work	NOUN
ejpam-5864	54	9	of	of	ADP
ejpam-5864	54	10	t.	t.	PROPN
ejpam-5864	54	11	yajima	yajima	PROPN
ejpam-5864	54	12	and	and	CCONJ
ejpam-5864	54	13	k.	k.	PROPN
ejpam-5864	54	14	kamasaki	kamasaki	PROPN
ejpam-5864	54	15	,	,	PUNCT
ejpam-5864	54	16	who	who	PRON
ejpam-5864	54	17	conducted	conduct	VERB
ejpam-5864	54	18	the	the	DET
ejpam-5864	54	19	first	first	ADJ
ejpam-5864	54	20	study	study	NOUN
ejpam-5864	54	21	employing	employ	VERB
ejpam-5864	54	22	fractional	fractional	ADJ
ejpam-5864	54	23	calculus	calculus	NOUN
ejpam-5864	54	24	to	to	PART
ejpam-5864	54	25	analyze	analyze	VERB
ejpam-5864	54	26	surfaces	surface	NOUN
ejpam-5864	54	27	[	[	X
ejpam-5864	54	28	24	24	NUM
ejpam-5864	54	29	]	]	PUNCT
ejpam-5864	54	30	.	.	PUNCT
ejpam-5864	55	1	subsequently	subsequently	ADV
ejpam-5864	55	2	,	,	PUNCT
ejpam-5864	55	3	t.	t.	PROPN
ejpam-5864	55	4	yajima	yajima	PROPN
ejpam-5864	55	5	et	et	PROPN
ejpam-5864	55	6	al	al	PROPN
ejpam-5864	55	7	.	.	PROPN
ejpam-5864	55	8	extended	extend	VERB
ejpam-5864	55	9	this	this	DET
ejpam-5864	55	10	exploration	exploration	NOUN
ejpam-5864	55	11	by	by	ADP
ejpam-5864	55	12	deriving	derive	VERB
ejpam-5864	55	13	frenet	frenet	ADJ
ejpam-5864	55	14	formulas	formula	NOUN
ejpam-5864	55	15	using	use	VERB
ejpam-5864	55	16	fractional	fractional	ADJ
ejpam-5864	55	17	derivatives	derivative	NOUN
ejpam-5864	55	18	[	[	X
ejpam-5864	55	19	25	25	NUM
ejpam-5864	55	20	]	]	PUNCT
ejpam-5864	55	21	.	.	PUNCT
ejpam-5864	56	1	another	another	DET
ejpam-5864	56	2	significant	significant	ADJ
ejpam-5864	56	3	contribution	contribution	NOUN
ejpam-5864	56	4	came	come	VERB
ejpam-5864	56	5	from	from	ADP
ejpam-5864	56	6	k.a	k.a	PROPN
ejpam-5864	56	7	.	.	PUNCT
ejpam-5864	57	1	lazopoulos	lazopoulos	PROPN
ejpam-5864	57	2	and	and	CCONJ
ejpam-5864	57	3	a.k	a.k	PROPN
ejpam-5864	57	4	.	.	PROPN
ejpam-5864	57	5	lazopoulos	lazopoulos	PROPN
ejpam-5864	57	6	,	,	PUNCT
ejpam-5864	57	7	who	who	PRON
ejpam-5864	57	8	delved	delve	VERB
ejpam-5864	57	9	into	into	ADP
ejpam-5864	57	10	the	the	DET
ejpam-5864	57	11	realm	realm	NOUN
ejpam-5864	57	12	of	of	ADP
ejpam-5864	57	13	fractional	fractional	ADJ
ejpam-5864	57	14	differentiable	differentiable	ADJ
ejpam-5864	57	15	manifolds	manifold	NOUN
ejpam-5864	58	1	[	[	X
ejpam-5864	58	2	26	26	NUM
ejpam-5864	58	3	]	]	PUNCT
ejpam-5864	58	4	.	.	PUNCT
ejpam-5864	59	1	additionally	additionally	ADV
ejpam-5864	59	2	,	,	PUNCT
ejpam-5864	59	3	m.e	m.e	PROPN
ejpam-5864	59	4	.	.	PROPN
ejpam-5864	59	5	aydın	aydın	PROPN
ejpam-5864	59	6	et	et	PROPN
ejpam-5864	59	7	al	al	PROPN
ejpam-5864	59	8	.	.	PROPN
ejpam-5864	59	9	investigated	investigate	VERB
ejpam-5864	59	10	plane	plane	NOUN
ejpam-5864	59	11	curves	curve	NOUN
ejpam-5864	59	12	within	within	ADP
ejpam-5864	59	13	the	the	DET
ejpam-5864	59	14	context	context	NOUN
ejpam-5864	59	15	of	of	ADP
ejpam-5864	59	16	fractional	fractional	ADJ
ejpam-5864	59	17	order	order	NOUN
ejpam-5864	59	18	equiaffine	equiaffine	NOUN
ejpam-5864	59	19	geometry	geometry	NOUN
ejpam-5864	59	20	[	[	X
ejpam-5864	59	21	27	27	NUM
ejpam-5864	59	22	]	]	PUNCT
ejpam-5864	59	23	.	.	PUNCT
ejpam-5864	60	1	exploring	explore	VERB
ejpam-5864	60	2	the	the	DET
ejpam-5864	60	3	foundational	foundational	ADJ
ejpam-5864	60	4	concepts	concept	NOUN
ejpam-5864	60	5	of	of	ADP
ejpam-5864	60	6	curves	curve	NOUN
ejpam-5864	60	7	and	and	CCONJ
ejpam-5864	60	8	the	the	DET
ejpam-5864	60	9	frenet	frenet	ADJ
ejpam-5864	60	10	frame	frame	NOUN
ejpam-5864	60	11	within	within	ADP
ejpam-5864	60	12	the	the	DET
ejpam-5864	60	13	domain	domain	NOUN
ejpam-5864	60	14	of	of	ADP
ejpam-5864	60	15	fractional	fractional	ADJ
ejpam-5864	60	16	order	order	NOUN
ejpam-5864	60	17	,	,	PUNCT
ejpam-5864	60	18	u.	u.	PROPN
ejpam-5864	60	19	gozutok	gozutok	PROPN
ejpam-5864	60	20	et	et	PROPN
ejpam-5864	60	21	al	al	PROPN
ejpam-5864	60	22	.	.	PROPN
ejpam-5864	60	23	conducted	conduct	VERB
ejpam-5864	60	24	an	an	DET
ejpam-5864	60	25	analysis	analysis	NOUN
ejpam-5864	60	26	utilizing	utilize	VERB
ejpam-5864	60	27	conformable	conformable	ADJ
ejpam-5864	60	28	local	local	ADJ
ejpam-5864	60	29	fractional	fractional	ADJ
ejpam-5864	60	30	derivatives	derivative	NOUN
ejpam-5864	60	31	[	[	X
ejpam-5864	60	32	28	28	NUM
ejpam-5864	60	33	]	]	PUNCT
ejpam-5864	60	34	.	.	PUNCT
ejpam-5864	61	1	furthermore	furthermore	ADV
ejpam-5864	61	2	,	,	PUNCT
ejpam-5864	61	3	a.	a.	NOUN
ejpam-5864	61	4	has	have	AUX
ejpam-5864	61	5	and	and	CCONJ
ejpam-5864	61	6	b.	b.	PROPN
ejpam-5864	61	7	yılmaz	yılmaz	PROPN
ejpam-5864	61	8	investigated	investigate	VERB
ejpam-5864	61	9	specific	specific	ADJ
ejpam-5864	61	10	curves	curve	NOUN
ejpam-5864	61	11	and	and	CCONJ
ejpam-5864	61	12	curve	curve	NOUN
ejpam-5864	61	13	pairs	pair	NOUN
ejpam-5864	61	14	within	within	ADP
ejpam-5864	61	15	the	the	DET
ejpam-5864	61	16	context	context	NOUN
ejpam-5864	61	17	of	of	ADP
ejpam-5864	61	18	fractional	fractional	ADJ
ejpam-5864	61	19	order	order	NOUN
ejpam-5864	61	20	,	,	PUNCT
ejpam-5864	61	21	employing	employ	VERB
ejpam-5864	61	22	conformable	conformable	ADJ
ejpam-5864	61	23	frenet	frenet	NOUN
ejpam-5864	61	24	frames	frame	NOUN
ejpam-5864	61	25	[	[	X
ejpam-5864	61	26	29	29	NUM
ejpam-5864	61	27	,	,	PUNCT
ejpam-5864	61	28	30	30	NUM
ejpam-5864	61	29	]	]	PUNCT
ejpam-5864	61	30	.	.	PUNCT
ejpam-5864	62	1	moreover	moreover	ADV
ejpam-5864	62	2	,	,	PUNCT
ejpam-5864	62	3	the	the	DET
ejpam-5864	62	4	exploration	exploration	NOUN
ejpam-5864	62	5	of	of	ADP
ejpam-5864	62	6	electromagnetic	electromagnetic	ADJ
ejpam-5864	62	7	fields	field	NOUN
ejpam-5864	62	8	and	and	CCONJ
ejpam-5864	62	9	magnetic	magnetic	ADJ
ejpam-5864	62	10	curves	curve	NOUN
ejpam-5864	62	11	under	under	ADP
ejpam-5864	62	12	fractional	fractional	ADJ
ejpam-5864	62	13	derivatives	derivative	NOUN
ejpam-5864	62	14	has	have	AUX
ejpam-5864	62	15	been	be	AUX
ejpam-5864	62	16	undertaken	undertake	VERB
ejpam-5864	62	17	by	by	ADP
ejpam-5864	62	18	a.	a.	NOUN
ejpam-5864	62	19	has	have	AUX
ejpam-5864	62	20	and	and	CCONJ
ejpam-5864	62	21	b.	b.	PROPN
ejpam-5864	62	22	yılmaz	yılmaz	PROPN
ejpam-5864	63	1	[	[	X
ejpam-5864	63	2	31–33	31–33	NUM
ejpam-5864	63	3	]	]	PUNCT
ejpam-5864	63	4	.	.	PUNCT
ejpam-5864	64	1	these	these	DET
ejpam-5864	64	2	studies	study	NOUN
ejpam-5864	64	3	collectively	collectively	ADV
ejpam-5864	64	4	showcase	showcase	VERB
ejpam-5864	64	5	the	the	DET
ejpam-5864	64	6	burgeoning	burgeon	VERB
ejpam-5864	64	7	interest	interest	NOUN
ejpam-5864	64	8	and	and	CCONJ
ejpam-5864	64	9	application	application	NOUN
ejpam-5864	64	10	of	of	ADP
ejpam-5864	64	11	fractional	fractional	ADJ
ejpam-5864	64	12	calculus	calculus	NOUN
ejpam-5864	64	13	in	in	ADP
ejpam-5864	64	14	diverse	diverse	ADJ
ejpam-5864	64	15	aspects	aspect	NOUN
ejpam-5864	64	16	of	of	ADP
ejpam-5864	64	17	curve	curve	NOUN
ejpam-5864	64	18	theory	theory	NOUN
ejpam-5864	64	19	,	,	PUNCT
ejpam-5864	64	20	bringing	bring	VERB
ejpam-5864	64	21	forth	forth	ADP
ejpam-5864	64	22	new	new	ADJ
ejpam-5864	64	23	insights	insight	NOUN
ejpam-5864	64	24	and	and	CCONJ
ejpam-5864	64	25	methodologies	methodology	NOUN
ejpam-5864	64	26	within	within	ADP
ejpam-5864	64	27	the	the	DET
ejpam-5864	64	28	field	field	NOUN
ejpam-5864	64	29	of	of	ADP
ejpam-5864	64	30	differential	differential	ADJ
ejpam-5864	64	31	geometry	geometry	NOUN
ejpam-5864	64	32	.	.	PUNCT
ejpam-5864	65	1	in	in	ADP
ejpam-5864	65	2	this	this	DET
ejpam-5864	65	3	study	study	NOUN
ejpam-5864	65	4	,	,	PUNCT
ejpam-5864	65	5	algebraic	algebraic	ADJ
ejpam-5864	65	6	and	and	CCONJ
ejpam-5864	65	7	calculus	calculus	NOUN
ejpam-5864	65	8	-	-	PUNCT
ejpam-5864	65	9	based	base	VERB
ejpam-5864	65	10	properties	property	NOUN
ejpam-5864	65	11	of	of	ADP
ejpam-5864	65	12	curves	curve	NOUN
ejpam-5864	65	13	are	be	AUX
ejpam-5864	65	14	reconstructed	reconstruct	VERB
ejpam-5864	65	15	with	with	ADP
ejpam-5864	65	16	the	the	DET
ejpam-5864	65	17	help	help	NOUN
ejpam-5864	65	18	of	of	ADP
ejpam-5864	65	19	conformable	conformable	ADJ
ejpam-5864	65	20	local	local	ADJ
ejpam-5864	65	21	fractional	fractional	ADJ
ejpam-5864	65	22	derivatives	derivative	NOUN
ejpam-5864	65	23	.	.	PUNCT
ejpam-5864	66	1	first	first	ADV
ejpam-5864	66	2	of	of	ADP
ejpam-5864	66	3	all	all	PRON
ejpam-5864	66	4	,	,	PUNCT
ejpam-5864	66	5	line	line	NOUN
ejpam-5864	66	6	,	,	PUNCT
ejpam-5864	66	7	plane	plane	NOUN
ejpam-5864	66	8	and	and	CCONJ
ejpam-5864	66	9	sphere	sphere	NOUN
ejpam-5864	66	10	,	,	PUNCT
ejpam-5864	66	11	which	which	PRON
ejpam-5864	66	12	are	be	AUX
ejpam-5864	66	13	the	the	DET
ejpam-5864	66	14	most	most	ADV
ejpam-5864	66	15	basic	basic	ADJ
ejpam-5864	66	16	concepts	concept	NOUN
ejpam-5864	66	17	of	of	ADP
ejpam-5864	66	18	geometry	geometry	NOUN
ejpam-5864	66	19	,	,	PUNCT
ejpam-5864	66	20	are	be	AUX
ejpam-5864	66	21	redefined	redefine	VERB
ejpam-5864	66	22	in	in	ADP
ejpam-5864	66	23	fractional	fractional	ADJ
ejpam-5864	66	24	order	order	NOUN
ejpam-5864	66	25	.	.	PUNCT
ejpam-5864	67	1	afterward	afterward	ADV
ejpam-5864	67	2	,	,	PUNCT
ejpam-5864	67	3	the	the	DET
ejpam-5864	67	4	concepts	concept	NOUN
ejpam-5864	67	5	of	of	ADP
ejpam-5864	67	6	unit	unit	NOUN
ejpam-5864	67	7	and	and	CCONJ
ejpam-5864	67	8	orthogonality	orthogonality	NOUN
ejpam-5864	67	9	,	,	PUNCT
ejpam-5864	67	10	which	which	PRON
ejpam-5864	67	11	are	be	AUX
ejpam-5864	67	12	the	the	DET
ejpam-5864	67	13	algebraic	algebraic	ADJ
ejpam-5864	67	14	basis	basis	NOUN
ejpam-5864	67	15	of	of	ADP
ejpam-5864	67	16	curves	curve	NOUN
ejpam-5864	67	17	,	,	PUNCT
ejpam-5864	67	18	are	be	AUX
ejpam-5864	67	19	defined	define	VERB
ejpam-5864	67	20	in	in	ADP
ejpam-5864	67	21	accordance	accordance	NOUN
ejpam-5864	67	22	with	with	ADP
ejpam-5864	67	23	the	the	DET
ejpam-5864	67	24	fractional	fractional	ADJ
ejpam-5864	67	25	order	order	NOUN
ejpam-5864	67	26	.	.	PUNCT
ejpam-5864	68	1	then	then	ADV
ejpam-5864	68	2	,	,	PUNCT
ejpam-5864	68	3	the	the	DET
ejpam-5864	68	4	conformable	conformable	ADJ
ejpam-5864	68	5	frame	frame	NOUN
ejpam-5864	68	6	of	of	ADP
ejpam-5864	68	7	the	the	DET
ejpam-5864	68	8	conformable	conformable	ADJ
ejpam-5864	68	9	naturally	naturally	ADV
ejpam-5864	68	10	parameterized	parameterized	ADJ
ejpam-5864	68	11	curve	curve	NOUN
ejpam-5864	68	12	is	be	AUX
ejpam-5864	68	13	defined	define	VERB
ejpam-5864	68	14	.	.	PUNCT
ejpam-5864	69	1	throughout	throughout	ADP
ejpam-5864	69	2	this	this	DET
ejpam-5864	69	3	study	study	NOUN
ejpam-5864	69	4	,	,	PUNCT
ejpam-5864	69	5	definitions	definition	NOUN
ejpam-5864	69	6	based	base	VERB
ejpam-5864	69	7	on	on	ADP
ejpam-5864	69	8	conformable	conformable	ADJ
ejpam-5864	69	9	analysis	analysis	NOUN
ejpam-5864	69	10	are	be	AUX
ejpam-5864	69	11	denoted	denote	VERB
ejpam-5864	69	12	by	by	ADP
ejpam-5864	69	13	cα	cα	PROPN
ejpam-5864	69	14	.	.	PROPN
ejpam-5864	70	1	for	for	ADP
ejpam-5864	70	2	example	example	NOUN
ejpam-5864	70	3	cα−frame	cα−frame	NOUN
ejpam-5864	70	4	,	,	PUNCT
ejpam-5864	70	5	cα−naturally	cα−naturally	ADV
ejpam-5864	70	6	parameterized	parameterized	ADJ
ejpam-5864	70	7	curve	curve	NOUN
ejpam-5864	70	8	etc	etc	X
ejpam-5864	70	9	.	.	X
ejpam-5864	71	1	it	it	PRON
ejpam-5864	71	2	should	should	AUX
ejpam-5864	71	3	be	be	AUX
ejpam-5864	71	4	noted	note	VERB
ejpam-5864	71	5	here	here	ADV
ejpam-5864	71	6	that	that	SCONJ
ejpam-5864	71	7	the	the	DET
ejpam-5864	71	8	conformable	conformable	ADJ
ejpam-5864	71	9	frame	frame	NOUN
ejpam-5864	71	10	defined	define	VERB
ejpam-5864	71	11	in	in	ADP
ejpam-5864	71	12	this	this	DET
ejpam-5864	71	13	study	study	NOUN
ejpam-5864	71	14	is	be	AUX
ejpam-5864	71	15	different	different	ADJ
ejpam-5864	71	16	from	from	ADP
ejpam-5864	71	17	the	the	DET
ejpam-5864	71	18	frame	frame	NOUN
ejpam-5864	71	19	discussed	discuss	VERB
ejpam-5864	71	20	in	in	ADP
ejpam-5864	71	21	the	the	DET
ejpam-5864	71	22	study	study	NOUN
ejpam-5864	71	23	[	[	X
ejpam-5864	71	24	28	28	NUM
ejpam-5864	71	25	]	]	PUNCT
ejpam-5864	71	26	.	.	PUNCT
ejpam-5864	72	1	the	the	DET
ejpam-5864	72	2	conformable	conformable	ADJ
ejpam-5864	72	3	frame	frame	NOUN
ejpam-5864	72	4	mentioned	mention	VERB
ejpam-5864	72	5	in	in	ADP
ejpam-5864	72	6	this	this	DET
ejpam-5864	72	7	article	article	NOUN
ejpam-5864	72	8	is	be	AUX
ejpam-5864	72	9	completely	completely	ADV
ejpam-5864	72	10	defined	define	VERB
ejpam-5864	72	11	by	by	ADP
ejpam-5864	72	12	the	the	DET
ejpam-5864	72	13	vectors	vector	NOUN
ejpam-5864	72	14	’	'	PUNCT
ejpam-5864	72	15	conformable	conformable	ADJ
ejpam-5864	72	16	local	local	ADJ
ejpam-5864	72	17	fractional	fractional	ADJ
ejpam-5864	72	18	derivative	derivative	NOUN
ejpam-5864	72	19	and	and	CCONJ
ejpam-5864	72	20	gives	give	VERB
ejpam-5864	72	21	different	different	ADJ
ejpam-5864	72	22	results	result	NOUN
ejpam-5864	72	23	from	from	ADP
ejpam-5864	72	24	the	the	DET
ejpam-5864	72	25	classical	classical	ADJ
ejpam-5864	72	26	frenet	frenet	ADJ
ejpam-5864	72	27	frame	frame	NOUN
ejpam-5864	72	28	.	.	PUNCT
ejpam-5864	73	1	in	in	ADP
ejpam-5864	73	2	addition	addition	NOUN
ejpam-5864	73	3	,	,	PUNCT
ejpam-5864	73	4	the	the	DET
ejpam-5864	73	5	rectifying	rectifying	NOUN
ejpam-5864	73	6	curves	curve	NOUN
ejpam-5864	73	7	defined	define	VERB
ejpam-5864	73	8	by	by	ADP
ejpam-5864	73	9	chen	chen	PROPN
ejpam-5864	73	10	and	and	CCONJ
ejpam-5864	73	11	also	also	ADV
ejpam-5864	73	12	called	call	VERB
ejpam-5864	73	13	chen	chen	PROPN
ejpam-5864	73	14	curves	curve	NOUN
ejpam-5864	73	15	in	in	ADP
ejpam-5864	73	16	the	the	DET
ejpam-5864	73	17	article	article	NOUN
ejpam-5864	73	18	are	be	AUX
ejpam-5864	73	19	examined	examine	VERB
ejpam-5864	73	20	with	with	ADP
ejpam-5864	73	21	a	a	DET
ejpam-5864	73	22	conformable	conformable	ADJ
ejpam-5864	73	23	local	local	ADJ
ejpam-5864	73	24	fractional	fractional	ADJ
ejpam-5864	73	25	derivative	derivative	NOUN
ejpam-5864	73	26	and	and	CCONJ
ejpam-5864	73	27	their	their	PRON
ejpam-5864	73	28	fractional	fractional	ADJ
ejpam-5864	73	29	order	order	NOUN
ejpam-5864	73	30	characterizations	characterization	NOUN
ejpam-5864	73	31	are	be	AUX
ejpam-5864	73	32	obtained	obtain	VERB
ejpam-5864	73	33	.	.	PUNCT
ejpam-5864	74	1	finally	finally	ADV
ejpam-5864	74	2	,	,	PUNCT
ejpam-5864	74	3	in	in	ADP
ejpam-5864	74	4	the	the	DET
ejpam-5864	74	5	study	study	NOUN
ejpam-5864	74	6	,	,	PUNCT
ejpam-5864	74	7	examples	example	NOUN
ejpam-5864	74	8	of	of	ADP
ejpam-5864	74	9	the	the	DET
ejpam-5864	74	10	concepts	concept	NOUN
ejpam-5864	74	11	obtained	obtain	VERB
ejpam-5864	74	12	from	from	ADP
ejpam-5864	74	13	fractional	fractional	ADJ
ejpam-5864	74	14	order	order	NOUN
ejpam-5864	74	15	are	be	AUX
ejpam-5864	74	16	given	give	VERB
ejpam-5864	74	17	and	and	CCONJ
ejpam-5864	74	18	their	their	PRON
ejpam-5864	74	19	graphs	graph	NOUN
ejpam-5864	74	20	are	be	AUX
ejpam-5864	74	21	drawn	draw	VERB
ejpam-5864	74	22	.	.	PUNCT
ejpam-5864	75	1	2	2	X
ejpam-5864	75	2	.	.	NUM
ejpam-5864	75	3	preliminaries	preliminary	NOUN
ejpam-5864	75	4	2.1	2.1	NUM
ejpam-5864	75	5	.	.	PUNCT
ejpam-5864	76	1	basics	basic	NOUN
ejpam-5864	76	2	parametrized	parametrize	VERB
ejpam-5864	76	3	curves	curve	VERB
ejpam-5864	76	4	a	a	DET
ejpam-5864	76	5	regular	regular	ADJ
ejpam-5864	76	6	natural	natural	ADJ
ejpam-5864	76	7	parametrization	parametrization	NOUN
ejpam-5864	76	8	of	of	ADP
ejpam-5864	76	9	class	class	NOUN
ejpam-5864	76	10	ck	ck	PROPN
ejpam-5864	76	11	,	,	PUNCT
ejpam-5864	76	12	with	with	SCONJ
ejpam-5864	76	13	k	k	PROPN
ejpam-5864	76	14	≥	≥	NUM
ejpam-5864	76	15	1	1	NUM
ejpam-5864	76	16	of	of	ADP
ejpam-5864	76	17	a	a	DET
ejpam-5864	76	18	curve	curve	NOUN
ejpam-5864	76	19	in	in	ADP
ejpam-5864	76	20	r3	r3	PROPN
ejpam-5864	76	21	is	be	AUX
ejpam-5864	76	22	a	a	DET
ejpam-5864	76	23	vector	vector	NOUN
ejpam-5864	76	24	valued	value	VERB
ejpam-5864	76	25	function	function	NOUN
ejpam-5864	77	1	x	x	X
ejpam-5864	77	2	:	:	PUNCT
ejpam-5864	77	3	i	i	PRON
ejpam-5864	77	4	⊂	⊂	VERB
ejpam-5864	77	5	r	r	NOUN
ejpam-5864	77	6	→	→	SYM
ejpam-5864	77	7	e3	e3	NOUN
ejpam-5864	77	8	,	,	PUNCT
ejpam-5864	77	9	s	s	PART
ejpam-5864	77	10	7→	7→	NUM
ejpam-5864	77	11	x(s	x(s	PROPN
ejpam-5864	77	12	)	)	PUNCT
ejpam-5864	78	1	=	=	PRON
ejpam-5864	78	2	(	(	PUNCT
ejpam-5864	78	3	x1(s),x2(s),x3(s	x1(s),x2(s),x3(s	PROPN
ejpam-5864	78	4	)	)	PUNCT
ejpam-5864	78	5	)	)	PUNCT
ejpam-5864	79	1	defined	define	VERB
ejpam-5864	79	2	on	on	ADP
ejpam-5864	79	3	an	an	DET
ejpam-5864	79	4	interval	interval	NOUN
ejpam-5864	79	5	i	i	PRON
ejpam-5864	79	6	which	which	PRON
ejpam-5864	79	7	satisfies	satisfy	VERB
ejpam-5864	79	8	x	x	VERB
ejpam-5864	79	9	is	be	AUX
ejpam-5864	79	10	of	of	ADP
ejpam-5864	79	11	class	class	NOUN
ejpam-5864	79	12	ck	ck	NOUN
ejpam-5864	79	13	and	and	CCONJ
ejpam-5864	79	14	x′(s	x′(s	CCONJ
ejpam-5864	79	15	)	)	PUNCT
ejpam-5864	80	1	̸=	̸=	NOUN
ejpam-5864	80	2	0	0	NUM
ejpam-5864	80	3	for	for	ADP
ejpam-5864	80	4	all	all	PRON
ejpam-5864	80	5	s	s	VERB
ejpam-5864	80	6	∈	∈	NOUN
ejpam-5864	80	7	i	i	PRON
ejpam-5864	80	8	where	where	SCONJ
ejpam-5864	80	9	e	e	NOUN
ejpam-5864	80	10	denotes	denote	VERB
ejpam-5864	80	11	euclidean	euclidean	ADJ
ejpam-5864	80	12	space	space	NOUN
ejpam-5864	80	13	.	.	PUNCT
ejpam-5864	81	1	a	a	DET
ejpam-5864	81	2	curve	curve	NOUN
ejpam-5864	81	3	x	x	PUNCT
ejpam-5864	81	4	is	be	AUX
ejpam-5864	81	5	continuously	continuously	ADV
ejpam-5864	81	6	differentiable	differentiable	ADJ
ejpam-5864	81	7	if	if	SCONJ
ejpam-5864	81	8	x′(s	x′(s	X
ejpam-5864	81	9	)	)	PUNCT
ejpam-5864	81	10	exists	exist	VERB
ejpam-5864	81	11	for	for	ADP
ejpam-5864	81	12	all	all	PRON
ejpam-5864	81	13	s	s	PART
ejpam-5864	81	14	∈	∈	PRON
ejpam-5864	82	1	i	i	PRON
ejpam-5864	82	2	and	and	CCONJ
ejpam-5864	82	3	the	the	DET
ejpam-5864	82	4	derivative	derivative	NOUN
ejpam-5864	82	5	x′(s	x′(s	X
ejpam-5864	82	6	)	)	PUNCT
ejpam-5864	82	7	is	be	AUX
ejpam-5864	82	8	a	a	DET
ejpam-5864	82	9	continuous	continuous	ADJ
ejpam-5864	82	10	function	function	NOUN
ejpam-5864	82	11	;	;	PUNCT
ejpam-5864	82	12	thinking	think	VERB
ejpam-5864	82	13	dynamically	dynamically	ADV
ejpam-5864	82	14	,	,	PUNCT
ejpam-5864	82	15	the	the	DET
ejpam-5864	82	16	vector	vector	NOUN
ejpam-5864	82	17	x′(s	x′(s	PROPN
ejpam-5864	82	18	)	)	PUNCT
ejpam-5864	82	19	is	be	AUX
ejpam-5864	82	20	the	the	DET
ejpam-5864	82	21	velocity	velocity	NOUN
ejpam-5864	82	22	of	of	ADP
ejpam-5864	82	23	the	the	DET
ejpam-5864	82	24	curve	curve	NOUN
ejpam-5864	82	25	a.	a.	NOUN
ejpam-5864	82	26	has	have	VERB
ejpam-5864	82	27	,	,	PUNCT
ejpam-5864	82	28	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	82	29	,	,	PUNCT
ejpam-5864	82	30	t.	t.	PROPN
ejpam-5864	82	31	abdeljawad	abdeljawad	PROPN
ejpam-5864	82	32	/	/	SYM
ejpam-5864	82	33	eur	eur	PROPN
ejpam-5864	82	34	.	.	PUNCT
ejpam-5864	83	1	j.	j.	PROPN
ejpam-5864	83	2	pure	pure	PROPN
ejpam-5864	83	3	appl	appl	PROPN
ejpam-5864	83	4	.	.	PROPN
ejpam-5864	83	5	math	math	PROPN
ejpam-5864	83	6	,	,	PUNCT
ejpam-5864	83	7	18	18	NUM
ejpam-5864	83	8	(	(	PUNCT
ejpam-5864	83	9	2	2	NUM
ejpam-5864	83	10	)	)	PUNCT
ejpam-5864	83	11	(	(	PUNCT
ejpam-5864	83	12	2025	2025	NUM
ejpam-5864	83	13	)	)	PUNCT
ejpam-5864	83	14	,	,	PUNCT
ejpam-5864	83	15	5864	5864	NUM
ejpam-5864	83	16	4	4	NUM
ejpam-5864	83	17	of	of	ADP
ejpam-5864	83	18	14	14	NUM
ejpam-5864	83	19	at	at	ADP
ejpam-5864	83	20	time	time	NOUN
ejpam-5864	83	21	s.	s.	PROPN
ejpam-5864	83	22	we	we	PRON
ejpam-5864	83	23	call	call	VERB
ejpam-5864	83	24	x(s	x(s	PROPN
ejpam-5864	83	25	)	)	PUNCT
ejpam-5864	83	26	a	a	DET
ejpam-5864	83	27	naturally	naturally	ADV
ejpam-5864	83	28	parametrized	parametrized	ADJ
ejpam-5864	83	29	curve	curve	NOUN
ejpam-5864	83	30	if	if	SCONJ
ejpam-5864	83	31	xi(s	xi(s	NUM
ejpam-5864	83	32	)	)	PUNCT
ejpam-5864	84	1	(	(	PUNCT
ejpam-5864	84	2	i	i	NOUN
ejpam-5864	84	3	=	=	NOUN
ejpam-5864	84	4	1	1	NUM
ejpam-5864	84	5	,	,	PUNCT
ejpam-5864	84	6	2	2	NUM
ejpam-5864	84	7	,	,	PUNCT
ejpam-5864	84	8	3	3	NUM
ejpam-5864	84	9	)	)	PUNCT
ejpam-5864	84	10	is	be	AUX
ejpam-5864	84	11	of	of	ADP
ejpam-5864	84	12	class	class	NOUN
ejpam-5864	84	13	ck	ck	NOUN
ejpam-5864	84	14	and	and	CCONJ
ejpam-5864	84	15	∥x′(s)∥	∥x′(s)∥	PRON
ejpam-5864	85	1	=	=	SYM
ejpam-5864	85	2	1	1	NUM
ejpam-5864	85	3	,	,	PUNCT
ejpam-5864	85	4	for	for	ADP
ejpam-5864	85	5	each	each	DET
ejpam-5864	85	6	s	s	X
ejpam-5864	85	7	∈	∈	NOUN
ejpam-5864	86	1	i	i	PRON
ejpam-5864	87	1	[	[	X
ejpam-5864	87	2	34	34	NUM
ejpam-5864	87	3	]	]	PUNCT
ejpam-5864	87	4	.	.	PUNCT
ejpam-5864	88	1	let	let	AUX
ejpam-5864	88	2	x(s	x(s	PROPN
ejpam-5864	88	3	)	)	PUNCT
ejpam-5864	88	4	be	be	AUX
ejpam-5864	88	5	biregular	biregular	ADJ
ejpam-5864	88	6	,	,	PUNCT
ejpam-5864	88	7	that	that	ADV
ejpam-5864	88	8	is	is	ADV
ejpam-5864	88	9	,	,	PUNCT
ejpam-5864	88	10	x′(s)×x′′(s	x′(s)×x′′(s	ADJ
ejpam-5864	88	11	)	)	PUNCT
ejpam-5864	88	12	̸=	̸=	PROPN
ejpam-5864	88	13	0	0	NUM
ejpam-5864	88	14	,	,	PUNCT
ejpam-5864	88	15	for	for	ADP
ejpam-5864	88	16	each	each	DET
ejpam-5864	88	17	s	s	PROPN
ejpam-5864	88	18	∈	∈	PROPN
ejpam-5864	88	19	i.	i.	NOUN
ejpam-5864	88	20	we	we	PRON
ejpam-5864	88	21	consider	consider	VERB
ejpam-5864	88	22	a	a	DET
ejpam-5864	88	23	trihedron	trihedron	NOUN
ejpam-5864	88	24	{	{	PUNCT
ejpam-5864	88	25	t	t	PROPN
ejpam-5864	88	26	(	(	PUNCT
ejpam-5864	88	27	s	s	NOUN
ejpam-5864	88	28	)	)	PUNCT
ejpam-5864	88	29	,	,	PUNCT
ejpam-5864	88	30	n(s	n(s	PROPN
ejpam-5864	88	31	)	)	PUNCT
ejpam-5864	88	32	,	,	PUNCT
ejpam-5864	88	33	b(s	b(	NOUN
ejpam-5864	88	34	)	)	PUNCT
ejpam-5864	88	35	}	}	PUNCT
ejpam-5864	88	36	along	along	ADP
ejpam-5864	88	37	x(s	x(s	PROPN
ejpam-5864	88	38	)	)	PUNCT
ejpam-5864	88	39	,	,	PUNCT
ejpam-5864	88	40	so	so	ADV
ejpam-5864	88	41	-	-	PUNCT
ejpam-5864	88	42	called	call	VERB
ejpam-5864	88	43	frenet	frenet	ADJ
ejpam-5864	88	44	frame	frame	NOUN
ejpam-5864	88	45	,	,	PUNCT
ejpam-5864	89	1	where	where	SCONJ
ejpam-5864	89	2	[	[	X
ejpam-5864	89	3	34	34	NUM
ejpam-5864	89	4	]	]	X
ejpam-5864	89	5	t	t	PROPN
ejpam-5864	89	6	(	(	PUNCT
ejpam-5864	89	7	s	s	NOUN
ejpam-5864	89	8	)	)	PUNCT
ejpam-5864	89	9	=	=	SYM
ejpam-5864	90	1	x′(s	x′(s	PROPN
ejpam-5864	90	2	)	)	PUNCT
ejpam-5864	90	3	,	,	PUNCT
ejpam-5864	90	4	n(s	n(s	PROPN
ejpam-5864	90	5	)	)	PUNCT
ejpam-5864	90	6	=	=	SYM
ejpam-5864	90	7	t	t	PROPN
ejpam-5864	90	8	′(s	′(s	NOUN
ejpam-5864	90	9	)	)	PUNCT
ejpam-5864	91	1	∥t	∥t	ADJ
ejpam-5864	91	2	′(s)∥	′(s)∥	NOUN
ejpam-5864	91	3	,	,	PUNCT
ejpam-5864	91	4	b(s	b(	NOUN
ejpam-5864	91	5	)	)	PUNCT
ejpam-5864	92	1	=	=	SYM
ejpam-5864	92	2	t	t	PROPN
ejpam-5864	92	3	(	(	PUNCT
ejpam-5864	92	4	s)×n(s	s)×n(s	NOUN
ejpam-5864	92	5	)	)	PUNCT
ejpam-5864	92	6	.	.	PUNCT
ejpam-5864	93	1	the	the	DET
ejpam-5864	93	2	curvature	curvature	NOUN
ejpam-5864	93	3	κ	κ	PROPN
ejpam-5864	93	4	,	,	PUNCT
ejpam-5864	93	5	a	a	DET
ejpam-5864	93	6	non	non	ADJ
ejpam-5864	93	7	-	-	ADJ
ejpam-5864	93	8	negative	negative	ADJ
ejpam-5864	93	9	scalar	scalar	ADJ
ejpam-5864	93	10	field	field	NOUN
ejpam-5864	93	11	,	,	PUNCT
ejpam-5864	93	12	is	be	AUX
ejpam-5864	93	13	defined	define	VERB
ejpam-5864	93	14	by	by	ADP
ejpam-5864	93	15	setting	set	VERB
ejpam-5864	93	16	κ(s	κ(s	PROPN
ejpam-5864	93	17	)	)	PUNCT
ejpam-5864	94	1	=	=	PUNCT
ejpam-5864	95	1	∥t	∥t	ADJ
ejpam-5864	95	2	′(s)∥	′(s)∥	NOUN
ejpam-5864	95	3	and	and	CCONJ
ejpam-5864	95	4	torsion	torsion	NOUN
ejpam-5864	95	5	is	be	AUX
ejpam-5864	95	6	defined	define	VERB
ejpam-5864	95	7	by	by	ADP
ejpam-5864	95	8	setting	set	VERB
ejpam-5864	95	9	τ(s	τ(s	NOUN
ejpam-5864	95	10	)	)	PUNCT
ejpam-5864	95	11	=	=	PUNCT
ejpam-5864	96	1	⟨n	⟨n	NUM
ejpam-5864	96	2	′(s	′(s	NOUN
ejpam-5864	96	3	)	)	PUNCT
ejpam-5864	96	4	,	,	PUNCT
ejpam-5864	96	5	b(s)⟩.	b(s)⟩.	VERB
ejpam-5864	96	6	the	the	DET
ejpam-5864	96	7	naturally	naturally	ADV
ejpam-5864	96	8	parametrized	parametrized	ADJ
ejpam-5864	96	9	curve	curve	NOUN
ejpam-5864	96	10	x	x	PUNCT
ejpam-5864	96	11	has	have	VERB
ejpam-5864	96	12	unit	unit	NOUN
ejpam-5864	96	13	speed	speed	NOUN
ejpam-5864	96	14	and	and	CCONJ
ejpam-5864	96	15	strictly	strictly	ADV
ejpam-5864	96	16	positive	positive	ADJ
ejpam-5864	96	17	curvature	curvature	NOUN
ejpam-5864	96	18	then	then	ADV
ejpam-5864	96	19	the	the	DET
ejpam-5864	96	20	following	follow	VERB
ejpam-5864	96	21	equations	equation	NOUN
ejpam-5864	96	22	hold	hold	VERB
ejpam-5864	97	1	[	[	X
ejpam-5864	97	2	34]t	34]t	NUM
ejpam-5864	97	3	′	′	NUM
ejpam-5864	98	1	n	n	CCONJ
ejpam-5864	98	2	′	′	NUM
ejpam-5864	98	3	b′	b′	NOUN
ejpam-5864	98	4			NOUN
ejpam-5864	98	5	=	=	PUNCT
ejpam-5864	98	6			NOUN
ejpam-5864	98	7	0	0	NUM
ejpam-5864	98	8	κ	κ	PROPN
ejpam-5864	98	9	0	0	NUM
ejpam-5864	98	10	−κ	−κ	NOUN
ejpam-5864	98	11	0	0	NUM
ejpam-5864	99	1	τ	τ	X
ejpam-5864	99	2	0	0	NUM
ejpam-5864	100	1	−τ	−τ	NOUN
ejpam-5864	100	2	0	0	PUNCT
ejpam-5864	101	1	tn	tn	ADJ
ejpam-5864	101	2	b	b	NOUN
ejpam-5864	101	3			NOUN
ejpam-5864	101	4	.	.	PUNCT
ejpam-5864	102	1	(	(	PUNCT
ejpam-5864	102	2	4	4	NUM
ejpam-5864	102	3	)	)	PUNCT
ejpam-5864	102	4	2.2	2.2	NUM
ejpam-5864	102	5	.	.	PUNCT
ejpam-5864	103	1	basics	basic	NOUN
ejpam-5864	103	2	in	in	ADP
ejpam-5864	103	3	conformable	conformable	ADJ
ejpam-5864	103	4	fractional	fractional	ADJ
ejpam-5864	103	5	calculus	calculus	NOUN
ejpam-5864	103	6	given	give	VERB
ejpam-5864	103	7	s	s	PROPN
ejpam-5864	103	8	7→	7→	NUM
ejpam-5864	103	9	x(s	x(s	PROPN
ejpam-5864	103	10	)	)	PUNCT
ejpam-5864	103	11	∈	∈	PROPN
ejpam-5864	103	12	e3	e3	NOUN
ejpam-5864	103	13	,	,	PUNCT
ejpam-5864	103	14	s	s	PART
ejpam-5864	103	15	∈	∈	X
ejpam-5864	104	1	i	i	PRON
ejpam-5864	104	2	⊂	⊂	PROPN
ejpam-5864	104	3	r	r	NOUN
ejpam-5864	104	4	,	,	PUNCT
ejpam-5864	104	5	the	the	DET
ejpam-5864	104	6	conformable	conformable	ADJ
ejpam-5864	104	7	derivative	derivative	NOUN
ejpam-5864	104	8	of	of	ADP
ejpam-5864	104	9	x	x	PUNCT
ejpam-5864	104	10	at	at	ADP
ejpam-5864	104	11	s	s	PROPN
ejpam-5864	104	12	is	be	AUX
ejpam-5864	104	13	defined	define	VERB
ejpam-5864	104	14	by	by	ADP
ejpam-5864	104	15	[	[	X
ejpam-5864	104	16	19	19	NUM
ejpam-5864	104	17	]	]	PUNCT
ejpam-5864	104	18	dα(x)(s	dα(x)(s	NUM
ejpam-5864	104	19	)	)	PUNCT
ejpam-5864	105	1	=	=	SYM
ejpam-5864	105	2	lim	lim	PROPN
ejpam-5864	105	3	ε→0	ε→0	NOUN
ejpam-5864	105	4	x(s+	x(s+	PROPN
ejpam-5864	105	5	εs1−α)−	εs1−α)−	X
ejpam-5864	105	6	x(s	x(s	PROPN
ejpam-5864	105	7	)	)	PUNCT
ejpam-5864	105	8	ε	ε	PROPN
ejpam-5864	105	9	.	.	PUNCT
ejpam-5864	106	1	let	let	VERB
ejpam-5864	106	2	dx(s	dx(s	X
ejpam-5864	106	3	)	)	PUNCT
ejpam-5864	106	4	=	=	PUNCT
ejpam-5864	107	1	dx(s)/ds	dx(s)/ds	NOUN
ejpam-5864	107	2	.	.	PUNCT
ejpam-5864	108	1	we	we	PRON
ejpam-5864	108	2	then	then	ADV
ejpam-5864	108	3	notice	notice	VERB
ejpam-5864	108	4	dαx(s	dαx(s	PROPN
ejpam-5864	108	5	)	)	PUNCT
ejpam-5864	108	6	=	=	SYM
ejpam-5864	109	1	s1−αdx(s)/ds	s1−αdx(s)/ds	PROPN
ejpam-5864	109	2	.	.	PUNCT
ejpam-5864	109	3	denote	denote	VERB
ejpam-5864	109	4	by	by	ADP
ejpam-5864	109	5	dαx(s	dαx(s	PROPN
ejpam-5864	109	6	)	)	PUNCT
ejpam-5864	109	7	the	the	DET
ejpam-5864	109	8	α	α	NOUN
ejpam-5864	109	9	-	-	PUNCT
ejpam-5864	109	10	th	th	VERB
ejpam-5864	109	11	order	order	NOUN
ejpam-5864	109	12	conformable	conformable	ADJ
ejpam-5864	109	13	derivative	derivative	NOUN
ejpam-5864	109	14	of	of	ADP
ejpam-5864	109	15	x(s	x(s	PROPN
ejpam-5864	109	16	)	)	PUNCT
ejpam-5864	109	17	for	for	ADP
ejpam-5864	109	18	each	each	PRON
ejpam-5864	109	19	s	s	X
ejpam-5864	109	20	>	>	X
ejpam-5864	109	21	0	0	NUM
ejpam-5864	109	22	,	,	PUNCT
ejpam-5864	109	23	0	0	NUM
ejpam-5864	109	24	<	<	X
ejpam-5864	109	25	α	α	X
ejpam-5864	109	26	<	<	X
ejpam-5864	109	27	1	1	NUM
ejpam-5864	109	28	.	.	PUNCT
ejpam-5864	110	1	it	it	PRON
ejpam-5864	110	2	can	can	AUX
ejpam-5864	110	3	be	be	AUX
ejpam-5864	110	4	said	say	VERB
ejpam-5864	110	5	that	that	SCONJ
ejpam-5864	110	6	the	the	DET
ejpam-5864	110	7	conformable	conformable	ADJ
ejpam-5864	110	8	derivative	derivative	NOUN
ejpam-5864	110	9	provides	provide	VERB
ejpam-5864	110	10	some	some	DET
ejpam-5864	110	11	properties	property	NOUN
ejpam-5864	110	12	such	such	ADJ
ejpam-5864	110	13	as	as	ADP
ejpam-5864	110	14	linearity	linearity	NOUN
ejpam-5864	110	15	,	,	PUNCT
ejpam-5864	110	16	leibniz	leibniz	NOUN
ejpam-5864	110	17	rule	rule	NOUN
ejpam-5864	110	18	and	and	CCONJ
ejpam-5864	110	19	chain	chain	NOUN
ejpam-5864	110	20	rule	rule	NOUN
ejpam-5864	110	21	as	as	ADP
ejpam-5864	110	22	in	in	ADP
ejpam-5864	110	23	the	the	DET
ejpam-5864	110	24	classical	classical	ADJ
ejpam-5864	110	25	derivative	derivative	NOUN
ejpam-5864	110	26	as	as	SCONJ
ejpam-5864	110	27	follows	follow	VERB
ejpam-5864	110	28	(	(	PUNCT
ejpam-5864	110	29	i	i	NOUN
ejpam-5864	110	30	)	)	PUNCT
ejpam-5864	110	31	dα(ax+	dα(ax+	PROPN
ejpam-5864	110	32	by)(s	by)(s	PROPN
ejpam-5864	110	33	)	)	PUNCT
ejpam-5864	111	1	=	=	PUNCT
ejpam-5864	111	2	adα(x)(s	adα(x)(s	ADV
ejpam-5864	111	3	)	)	PUNCT
ejpam-5864	111	4	+	+	CCONJ
ejpam-5864	111	5	bdα(y)(s	bdα(y)(s	NOUN
ejpam-5864	111	6	)	)	PUNCT
ejpam-5864	111	7	,	,	PUNCT
ejpam-5864	111	8	for	for	ADP
ejpam-5864	111	9	all	all	DET
ejpam-5864	111	10	a	a	PRON
ejpam-5864	111	11	,	,	PUNCT
ejpam-5864	111	12	b	b	X
ejpam-5864	111	13	∈	∈	PROPN
ejpam-5864	111	14	r	r	NOUN
ejpam-5864	111	15	,	,	PUNCT
ejpam-5864	111	16	(	(	PUNCT
ejpam-5864	111	17	ii	ii	NOUN
ejpam-5864	111	18	)	)	PUNCT
ejpam-5864	111	19	dα(s	dα(s	NOUN
ejpam-5864	111	20	p	p	X
ejpam-5864	111	21	)	)	PUNCT
ejpam-5864	111	22	=	=	SYM
ejpam-5864	111	23	psp−α	psp−α	NOUN
ejpam-5864	111	24	for	for	ADP
ejpam-5864	111	25	all	all	DET
ejpam-5864	111	26	p	p	NOUN
ejpam-5864	111	27	∈	∈	PROPN
ejpam-5864	111	28	r	r	NOUN
ejpam-5864	111	29	,	,	PUNCT
ejpam-5864	111	30	(	(	PUNCT
ejpam-5864	111	31	iii	iii	NOUN
ejpam-5864	111	32	)	)	PUNCT
ejpam-5864	111	33	dα(λ	dα(λ	X
ejpam-5864	111	34	)	)	PUNCT
ejpam-5864	111	35	=	=	SYM
ejpam-5864	112	1	0	0	NUM
ejpam-5864	112	2	,	,	PUNCT
ejpam-5864	112	3	for	for	ADP
ejpam-5864	112	4	all	all	DET
ejpam-5864	112	5	constant	constant	ADJ
ejpam-5864	112	6	functions	function	NOUN
ejpam-5864	112	7	x(s	x(s	PROPN
ejpam-5864	112	8	)	)	PUNCT
ejpam-5864	113	1	=	=	PUNCT
ejpam-5864	113	2	λ	λ	NOUN
ejpam-5864	113	3	,	,	PUNCT
ejpam-5864	113	4	(	(	PUNCT
ejpam-5864	113	5	iv	iv	NOUN
ejpam-5864	113	6	)	)	PUNCT
ejpam-5864	113	7	dα(xy)(s	dα(xy)(s	NOUN
ejpam-5864	113	8	)	)	PUNCT
ejpam-5864	113	9	=	=	SYM
ejpam-5864	113	10	x(s)dαy(s	x(s)dαy(	VERB
ejpam-5864	113	11	)	)	PUNCT
ejpam-5864	113	12	+	+	NUM
ejpam-5864	113	13	y(s)dαx(s	y(s)dαx(s	NOUN
ejpam-5864	113	14	)	)	PUNCT
ejpam-5864	113	15	,	,	PUNCT
ejpam-5864	113	16	(	(	PUNCT
ejpam-5864	113	17	v	v	NOUN
ejpam-5864	113	18	)	)	PUNCT
ejpam-5864	113	19	dα	dα	PROPN
ejpam-5864	113	20	(	(	PUNCT
ejpam-5864	113	21	x	x	NOUN
ejpam-5864	113	22	y	y	PROPN
ejpam-5864	113	23	)	)	PUNCT
ejpam-5864	113	24	(	(	PUNCT
ejpam-5864	113	25	s	s	X
ejpam-5864	113	26	)	)	PUNCT
ejpam-5864	113	27	=	=	SYM
ejpam-5864	113	28	x(s)dαy(s)−y(s)dαx(s	x(s)dαy(s)−y(s)dαx(s	PROPN
ejpam-5864	113	29	)	)	PUNCT
ejpam-5864	113	30	y2(s	y2(s	PROPN
ejpam-5864	113	31	)	)	PUNCT
ejpam-5864	113	32	,	,	PUNCT
ejpam-5864	113	33	(	(	PUNCT
ejpam-5864	113	34	vi	vi	NOUN
ejpam-5864	113	35	)	)	PUNCT
ejpam-5864	113	36	dα(y	dα(y	NOUN
ejpam-5864	113	37	◦	◦	NOUN
ejpam-5864	113	38	x)(s	x)(s	NUM
ejpam-5864	113	39	)	)	PUNCT
ejpam-5864	113	40	=	=	SYM
ejpam-5864	113	41	x(s)α−1dαx(s)dαy(x(s	x(s)α−1dαx(s)dαy(x(s	NOUN
ejpam-5864	113	42	)	)	PUNCT
ejpam-5864	113	43	)	)	PUNCT
ejpam-5864	113	44	where	where	SCONJ
ejpam-5864	113	45	x	x	X
ejpam-5864	113	46	,	,	PUNCT
ejpam-5864	113	47	y	y	PRON
ejpam-5864	113	48	be	be	VERB
ejpam-5864	113	49	conformable	conformable	ADJ
ejpam-5864	113	50	differentiable	differentiable	ADJ
ejpam-5864	113	51	for	for	ADP
ejpam-5864	113	52	each	each	PRON
ejpam-5864	113	53	s	s	X
ejpam-5864	113	54	>	>	X
ejpam-5864	113	55	0	0	PUNCT
ejpam-5864	113	56	and	and	CCONJ
ejpam-5864	113	57	0	0	NUM
ejpam-5864	113	58	<	<	X
ejpam-5864	113	59	α	α	X
ejpam-5864	113	60	<	<	X
ejpam-5864	113	61	1	1	NUM
ejpam-5864	113	62	[	[	X
ejpam-5864	113	63	19	19	NUM
ejpam-5864	113	64	]	]	PUNCT
ejpam-5864	113	65	.	.	PUNCT
ejpam-5864	114	1	the	the	DET
ejpam-5864	114	2	conformable	conformable	ADJ
ejpam-5864	114	3	integral	integral	NOUN
ejpam-5864	114	4	is	be	AUX
ejpam-5864	114	5	defined	define	VERB
ejpam-5864	114	6	as	as	ADP
ejpam-5864	114	7	the	the	DET
ejpam-5864	114	8	inverse	inverse	NOUN
ejpam-5864	114	9	operator	operator	NOUN
ejpam-5864	114	10	to	to	ADP
ejpam-5864	114	11	the	the	DET
ejpam-5864	114	12	conformable	conformable	ADJ
ejpam-5864	114	13	derivative	derivative	NOUN
ejpam-5864	114	14	.	.	PUNCT
ejpam-5864	115	1	specifically	specifically	ADV
ejpam-5864	115	2	,	,	PUNCT
ejpam-5864	115	3	the	the	DET
ejpam-5864	115	4	conformable	conformable	ADJ
ejpam-5864	115	5	integral	integral	ADJ
ejpam-5864	115	6	of	of	ADP
ejpam-5864	115	7	a	a	DET
ejpam-5864	115	8	function	function	NOUN
ejpam-5864	115	9	x(s	x(s	PROPN
ejpam-5864	115	10	)	)	PUNCT
ejpam-5864	115	11	is	be	AUX
ejpam-5864	115	12	formally	formally	ADV
ejpam-5864	115	13	expressed	express	VERB
ejpam-5864	115	14	as	as	ADP
ejpam-5864	115	15	[	[	X
ejpam-5864	115	16	19	19	NUM
ejpam-5864	115	17	]	]	SYM
ejpam-5864	115	18	iaαf(t	iaαf(t	X
ejpam-5864	115	19	)	)	PUNCT
ejpam-5864	115	20	=	=	SYM
ejpam-5864	115	21	ia1	ia1	NOUN
ejpam-5864	115	22	(	(	PUNCT
ejpam-5864	115	23	t	t	PROPN
ejpam-5864	115	24	α−1f	α−1f	PROPN
ejpam-5864	115	25	)	)	PUNCT
ejpam-5864	115	26	=	=	SYM
ejpam-5864	116	1	∫	∫	PROPN
ejpam-5864	116	2	t	t	PROPN
ejpam-5864	116	3	a	a	DET
ejpam-5864	116	4	f(x	f(x	PROPN
ejpam-5864	116	5	)	)	PUNCT
ejpam-5864	116	6	x1−α	x1−α	PROPN
ejpam-5864	116	7	dx	dx	PROPN
ejpam-5864	116	8	.	.	PUNCT
ejpam-5864	117	1	a.	a.	PROPN
ejpam-5864	117	2	has	have	VERB
ejpam-5864	117	3	,	,	PUNCT
ejpam-5864	117	4	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	117	5	,	,	PUNCT
ejpam-5864	117	6	t.	t.	PROPN
ejpam-5864	117	7	abdeljawad	abdeljawad	PROPN
ejpam-5864	117	8	/	/	SYM
ejpam-5864	117	9	eur	eur	PROPN
ejpam-5864	117	10	.	.	PUNCT
ejpam-5864	118	1	j.	j.	PROPN
ejpam-5864	118	2	pure	pure	PROPN
ejpam-5864	118	3	appl	appl	PROPN
ejpam-5864	118	4	.	.	PROPN
ejpam-5864	118	5	math	math	PROPN
ejpam-5864	118	6	,	,	PUNCT
ejpam-5864	118	7	18	18	NUM
ejpam-5864	118	8	(	(	PUNCT
ejpam-5864	118	9	2	2	NUM
ejpam-5864	118	10	)	)	PUNCT
ejpam-5864	118	11	(	(	PUNCT
ejpam-5864	118	12	2025	2025	NUM
ejpam-5864	118	13	)	)	PUNCT
ejpam-5864	118	14	,	,	PUNCT
ejpam-5864	118	15	5864	5864	NUM
ejpam-5864	118	16	5	5	NUM
ejpam-5864	118	17	of	of	ADP
ejpam-5864	118	18	14	14	NUM
ejpam-5864	118	19	the	the	DET
ejpam-5864	118	20	impact	impact	NOUN
ejpam-5864	118	21	of	of	ADP
ejpam-5864	118	22	conformable	conformable	ADJ
ejpam-5864	118	23	analysis	analysis	NOUN
ejpam-5864	118	24	on	on	ADP
ejpam-5864	118	25	vector	vector	NOUN
ejpam-5864	118	26	-	-	PUNCT
ejpam-5864	118	27	valued	value	VERB
ejpam-5864	118	28	functions	function	NOUN
ejpam-5864	118	29	is	be	AUX
ejpam-5864	118	30	a	a	DET
ejpam-5864	118	31	subject	subject	NOUN
ejpam-5864	118	32	of	of	ADP
ejpam-5864	118	33	investigation	investigation	NOUN
ejpam-5864	118	34	,	,	PUNCT
ejpam-5864	118	35	exploring	explore	VERB
ejpam-5864	118	36	both	both	CCONJ
ejpam-5864	118	37	the	the	DET
ejpam-5864	118	38	limits	limit	NOUN
ejpam-5864	118	39	and	and	CCONJ
ejpam-5864	118	40	derivatives	derivative	NOUN
ejpam-5864	118	41	of	of	ADP
ejpam-5864	118	42	these	these	DET
ejpam-5864	118	43	functions	function	NOUN
ejpam-5864	118	44	within	within	ADP
ejpam-5864	118	45	this	this	DET
ejpam-5864	118	46	framework	framework	NOUN
ejpam-5864	118	47	.	.	PUNCT
ejpam-5864	119	1	the	the	DET
ejpam-5864	119	2	subsequent	subsequent	ADJ
ejpam-5864	119	3	theorem	theorem	NOUN
ejpam-5864	119	4	delineates	delineate	VERB
ejpam-5864	119	5	the	the	DET
ejpam-5864	119	6	formulation	formulation	NOUN
ejpam-5864	119	7	of	of	ADP
ejpam-5864	119	8	the	the	DET
ejpam-5864	119	9	conformable	conformable	ADJ
ejpam-5864	119	10	derivative	derivative	NOUN
ejpam-5864	119	11	applied	apply	VERB
ejpam-5864	119	12	to	to	ADP
ejpam-5864	119	13	vector	vector	NOUN
ejpam-5864	119	14	-	-	PUNCT
ejpam-5864	119	15	valued	value	VERB
ejpam-5864	119	16	functions	function	NOUN
ejpam-5864	119	17	.	.	PUNCT
ejpam-5864	120	1	theorem	theorem	NOUN
ejpam-5864	120	2	1	1	NUM
ejpam-5864	120	3	.	.	PUNCT
ejpam-5864	121	1	[	[	X
ejpam-5864	121	2	35	35	NUM
ejpam-5864	121	3	]	]	PUNCT
ejpam-5864	121	4	let	let	VERB
ejpam-5864	121	5	x	x	SYM
ejpam-5864	121	6	=	=	SYM
ejpam-5864	121	7	(	(	PUNCT
ejpam-5864	121	8	x1(s	x1(s	NOUN
ejpam-5864	121	9	)	)	PUNCT
ejpam-5864	121	10	,	,	PUNCT
ejpam-5864	121	11	x2(s	x2(s	PROPN
ejpam-5864	121	12	)	)	PUNCT
ejpam-5864	121	13	,	,	PUNCT
ejpam-5864	121	14	x3(s	x3(s	PROPN
ejpam-5864	121	15	)	)	PUNCT
ejpam-5864	121	16	,	,	PUNCT
ejpam-5864	121	17	...	...	PUNCT
ejpam-5864	121	18	,	,	PUNCT
ejpam-5864	121	19	xn(s	xn(s	NUM
ejpam-5864	121	20	)	)	PUNCT
ejpam-5864	121	21	)	)	PUNCT
ejpam-5864	121	22	be	be	AUX
ejpam-5864	121	23	a	a	DET
ejpam-5864	121	24	vector	vector	NOUN
ejpam-5864	121	25	-	-	PUNCT
ejpam-5864	121	26	valued	value	VERB
ejpam-5864	121	27	function	function	NOUN
ejpam-5864	121	28	with	with	ADP
ejpam-5864	121	29	n	n	NOUN
ejpam-5864	121	30	variables	variable	NOUN
ejpam-5864	121	31	.	.	PUNCT
ejpam-5864	122	1	so	so	ADV
ejpam-5864	122	2	x	x	PUNCT
ejpam-5864	122	3	is	be	AUX
ejpam-5864	122	4	α−differentiable	α−differentiable	NUM
ejpam-5864	122	5	at	at	ADP
ejpam-5864	122	6	s	s	PROPN
ejpam-5864	122	7	∈	∈	PROPN
ejpam-5864	122	8	r	r	NOUN
ejpam-5864	122	9	,	,	PUNCT
ejpam-5864	122	10	as	as	SCONJ
ejpam-5864	122	11	follows	follow	VERB
ejpam-5864	122	12	dαx(t	dαx(t	PROPN
ejpam-5864	122	13	)	)	PUNCT
ejpam-5864	122	14	=	=	PUNCT
ejpam-5864	122	15	(	(	PUNCT
ejpam-5864	122	16	dαx1(t	dαx1(t	PROPN
ejpam-5864	122	17	)	)	PUNCT
ejpam-5864	122	18	,	,	PUNCT
ejpam-5864	122	19	...	...	PUNCT
ejpam-5864	122	20	,	,	PUNCT
ejpam-5864	122	21	dαxm(t	dαxm(t	NOUN
ejpam-5864	122	22	)	)	PUNCT
ejpam-5864	122	23	)	)	PUNCT
ejpam-5864	122	24	.	.	PUNCT
ejpam-5864	123	1	3	3	X
ejpam-5864	123	2	.	.	X
ejpam-5864	123	3	conformable	conformable	ADJ
ejpam-5864	123	4	parametrized	parametrized	ADJ
ejpam-5864	123	5	curves	curve	NOUN
ejpam-5864	123	6	and	and	CCONJ
ejpam-5864	123	7	their	their	PRON
ejpam-5864	123	8	conformable	conformable	ADJ
ejpam-5864	123	9	frame	frame	NOUN
ejpam-5864	123	10	in	in	ADP
ejpam-5864	123	11	this	this	DET
ejpam-5864	123	12	section	section	NOUN
ejpam-5864	123	13	,	,	PUNCT
ejpam-5864	123	14	basic	basic	ADJ
ejpam-5864	123	15	vector	vector	NOUN
ejpam-5864	123	16	operations	operation	NOUN
ejpam-5864	123	17	and	and	CCONJ
ejpam-5864	123	18	parameterized	parameterized	ADJ
ejpam-5864	123	19	curves	curve	NOUN
ejpam-5864	123	20	will	will	AUX
ejpam-5864	123	21	be	be	AUX
ejpam-5864	123	22	reconstructed	reconstruct	VERB
ejpam-5864	123	23	with	with	ADP
ejpam-5864	123	24	conformable	conformable	ADJ
ejpam-5864	123	25	calculus	calculus	NOUN
ejpam-5864	123	26	.	.	PUNCT
ejpam-5864	124	1	first	first	ADV
ejpam-5864	124	2	of	of	ADP
ejpam-5864	124	3	all	all	PRON
ejpam-5864	124	4	,	,	PUNCT
ejpam-5864	124	5	let	let	VERB
ejpam-5864	124	6	’s	’s	PRON
ejpam-5864	124	7	define	define	VERB
ejpam-5864	124	8	the	the	DET
ejpam-5864	124	9	concepts	concept	NOUN
ejpam-5864	124	10	of	of	ADP
ejpam-5864	124	11	conformable	conformable	ADJ
ejpam-5864	124	12	angle	angle	NOUN
ejpam-5864	124	13	and	and	CCONJ
ejpam-5864	124	14	conformable	conformable	ADJ
ejpam-5864	124	15	orthogonality	orthogonality	NOUN
ejpam-5864	124	16	,	,	PUNCT
ejpam-5864	124	17	which	which	PRON
ejpam-5864	124	18	are	be	AUX
ejpam-5864	124	19	the	the	DET
ejpam-5864	124	20	most	most	ADV
ejpam-5864	124	21	important	important	ADJ
ejpam-5864	124	22	concepts	concept	NOUN
ejpam-5864	124	23	of	of	ADP
ejpam-5864	124	24	geometry	geometry	NOUN
ejpam-5864	124	25	,	,	PUNCT
ejpam-5864	124	26	with	with	ADP
ejpam-5864	124	27	the	the	DET
ejpam-5864	124	28	help	help	NOUN
ejpam-5864	124	29	of	of	ADP
ejpam-5864	124	30	conformable	conformable	ADJ
ejpam-5864	124	31	calculus	calculus	NOUN
ejpam-5864	124	32	as	as	SCONJ
ejpam-5864	124	33	follows	follow	VERB
ejpam-5864	124	34	.	.	PUNCT
ejpam-5864	125	1	the	the	DET
ejpam-5864	125	2	geometric	geometric	ADJ
ejpam-5864	125	3	interpretation	interpretation	NOUN
ejpam-5864	125	4	of	of	ADP
ejpam-5864	125	5	the	the	DET
ejpam-5864	125	6	conformable	conformable	ADJ
ejpam-5864	125	7	derivative	derivative	NOUN
ejpam-5864	125	8	is	be	AUX
ejpam-5864	125	9	based	base	VERB
ejpam-5864	125	10	on	on	ADP
ejpam-5864	125	11	the	the	DET
ejpam-5864	125	12	notion	notion	NOUN
ejpam-5864	125	13	of	of	ADP
ejpam-5864	125	14	fractal	fractal	ADJ
ejpam-5864	125	15	geometry	geometry	NOUN
ejpam-5864	125	16	.	.	PUNCT
ejpam-5864	126	1	in	in	ADP
ejpam-5864	126	2	fractal	fractal	ADJ
ejpam-5864	126	3	geometry	geometry	NOUN
ejpam-5864	126	4	,	,	PUNCT
ejpam-5864	126	5	objects	object	NOUN
ejpam-5864	126	6	exhibit	exhibit	VERB
ejpam-5864	126	7	self	self	NOUN
ejpam-5864	126	8	-	-	PUNCT
ejpam-5864	126	9	similarity	similarity	NOUN
ejpam-5864	126	10	at	at	ADP
ejpam-5864	126	11	different	different	ADJ
ejpam-5864	126	12	scales	scale	NOUN
ejpam-5864	126	13	.	.	PUNCT
ejpam-5864	127	1	the	the	DET
ejpam-5864	127	2	conformable	conformable	ADJ
ejpam-5864	127	3	derivative	derivative	ADJ
ejpam-5864	127	4	captures	capture	NOUN
ejpam-5864	127	5	this	this	DET
ejpam-5864	127	6	self	self	NOUN
ejpam-5864	127	7	-	-	PUNCT
ejpam-5864	127	8	similar	similar	ADJ
ejpam-5864	127	9	behavior	behavior	NOUN
ejpam-5864	127	10	of	of	ADP
ejpam-5864	127	11	a	a	DET
ejpam-5864	127	12	function	function	NOUN
ejpam-5864	127	13	by	by	ADP
ejpam-5864	127	14	considering	consider	VERB
ejpam-5864	127	15	its	its	PRON
ejpam-5864	127	16	local	local	ADJ
ejpam-5864	127	17	fractional	fractional	ADJ
ejpam-5864	127	18	variations	variation	NOUN
ejpam-5864	127	19	.	.	PUNCT
ejpam-5864	128	1	geometrically	geometrically	ADV
ejpam-5864	128	2	,	,	PUNCT
ejpam-5864	128	3	it	it	PRON
ejpam-5864	128	4	can	can	AUX
ejpam-5864	128	5	be	be	AUX
ejpam-5864	128	6	understood	understand	VERB
ejpam-5864	128	7	as	as	ADP
ejpam-5864	128	8	analyzing	analyze	VERB
ejpam-5864	128	9	the	the	DET
ejpam-5864	128	10	”	"	PUNCT
ejpam-5864	128	11	zooming	zoom	VERB
ejpam-5864	128	12	in	in	ADP
ejpam-5864	128	13	”	"	PUNCT
ejpam-5864	128	14	behavior	behavior	NOUN
ejpam-5864	128	15	of	of	ADP
ejpam-5864	128	16	the	the	DET
ejpam-5864	128	17	function	function	NOUN
ejpam-5864	128	18	at	at	ADP
ejpam-5864	128	19	that	that	DET
ejpam-5864	128	20	point	point	NOUN
ejpam-5864	128	21	,	,	PUNCT
ejpam-5864	128	22	similar	similar	ADJ
ejpam-5864	128	23	to	to	ADP
ejpam-5864	128	24	the	the	DET
ejpam-5864	128	25	classical	classical	ADJ
ejpam-5864	128	26	derivative	derivative	NOUN
ejpam-5864	128	27	capturing	capture	VERB
ejpam-5864	128	28	the	the	DET
ejpam-5864	128	29	local	local	ADJ
ejpam-5864	128	30	linear	linear	ADJ
ejpam-5864	128	31	behavior	behavior	NOUN
ejpam-5864	128	32	.	.	PUNCT
ejpam-5864	129	1	overall	overall	ADV
ejpam-5864	129	2	,	,	PUNCT
ejpam-5864	129	3	the	the	DET
ejpam-5864	129	4	geometric	geometric	ADJ
ejpam-5864	129	5	interpretation	interpretation	NOUN
ejpam-5864	129	6	of	of	ADP
ejpam-5864	129	7	the	the	DET
ejpam-5864	129	8	conformable	conformable	ADJ
ejpam-5864	129	9	derivative	derivative	NOUN
ejpam-5864	129	10	relates	relate	VERB
ejpam-5864	129	11	to	to	ADP
ejpam-5864	129	12	the	the	DET
ejpam-5864	129	13	self	self	NOUN
ejpam-5864	129	14	-	-	PUNCT
ejpam-5864	129	15	similarity	similarity	NOUN
ejpam-5864	129	16	and	and	CCONJ
ejpam-5864	129	17	scaling	scale	VERB
ejpam-5864	129	18	properties	property	NOUN
ejpam-5864	129	19	of	of	ADP
ejpam-5864	129	20	functions	function	NOUN
ejpam-5864	129	21	,	,	PUNCT
ejpam-5864	129	22	enabling	enable	VERB
ejpam-5864	129	23	us	we	PRON
ejpam-5864	129	24	to	to	PART
ejpam-5864	129	25	understand	understand	VERB
ejpam-5864	129	26	their	their	PRON
ejpam-5864	129	27	behavior	behavior	NOUN
ejpam-5864	129	28	at	at	ADP
ejpam-5864	129	29	different	different	ADJ
ejpam-5864	129	30	levels	level	NOUN
ejpam-5864	129	31	of	of	ADP
ejpam-5864	129	32	detail	detail	NOUN
ejpam-5864	129	33	and	and	CCONJ
ejpam-5864	129	34	resolution	resolution	NOUN
ejpam-5864	129	35	.	.	PUNCT
ejpam-5864	130	1	more	more	ADV
ejpam-5864	130	2	specifically	specifically	ADV
ejpam-5864	130	3	,	,	PUNCT
ejpam-5864	130	4	the	the	DET
ejpam-5864	130	5	conformable	conformable	ADJ
ejpam-5864	130	6	derivative	derivative	NOUN
ejpam-5864	130	7	can	can	AUX
ejpam-5864	130	8	be	be	AUX
ejpam-5864	130	9	explained	explain	VERB
ejpam-5864	130	10	as	as	ADP
ejpam-5864	130	11	a	a	DET
ejpam-5864	130	12	measure	measure	NOUN
ejpam-5864	130	13	of	of	ADP
ejpam-5864	130	14	how	how	SCONJ
ejpam-5864	130	15	much	much	ADJ
ejpam-5864	130	16	a	a	DET
ejpam-5864	130	17	straight	straight	ADJ
ejpam-5864	130	18	line	line	NOUN
ejpam-5864	130	19	and	and	CCONJ
ejpam-5864	130	20	plane	plane	NOUN
ejpam-5864	130	21	bends	bend	NOUN
ejpam-5864	130	22	to	to	PART
ejpam-5864	130	23	form	form	VERB
ejpam-5864	130	24	a	a	DET
ejpam-5864	130	25	curve	curve	NOUN
ejpam-5864	130	26	and	and	CCONJ
ejpam-5864	130	27	a	a	DET
ejpam-5864	130	28	surface	surface	NOUN
ejpam-5864	130	29	.	.	PUNCT
ejpam-5864	131	1	figure	figure	NOUN
ejpam-5864	131	2	1	1	NUM
ejpam-5864	131	3	shows	show	VERB
ejpam-5864	131	4	how	how	SCONJ
ejpam-5864	131	5	a	a	DET
ejpam-5864	131	6	line	line	NOUN
ejpam-5864	131	7	is	be	AUX
ejpam-5864	131	8	curved	curve	VERB
ejpam-5864	131	9	with	with	ADP
ejpam-5864	131	10	the	the	DET
ejpam-5864	131	11	conformable	conformable	ADJ
ejpam-5864	131	12	calculus	calculus	NOUN
ejpam-5864	131	13	effect	effect	NOUN
ejpam-5864	131	14	.	.	PUNCT
ejpam-5864	132	1	example	example	NOUN
ejpam-5864	133	1	1	1	NUM
ejpam-5864	133	2	.	.	PUNCT
ejpam-5864	133	3	let	let	AUX
ejpam-5864	133	4	consider	consider	VERB
ejpam-5864	133	5	the	the	DET
ejpam-5864	133	6	s	s	PROPN
ejpam-5864	133	7	7→	7→	NUM
ejpam-5864	133	8	x(s	x(s	PROPN
ejpam-5864	133	9	)	)	PUNCT
ejpam-5864	134	1	=	=	PUNCT
ejpam-5864	134	2	(	(	PUNCT
ejpam-5864	134	3	s	s	PROPN
ejpam-5864	134	4	,	,	PUNCT
ejpam-5864	134	5	∫	∫	PROPN
ejpam-5864	134	6	s1−αds	s1−αd	NOUN
ejpam-5864	134	7	)	)	PUNCT
ejpam-5864	134	8	,	,	PUNCT
ejpam-5864	134	9	cα−line	cα−line	NOUN
ejpam-5864	134	10	passing	pass	VERB
ejpam-5864	134	11	through	through	ADP
ejpam-5864	134	12	the	the	DET
ejpam-5864	134	13	point	point	NOUN
ejpam-5864	134	14	p	p	X
ejpam-5864	134	15	=	=	X
ejpam-5864	134	16	(	(	PUNCT
ejpam-5864	134	17	0	0	NUM
ejpam-5864	134	18	,	,	PUNCT
ejpam-5864	134	19	0	0	NUM
ejpam-5864	134	20	)	)	PUNCT
ejpam-5864	134	21	and	and	CCONJ
ejpam-5864	134	22	whose	whose	DET
ejpam-5864	134	23	direction	direction	NOUN
ejpam-5864	134	24	is	be	AUX
ejpam-5864	134	25	v	v	NOUN
ejpam-5864	134	26	=	=	PUNCT
ejpam-5864	134	27	(	(	PUNCT
ejpam-5864	134	28	s1−α	s1−α	PROPN
ejpam-5864	134	29	,	,	PUNCT
ejpam-5864	134	30	s1−α	s1−α	PROPN
ejpam-5864	134	31	)	)	PUNCT
ejpam-5864	134	32	.	.	PUNCT
ejpam-5864	135	1	in	in	ADP
ejpam-5864	135	2	figure	figure	NOUN
ejpam-5864	135	3	1	1	NUM
ejpam-5864	135	4	we	we	PRON
ejpam-5864	135	5	present	present	VERB
ejpam-5864	135	6	the	the	DET
ejpam-5864	135	7	graph	graph	NOUN
ejpam-5864	135	8	of	of	ADP
ejpam-5864	135	9	the	the	DET
ejpam-5864	135	10	conformable	conformable	ADJ
ejpam-5864	135	11	line	line	NOUN
ejpam-5864	135	12	for	for	ADP
ejpam-5864	135	13	different	different	ADJ
ejpam-5864	135	14	α	α	NOUN
ejpam-5864	135	15	values	value	NOUN
ejpam-5864	135	16	.	.	PUNCT
ejpam-5864	136	1	as	as	SCONJ
ejpam-5864	136	2	seen	see	VERB
ejpam-5864	136	3	in	in	ADP
ejpam-5864	136	4	figure	figure	NOUN
ejpam-5864	136	5	1	1	NUM
ejpam-5864	136	6	,	,	PUNCT
ejpam-5864	136	7	there	there	PRON
ejpam-5864	136	8	is	be	VERB
ejpam-5864	136	9	no	no	DET
ejpam-5864	136	10	classical	classical	ADJ
ejpam-5864	136	11	line	line	NOUN
ejpam-5864	136	12	in	in	ADP
ejpam-5864	136	13	the	the	DET
ejpam-5864	136	14	cα−	cα−	PUNCT
ejpam-5864	136	15	(	(	PUNCT
ejpam-5864	136	16	fractional	fractional	ADJ
ejpam-5864	136	17	)	)	PUNCT
ejpam-5864	136	18	system	system	NOUN
ejpam-5864	136	19	.	.	PUNCT
ejpam-5864	137	1	this	this	PRON
ejpam-5864	137	2	is	be	AUX
ejpam-5864	137	3	only	only	ADV
ejpam-5864	137	4	achieved	achieve	VERB
ejpam-5864	137	5	when	when	SCONJ
ejpam-5864	137	6	α	α	PROPN
ejpam-5864	137	7	→	→	SYM
ejpam-5864	137	8	1	1	X
ejpam-5864	137	9	.	.	PUNCT
ejpam-5864	137	10	accordingly	accordingly	ADV
ejpam-5864	137	11	,	,	PUNCT
ejpam-5864	137	12	it	it	PRON
ejpam-5864	137	13	requires	require	VERB
ejpam-5864	137	14	a	a	DET
ejpam-5864	137	15	new	new	ADJ
ejpam-5864	137	16	concept	concept	NOUN
ejpam-5864	137	17	of	of	ADP
ejpam-5864	137	18	angle	angle	NOUN
ejpam-5864	137	19	in	in	ADP
ejpam-5864	137	20	cα−	cα−	NOUN
ejpam-5864	137	21	space	space	NOUN
ejpam-5864	137	22	.	.	PUNCT
ejpam-5864	138	1	this	this	DET
ejpam-5864	138	2	angle	angle	NOUN
ejpam-5864	138	3	is	be	AUX
ejpam-5864	138	4	called	call	VERB
ejpam-5864	138	5	the	the	DET
ejpam-5864	138	6	cα−	cα−	PUNCT
ejpam-5864	138	7	angle	angle	NOUN
ejpam-5864	138	8	,	,	PUNCT
ejpam-5864	138	9	which	which	PRON
ejpam-5864	138	10	gives	give	VERB
ejpam-5864	138	11	the	the	DET
ejpam-5864	138	12	angle	angle	NOUN
ejpam-5864	138	13	between	between	ADP
ejpam-5864	138	14	two	two	NUM
ejpam-5864	138	15	cα−	cα−	NOUN
ejpam-5864	138	16	lines	line	NOUN
ejpam-5864	138	17	.	.	PUNCT
ejpam-5864	139	1	in	in	ADP
ejpam-5864	139	2	addition	addition	NOUN
ejpam-5864	139	3	,	,	PUNCT
ejpam-5864	139	4	the	the	DET
ejpam-5864	139	5	concept	concept	NOUN
ejpam-5864	139	6	of	of	ADP
ejpam-5864	139	7	orthogonality	orthogonality	NOUN
ejpam-5864	139	8	in	in	ADP
ejpam-5864	139	9	this	this	PRON
ejpam-5864	139	10	cα−	cα−	PUNCT
ejpam-5864	139	11	space	space	NOUN
ejpam-5864	139	12	is	be	AUX
ejpam-5864	139	13	different	different	ADJ
ejpam-5864	139	14	from	from	ADP
ejpam-5864	139	15	the	the	DET
ejpam-5864	139	16	classical	classical	ADJ
ejpam-5864	139	17	one	one	NOUN
ejpam-5864	139	18	.	.	PUNCT
ejpam-5864	140	1	because	because	SCONJ
ejpam-5864	140	2	we	we	PRON
ejpam-5864	140	3	can	can	AUX
ejpam-5864	140	4	not	not	PART
ejpam-5864	140	5	talk	talk	VERB
ejpam-5864	140	6	about	about	ADP
ejpam-5864	140	7	classical	classical	ADJ
ejpam-5864	140	8	directness	directness	NOUN
ejpam-5864	140	9	,	,	PUNCT
ejpam-5864	140	10	we	we	PRON
ejpam-5864	140	11	can	can	AUX
ejpam-5864	140	12	not	not	PART
ejpam-5864	140	13	talk	talk	VERB
ejpam-5864	140	14	about	about	ADP
ejpam-5864	140	15	steepness	steepness	NOUN
ejpam-5864	140	16	in	in	ADP
ejpam-5864	140	17	the	the	DET
ejpam-5864	140	18	classical	classical	ADJ
ejpam-5864	140	19	sense	sense	NOUN
ejpam-5864	140	20	.	.	PUNCT
ejpam-5864	141	1	we	we	PRON
ejpam-5864	141	2	will	will	AUX
ejpam-5864	141	3	explain	explain	VERB
ejpam-5864	141	4	this	this	PRON
ejpam-5864	141	5	below	below	ADV
ejpam-5864	141	6	.	.	PUNCT
ejpam-5864	142	1	notation	notation	NOUN
ejpam-5864	142	2	:	:	PUNCT
ejpam-5864	142	3	along	along	ADP
ejpam-5864	142	4	the	the	DET
ejpam-5864	142	5	study	study	NOUN
ejpam-5864	142	6	,	,	PUNCT
ejpam-5864	142	7	expressions	expression	NOUN
ejpam-5864	142	8	that	that	PRON
ejpam-5864	142	9	are	be	AUX
ejpam-5864	142	10	equal	equal	ADJ
ejpam-5864	142	11	to	to	ADP
ejpam-5864	142	12	1	1	NUM
ejpam-5864	142	13	when	when	SCONJ
ejpam-5864	142	14	α	α	PROPN
ejpam-5864	142	15	→	→	SYM
ejpam-5864	142	16	1	1	NUM
ejpam-5864	142	17	will	will	AUX
ejpam-5864	142	18	be	be	AUX
ejpam-5864	142	19	denoted	denote	VERB
ejpam-5864	142	20	as	as	ADP
ejpam-5864	142	21	1α	1α	NUM
ejpam-5864	142	22	,	,	PUNCT
ejpam-5864	142	23	and	and	CCONJ
ejpam-5864	142	24	expressions	expression	NOUN
ejpam-5864	142	25	that	that	PRON
ejpam-5864	142	26	are	be	AUX
ejpam-5864	142	27	equal	equal	ADJ
ejpam-5864	142	28	to	to	ADP
ejpam-5864	142	29	0	0	NUM
ejpam-5864	142	30	when	when	SCONJ
ejpam-5864	142	31	α	α	PROPN
ejpam-5864	142	32	→	→	SYM
ejpam-5864	142	33	1	1	NUM
ejpam-5864	142	34	will	will	AUX
ejpam-5864	142	35	be	be	AUX
ejpam-5864	142	36	denoted	denote	VERB
ejpam-5864	142	37	as	as	ADP
ejpam-5864	142	38	0α	0α	PROPN
ejpam-5864	142	39	.	.	PUNCT
ejpam-5864	142	40	suppose	suppose	VERB
ejpam-5864	142	41	that	that	SCONJ
ejpam-5864	142	42	x	x	PROPN
ejpam-5864	142	43	and	and	CCONJ
ejpam-5864	142	44	y	y	PROPN
ejpam-5864	142	45	are	be	AUX
ejpam-5864	142	46	cα−unit	cα−unit	NOUN
ejpam-5864	142	47	vector	vector	NOUN
ejpam-5864	142	48	that	that	PRON
ejpam-5864	142	49	is	be	AUX
ejpam-5864	142	50	,	,	PUNCT
ejpam-5864	142	51	they	they	PRON
ejpam-5864	142	52	are	be	AUX
ejpam-5864	142	53	vectors	vector	NOUN
ejpam-5864	142	54	of	of	ADP
ejpam-5864	142	55	the	the	DET
ejpam-5864	142	56	form	form	NOUN
ejpam-5864	142	57	∥x∥	∥x∥	NOUN
ejpam-5864	142	58	=	=	SYM
ejpam-5864	142	59	1α	1α	NUM
ejpam-5864	142	60	and	and	CCONJ
ejpam-5864	142	61	∥y∥	∥y∥	NOUN
ejpam-5864	142	62	=	=	SYM
ejpam-5864	142	63	1α	1α	NUM
ejpam-5864	142	64	.	.	PUNCT
ejpam-5864	143	1	then	then	ADV
ejpam-5864	143	2	,	,	PUNCT
ejpam-5864	143	3	the	the	DET
ejpam-5864	143	4	α−conformable	α−conformable	ADJ
ejpam-5864	143	5	radian	radian	ADJ
ejpam-5864	143	6	measure	measure	NOUN
ejpam-5864	143	7	of	of	ADP
ejpam-5864	143	8	cα−angle	cα−angle	NOUN
ejpam-5864	143	9	between	between	ADP
ejpam-5864	143	10	x	x	PUNCT
ejpam-5864	143	11	and	and	CCONJ
ejpam-5864	143	12	y	y	PROPN
ejpam-5864	143	13	is	be	AUX
ejpam-5864	143	14	defined	define	VERB
ejpam-5864	143	15	by	by	ADP
ejpam-5864	143	16	θα	θα	NOUN
ejpam-5864	143	17	=	=	SYM
ejpam-5864	143	18	arccos	arccos	X
ejpam-5864	143	19	(	(	PUNCT
ejpam-5864	143	20	⟨x	⟨x	NUM
ejpam-5864	143	21	,	,	PUNCT
ejpam-5864	143	22	y⟩	y⟩	NOUN
ejpam-5864	143	23	∥x∥∥y∥	∥x∥∥y∥	PROPN
ejpam-5864	143	24	)	)	PUNCT
ejpam-5864	143	25	.	.	PUNCT
ejpam-5864	144	1	a.	a.	PROPN
ejpam-5864	144	2	has	have	VERB
ejpam-5864	144	3	,	,	PUNCT
ejpam-5864	144	4	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	144	5	,	,	PUNCT
ejpam-5864	144	6	t.	t.	PROPN
ejpam-5864	144	7	abdeljawad	abdeljawad	PROPN
ejpam-5864	144	8	/	/	SYM
ejpam-5864	144	9	eur	eur	PROPN
ejpam-5864	144	10	.	.	PUNCT
ejpam-5864	145	1	j.	j.	PROPN
ejpam-5864	145	2	pure	pure	PROPN
ejpam-5864	145	3	appl	appl	PROPN
ejpam-5864	145	4	.	.	PROPN
ejpam-5864	145	5	math	math	PROPN
ejpam-5864	145	6	,	,	PUNCT
ejpam-5864	145	7	18	18	NUM
ejpam-5864	145	8	(	(	PUNCT
ejpam-5864	145	9	2	2	NUM
ejpam-5864	145	10	)	)	PUNCT
ejpam-5864	145	11	(	(	PUNCT
ejpam-5864	145	12	2025	2025	NUM
ejpam-5864	145	13	)	)	PUNCT
ejpam-5864	145	14	,	,	PUNCT
ejpam-5864	145	15	5864	5864	NUM
ejpam-5864	145	16	6	6	NUM
ejpam-5864	145	17	of	of	ADP
ejpam-5864	145	18	14	14	NUM
ejpam-5864	145	19	figure	figure	NOUN
ejpam-5864	145	20	1	1	NUM
ejpam-5864	145	21	:	:	PUNCT
ejpam-5864	145	22	transformation	transformation	NOUN
ejpam-5864	145	23	from	from	ADP
ejpam-5864	145	24	line	line	NOUN
ejpam-5864	145	25	to	to	PART
ejpam-5864	145	26	curve	curve	VERB
ejpam-5864	145	27	.	.	PUNCT
ejpam-5864	146	1	in	in	ADP
ejpam-5864	146	2	this	this	DET
ejpam-5864	146	3	sense	sense	NOUN
ejpam-5864	146	4	,	,	PUNCT
ejpam-5864	146	5	⟨x	⟨x	VERB
ejpam-5864	146	6	,	,	PUNCT
ejpam-5864	146	7	y⟩	y⟩	NOUN
ejpam-5864	146	8	=	=	PUNCT
ejpam-5864	146	9	0α	0α	PROPN
ejpam-5864	146	10	when	when	SCONJ
ejpam-5864	146	11	x	x	PRON
ejpam-5864	146	12	and	and	CCONJ
ejpam-5864	146	13	y	y	PROPN
ejpam-5864	146	14	are	be	AUX
ejpam-5864	146	15	cα−orthogonal	cα−orthogonal	ADJ
ejpam-5864	146	16	.	.	PUNCT
ejpam-5864	147	1	for	for	ADP
ejpam-5864	147	2	example	example	NOUN
ejpam-5864	147	3	,	,	PUNCT
ejpam-5864	147	4	the	the	DET
ejpam-5864	147	5	cα−	cα−	NUM
ejpam-5864	147	6	vectors	vector	NOUN
ejpam-5864	147	7	u	u	NOUN
ejpam-5864	147	8	=	=	SYM
ejpam-5864	147	9	(	(	PUNCT
ejpam-5864	147	10	s1−α	s1−α	PROPN
ejpam-5864	147	11	,	,	PUNCT
ejpam-5864	147	12	1	1	NUM
ejpam-5864	147	13	−	−	NOUN
ejpam-5864	147	14	α	α	NOUN
ejpam-5864	147	15	,	,	PUNCT
ejpam-5864	147	16	1	1	NUM
ejpam-5864	147	17	s1−α	s1−α	PROPN
ejpam-5864	147	18	)	)	PUNCT
ejpam-5864	147	19	and	and	CCONJ
ejpam-5864	147	20	v	v	X
ejpam-5864	147	21	=	=	SYM
ejpam-5864	147	22	(	(	PUNCT
ejpam-5864	147	23	1−α	1−α	NUM
ejpam-5864	147	24	sα	sα	ADV
ejpam-5864	147	25	,	,	PUNCT
ejpam-5864	147	26	sα	sα	ADV
ejpam-5864	147	27	,	,	PUNCT
ejpam-5864	147	28	2	2	NUM
ejpam-5864	147	29	−	−	NOUN
ejpam-5864	147	30	2α	2α	NOUN
ejpam-5864	147	31	)	)	PUNCT
ejpam-5864	147	32	are	be	AUX
ejpam-5864	147	33	orthogonal	orthogonal	ADJ
ejpam-5864	147	34	to	to	ADP
ejpam-5864	147	35	each	each	DET
ejpam-5864	147	36	other	other	ADJ
ejpam-5864	147	37	in	in	ADP
ejpam-5864	147	38	the	the	DET
ejpam-5864	147	39	cα−	cα−	PUNCT
ejpam-5864	147	40	sense	sense	NOUN
ejpam-5864	147	41	,	,	PUNCT
ejpam-5864	147	42	and	and	CCONJ
ejpam-5864	147	43	we	we	PRON
ejpam-5864	147	44	present	present	VERB
ejpam-5864	147	45	this	this	PRON
ejpam-5864	147	46	in	in	ADP
ejpam-5864	147	47	figure	figure	NOUN
ejpam-5864	147	48	2	2	NUM
ejpam-5864	147	49	.	.	PUNCT
ejpam-5864	147	50	figure	figure	NOUN
ejpam-5864	147	51	2	2	NUM
ejpam-5864	147	52	:	:	PUNCT
ejpam-5864	147	53	cα−orthogonal	cα−orthogonal	ADJ
ejpam-5864	147	54	vectors	vector	NOUN
ejpam-5864	147	55	.	.	PUNCT
ejpam-5864	148	1	in	in	ADP
ejpam-5864	148	2	addition	addition	NOUN
ejpam-5864	148	3	,	,	PUNCT
ejpam-5864	148	4	vectors	vector	NOUN
ejpam-5864	148	5	u	u	NOUN
ejpam-5864	148	6	,	,	PUNCT
ejpam-5864	148	7	v	v	NOUN
ejpam-5864	148	8	and	and	CCONJ
ejpam-5864	148	9	u×v	u×v	PROPN
ejpam-5864	148	10	form	form	VERB
ejpam-5864	148	11	the	the	DET
ejpam-5864	148	12	fractional	fractional	ADJ
ejpam-5864	148	13	orthogonal	orthogonal	ADJ
ejpam-5864	148	14	system	system	NOUN
ejpam-5864	148	15	.	.	PUNCT
ejpam-5864	149	1	for	for	ADP
ejpam-5864	149	2	example	example	NOUN
ejpam-5864	149	3	,	,	PUNCT
ejpam-5864	149	4	if	if	SCONJ
ejpam-5864	149	5	u	u	PRON
ejpam-5864	149	6	=	=	X
ejpam-5864	149	7	(	(	PUNCT
ejpam-5864	149	8	s1−α	s1−α	PROPN
ejpam-5864	149	9	,	,	PUNCT
ejpam-5864	149	10	1−α	1−α	NUM
ejpam-5864	149	11	,	,	PUNCT
ejpam-5864	149	12	1	1	NUM
ejpam-5864	149	13	s1−α	s1−α	PROPN
ejpam-5864	149	14	)	)	PUNCT
ejpam-5864	149	15	and	and	CCONJ
ejpam-5864	149	16	v	v	X
ejpam-5864	149	17	=	=	SYM
ejpam-5864	149	18	(	(	PUNCT
ejpam-5864	149	19	1−α	1−α	NUM
ejpam-5864	149	20	sα	sα	ADV
ejpam-5864	149	21	,	,	PUNCT
ejpam-5864	149	22	sα	sα	ADV
ejpam-5864	149	23	,	,	PUNCT
ejpam-5864	149	24	2−2α	2−2α	NUM
ejpam-5864	149	25	)	)	PUNCT
ejpam-5864	149	26	,	,	PUNCT
ejpam-5864	149	27	it	it	PRON
ejpam-5864	149	28	becomes	become	VERB
ejpam-5864	149	29	u×v	u×v	PROPN
ejpam-5864	149	30	=	=	PUNCT
ejpam-5864	149	31	(	(	PUNCT
ejpam-5864	149	32	2α2−4α−s2α−1	2α2−4α−s2α−1	NOUN
ejpam-5864	149	33	+	+	CCONJ
ejpam-5864	149	34	2	2	NUM
ejpam-5864	149	35	,	,	PUNCT
ejpam-5864	149	36	2αs1−α	2αs1−α	NUM
ejpam-5864	149	37	−	−	NOUN
ejpam-5864	149	38	2s1−α	2s1−α	NUM
ejpam-5864	150	1	−	−	NOUN
ejpam-5864	151	1	α	α	PRON
ejpam-5864	151	2	s	s	PART
ejpam-5864	151	3	+	+	ADJ
ejpam-5864	151	4	1	1	NUM
ejpam-5864	151	5	s	s	NOUN
ejpam-5864	151	6	,	,	PUNCT
ejpam-5864	151	7	−α2s−α	−α2s−α	VERB
ejpam-5864	151	8	+2αs−α	+2αs−α	PROPN
ejpam-5864	151	9	−	−	PROPN
ejpam-5864	151	10	s−α	s−α	NOUN
ejpam-5864	151	11	+	+	CCONJ
ejpam-5864	151	12	s	s	NOUN
ejpam-5864	151	13	)	)	PUNCT
ejpam-5864	151	14	.	.	PUNCT
ejpam-5864	152	1	the	the	DET
ejpam-5864	152	2	fractional	fractional	ADJ
ejpam-5864	152	3	orthogonal	orthogonal	ADJ
ejpam-5864	152	4	system	system	NOUN
ejpam-5864	152	5	is	be	AUX
ejpam-5864	152	6	shown	show	VERB
ejpam-5864	152	7	in	in	ADP
ejpam-5864	152	8	figure	figure	NOUN
ejpam-5864	152	9	3	3	NUM
ejpam-5864	152	10	.	.	PUNCT
ejpam-5864	152	11	a.	a.	NOUN
ejpam-5864	152	12	has	have	VERB
ejpam-5864	152	13	,	,	PUNCT
ejpam-5864	152	14	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	152	15	,	,	PUNCT
ejpam-5864	152	16	t.	t.	PROPN
ejpam-5864	152	17	abdeljawad	abdeljawad	PROPN
ejpam-5864	152	18	/	/	SYM
ejpam-5864	152	19	eur	eur	PROPN
ejpam-5864	152	20	.	.	PUNCT
ejpam-5864	153	1	j.	j.	PROPN
ejpam-5864	153	2	pure	pure	PROPN
ejpam-5864	153	3	appl	appl	PROPN
ejpam-5864	153	4	.	.	PROPN
ejpam-5864	153	5	math	math	PROPN
ejpam-5864	153	6	,	,	PUNCT
ejpam-5864	153	7	18	18	NUM
ejpam-5864	153	8	(	(	PUNCT
ejpam-5864	153	9	2	2	NUM
ejpam-5864	153	10	)	)	PUNCT
ejpam-5864	153	11	(	(	PUNCT
ejpam-5864	153	12	2025	2025	NUM
ejpam-5864	153	13	)	)	PUNCT
ejpam-5864	153	14	,	,	PUNCT
ejpam-5864	153	15	5864	5864	NUM
ejpam-5864	153	16	7	7	NUM
ejpam-5864	153	17	of	of	ADP
ejpam-5864	153	18	14	14	NUM
ejpam-5864	153	19	figure	figure	NOUN
ejpam-5864	153	20	3	3	NUM
ejpam-5864	153	21	:	:	PUNCT
ejpam-5864	153	22	cα−orthogonal	cα−orthogonal	ADJ
ejpam-5864	153	23	system	system	NOUN
ejpam-5864	153	24	.	.	PUNCT
ejpam-5864	154	1	let	let	VERB
ejpam-5864	154	2	x	x	PRON
ejpam-5864	154	3	:	:	PUNCT
ejpam-5864	154	4	i	i	PRON
ejpam-5864	154	5	⊂	⊂	VERB
ejpam-5864	154	6	r	r	X
ejpam-5864	154	7	→	→	PUNCT
ejpam-5864	154	8	e3	e3	NOUN
ejpam-5864	154	9	be	be	AUX
ejpam-5864	154	10	a	a	DET
ejpam-5864	154	11	vector	vector	NOUN
ejpam-5864	154	12	-	-	PUNCT
ejpam-5864	154	13	valued	value	VERB
ejpam-5864	154	14	function	function	NOUN
ejpam-5864	154	15	where	where	SCONJ
ejpam-5864	154	16	s	s	VERB
ejpam-5864	154	17	7→	7→	NUM
ejpam-5864	154	18	x(s	x(s	PROPN
ejpam-5864	154	19	)	)	PUNCT
ejpam-5864	155	1	=	=	PRON
ejpam-5864	155	2	(	(	PUNCT
ejpam-5864	155	3	x1(s),x2(s),x3(s	x1(s),x2(s),x3(s	PROPN
ejpam-5864	155	4	)	)	PUNCT
ejpam-5864	155	5	)	)	PUNCT
ejpam-5864	155	6	.	.	PUNCT
ejpam-5864	156	1	then	then	ADV
ejpam-5864	156	2	,	,	PUNCT
ejpam-5864	156	3	dαx(s	dαx(s	PROPN
ejpam-5864	156	4	)	)	PUNCT
ejpam-5864	156	5	=	=	SYM
ejpam-5864	156	6	(	(	PUNCT
ejpam-5864	156	7	dαx1(s	dαx1(	NOUN
ejpam-5864	156	8	)	)	PUNCT
ejpam-5864	156	9	,	,	PUNCT
ejpam-5864	156	10	dαx2(s	dαx2(s	NOUN
ejpam-5864	156	11	)	)	PUNCT
ejpam-5864	156	12	,	,	PUNCT
ejpam-5864	156	13	dαx3(s	dαx3(	NOUN
ejpam-5864	156	14	)	)	PUNCT
ejpam-5864	156	15	)	)	PUNCT
ejpam-5864	156	16	.	.	PUNCT
ejpam-5864	157	1	we	we	PRON
ejpam-5864	157	2	call	call	VERB
ejpam-5864	157	3	x(s	x(s	PROPN
ejpam-5864	157	4	)	)	PUNCT
ejpam-5864	157	5	cα−naturally	cα−naturally	ADV
ejpam-5864	157	6	parametrized	parametrized	ADJ
ejpam-5864	157	7	curve	curve	NOUN
ejpam-5864	157	8	if	if	SCONJ
ejpam-5864	157	9	xi(s	xi(s	NUM
ejpam-5864	157	10	)	)	PUNCT
ejpam-5864	158	1	(	(	PUNCT
ejpam-5864	158	2	i	i	NOUN
ejpam-5864	158	3	=	=	NOUN
ejpam-5864	158	4	1	1	NUM
ejpam-5864	158	5	,	,	PUNCT
ejpam-5864	158	6	2	2	NUM
ejpam-5864	158	7	,	,	PUNCT
ejpam-5864	158	8	3	3	NUM
ejpam-5864	158	9	)	)	PUNCT
ejpam-5864	158	10	is	be	AUX
ejpam-5864	158	11	of	of	ADP
ejpam-5864	158	12	class	class	NOUN
ejpam-5864	158	13	cα	cα	NOUN
ejpam-5864	158	14	and	and	CCONJ
ejpam-5864	158	15	∥dαx(s)∥	∥dαx(s)∥	PUNCT
ejpam-5864	158	16	=	=	SYM
ejpam-5864	159	1	s1−α	s1−α	PROPN
ejpam-5864	159	2	,	,	PUNCT
ejpam-5864	159	3	for	for	ADP
ejpam-5864	159	4	each	each	DET
ejpam-5864	159	5	s	s	PROPN
ejpam-5864	159	6	∈	∈	PROPN
ejpam-5864	159	7	i.	i.	NOUN
ejpam-5864	159	8	here	here	ADV
ejpam-5864	159	9	α	α	PROPN
ejpam-5864	159	10	is	be	AUX
ejpam-5864	159	11	the	the	DET
ejpam-5864	159	12	maximum	maximum	ADJ
ejpam-5864	159	13	order	order	NOUN
ejpam-5864	159	14	that	that	SCONJ
ejpam-5864	159	15	we	we	PRON
ejpam-5864	159	16	will	will	AUX
ejpam-5864	159	17	need	need	VERB
ejpam-5864	159	18	.	.	PUNCT
ejpam-5864	160	1	in	in	ADP
ejpam-5864	160	2	the	the	DET
ejpam-5864	160	3	remaining	remain	VERB
ejpam-5864	160	4	part	part	NOUN
ejpam-5864	160	5	,	,	PUNCT
ejpam-5864	160	6	unless	unless	SCONJ
ejpam-5864	160	7	otherwise	otherwise	ADV
ejpam-5864	160	8	specified	specify	VERB
ejpam-5864	160	9	,	,	PUNCT
ejpam-5864	160	10	we	we	PRON
ejpam-5864	160	11	will	will	AUX
ejpam-5864	160	12	assume	assume	VERB
ejpam-5864	160	13	that	that	SCONJ
ejpam-5864	160	14	x(s	x(s	PROPN
ejpam-5864	160	15	)	)	PUNCT
ejpam-5864	160	16	in	in	ADP
ejpam-5864	160	17	e3	e3	NOUN
ejpam-5864	160	18	is	be	AUX
ejpam-5864	160	19	a	a	DET
ejpam-5864	160	20	cα−naturally	cα−naturally	ADV
ejpam-5864	160	21	parametrized	parametrized	ADJ
ejpam-5864	160	22	curve	curve	NOUN
ejpam-5864	160	23	.	.	PUNCT
ejpam-5864	161	1	let	let	AUX
ejpam-5864	161	2	x(s	x(s	PROPN
ejpam-5864	161	3	)	)	PUNCT
ejpam-5864	161	4	be	be	VERB
ejpam-5864	161	5	cα−biregular	cα−biregular	ADJ
ejpam-5864	161	6	,	,	PUNCT
ejpam-5864	161	7	that	that	ADV
ejpam-5864	161	8	is	be	AUX
ejpam-5864	161	9	,	,	PUNCT
ejpam-5864	161	10	dαx(s)×d2	dαx(s)×d2	NOUN
ejpam-5864	161	11	αx(s	αx(s	PUNCT
ejpam-5864	161	12	)	)	PUNCT
ejpam-5864	161	13	̸=	̸=	PROPN
ejpam-5864	161	14	0α	0α	NUM
ejpam-5864	161	15	,	,	PUNCT
ejpam-5864	161	16	for	for	ADP
ejpam-5864	161	17	each	each	DET
ejpam-5864	161	18	s	s	PROPN
ejpam-5864	161	19	∈	∈	PROPN
ejpam-5864	161	20	i.	i.	NOUN
ejpam-5864	161	21	we	we	PRON
ejpam-5864	161	22	consider	consider	VERB
ejpam-5864	161	23	a	a	DET
ejpam-5864	161	24	trihedron	trihedron	NOUN
ejpam-5864	161	25	{	{	PUNCT
ejpam-5864	161	26	e1(s	e1(s	PROPN
ejpam-5864	161	27	)	)	PUNCT
ejpam-5864	161	28	,	,	PUNCT
ejpam-5864	161	29	e2(s	e2(s	NOUN
ejpam-5864	161	30	)	)	PUNCT
ejpam-5864	161	31	,	,	PUNCT
ejpam-5864	161	32	e3(s	e3(s	PROPN
ejpam-5864	161	33	)	)	PUNCT
ejpam-5864	161	34	}	}	PUNCT
ejpam-5864	161	35	along	along	ADP
ejpam-5864	161	36	x(s	x(s	PROPN
ejpam-5864	161	37	)	)	PUNCT
ejpam-5864	161	38	,	,	PUNCT
ejpam-5864	161	39	so	so	ADV
ejpam-5864	161	40	-	-	PUNCT
ejpam-5864	161	41	called	call	VERB
ejpam-5864	161	42	cα−frame	cα−frame	NOUN
ejpam-5864	161	43	,	,	PUNCT
ejpam-5864	161	44	where	where	SCONJ
ejpam-5864	161	45	e1(s	e1(	VERB
ejpam-5864	161	46	)	)	PUNCT
ejpam-5864	161	47	=	=	SYM
ejpam-5864	161	48	dαx(s	dαx(s	PROPN
ejpam-5864	161	49	)	)	PUNCT
ejpam-5864	161	50	,	,	PUNCT
ejpam-5864	161	51	e2(s	e2(s	NOUN
ejpam-5864	161	52	)	)	PUNCT
ejpam-5864	161	53	=	=	SYM
ejpam-5864	161	54	dαe1(s	dαe1(	NOUN
ejpam-5864	161	55	)	)	PUNCT
ejpam-5864	161	56	∥dαe1(s)∥	∥dαe1(s)∥	NUM
ejpam-5864	161	57	,	,	PUNCT
ejpam-5864	161	58	e3(s	e3(s	PROPN
ejpam-5864	161	59	)	)	PUNCT
ejpam-5864	161	60	=	=	PROPN
ejpam-5864	161	61	e1(s)×	e1(s)×	PROPN
ejpam-5864	161	62	e2(s	e2(s	PROPN
ejpam-5864	161	63	)	)	PUNCT
ejpam-5864	161	64	.	.	PUNCT
ejpam-5864	162	1	(	(	PUNCT
ejpam-5864	162	2	5	5	X
ejpam-5864	162	3	)	)	PUNCT
ejpam-5864	162	4	where	where	SCONJ
ejpam-5864	162	5	{	{	PUNCT
ejpam-5864	162	6	e1(s	e1(s	PROPN
ejpam-5864	162	7	)	)	PUNCT
ejpam-5864	162	8	,	,	PUNCT
ejpam-5864	162	9	e2(s	e2(s	NOUN
ejpam-5864	162	10	)	)	PUNCT
ejpam-5864	162	11	,	,	PUNCT
ejpam-5864	162	12	e3(s	e3(s	PROPN
ejpam-5864	162	13	)	)	PUNCT
ejpam-5864	162	14	}	}	PUNCT
ejpam-5864	162	15	trihedron	trihedron	NOUN
ejpam-5864	162	16	is	be	AUX
ejpam-5864	162	17	called	call	VERB
ejpam-5864	162	18	cα−tangent	cα−tangent	NOUN
ejpam-5864	162	19	,	,	PUNCT
ejpam-5864	162	20	cα−principal	cα−principal	NOUN
ejpam-5864	162	21	normal	normal	ADJ
ejpam-5864	162	22	and	and	CCONJ
ejpam-5864	162	23	the	the	DET
ejpam-5864	162	24	cα−binormal	cα−binormal	NOUN
ejpam-5864	162	25	of	of	ADP
ejpam-5864	162	26	the	the	DET
ejpam-5864	162	27	cα−curve	cα−curve	PROPN
ejpam-5864	162	28	x	x	NOUN
ejpam-5864	162	29	,	,	PUNCT
ejpam-5864	162	30	respectively	respectively	ADV
ejpam-5864	162	31	.	.	PUNCT
ejpam-5864	163	1	also	also	ADV
ejpam-5864	163	2	,	,	PUNCT
ejpam-5864	163	3	considering	consider	VERB
ejpam-5864	163	4	eq	eq	ADP
ejpam-5864	163	5	.	.	PUNCT
ejpam-5864	163	6	(	(	PUNCT
ejpam-5864	163	7	5	5	X
ejpam-5864	163	8	)	)	PUNCT
ejpam-5864	163	9	cα−tangent	cα−tangent	NOUN
ejpam-5864	163	10	,	,	PUNCT
ejpam-5864	163	11	cα−principal	cα−principal	NOUN
ejpam-5864	163	12	normal	normal	ADJ
ejpam-5864	163	13	and	and	CCONJ
ejpam-5864	163	14	cα−binormal	cα−binormal	NOUN
ejpam-5864	163	15	of	of	ADP
ejpam-5864	163	16	the	the	DET
ejpam-5864	163	17	cα−curve	cα−curve	PROPN
ejpam-5864	163	18	x	x	NOUN
ejpam-5864	163	19	,	,	PUNCT
ejpam-5864	163	20	they	they	PRON
ejpam-5864	163	21	different	different	ADJ
ejpam-5864	163	22	from	from	ADP
ejpam-5864	163	23	the	the	DET
ejpam-5864	163	24	frenet	frenet	ADJ
ejpam-5864	163	25	vectors	vector	NOUN
ejpam-5864	163	26	by	by	ADP
ejpam-5864	163	27	the	the	DET
ejpam-5864	163	28	effect	effect	NOUN
ejpam-5864	163	29	of	of	ADP
ejpam-5864	163	30	the	the	DET
ejpam-5864	163	31	conformable	conformable	ADJ
ejpam-5864	163	32	calculus	calculus	NOUN
ejpam-5864	163	33	.	.	PUNCT
ejpam-5864	164	1	however	however	ADV
ejpam-5864	164	2	,	,	PUNCT
ejpam-5864	164	3	these	these	DET
ejpam-5864	164	4	vectors	vector	NOUN
ejpam-5864	164	5	turn	turn	VERB
ejpam-5864	164	6	into	into	ADP
ejpam-5864	164	7	frenet	frenet	ADJ
ejpam-5864	164	8	vectors	vector	NOUN
ejpam-5864	164	9	,	,	PUNCT
ejpam-5864	164	10	respectively	respectively	ADV
ejpam-5864	164	11	,	,	PUNCT
ejpam-5864	164	12	in	in	ADP
ejpam-5864	164	13	case	case	NOUN
ejpam-5864	164	14	α	α	X
ejpam-5864	164	15	→	→	SYM
ejpam-5864	164	16	1	1	X
ejpam-5864	164	17	.	.	PUNCT
ejpam-5864	165	1	in	in	ADP
ejpam-5864	165	2	addition	addition	NOUN
ejpam-5864	165	3	,	,	PUNCT
ejpam-5864	165	4	the	the	DET
ejpam-5864	165	5	set	set	NOUN
ejpam-5864	165	6	{	{	PUNCT
ejpam-5864	165	7	e1(s	e1(s	PROPN
ejpam-5864	165	8	)	)	PUNCT
ejpam-5864	165	9	,	,	PUNCT
ejpam-5864	165	10	e2(s	e2(s	NOUN
ejpam-5864	165	11	)	)	PUNCT
ejpam-5864	165	12	,	,	PUNCT
ejpam-5864	165	13	e3(s	e3(s	PROPN
ejpam-5864	165	14	)	)	PUNCT
ejpam-5864	165	15	}	}	PUNCT
ejpam-5864	165	16	is	be	AUX
ejpam-5864	165	17	mutually	mutually	ADV
ejpam-5864	165	18	cα−orthogonal	cα−orthogonal	ADJ
ejpam-5864	165	19	and	and	CCONJ
ejpam-5864	165	20	cα−unit	cα−unit	NOUN
ejpam-5864	165	21	speed	speed	NOUN
ejpam-5864	165	22	vectors	vector	NOUN
ejpam-5864	165	23	.	.	PUNCT
ejpam-5864	166	1	we	we	PRON
ejpam-5864	166	2	call	call	VERB
ejpam-5864	166	3	κα(s	κα(s	PUNCT
ejpam-5864	166	4	)	)	PUNCT
ejpam-5864	167	1	=	=	SYM
ejpam-5864	167	2	∥dαe1(s)∥	∥dαe1(s)∥	ADP
ejpam-5864	167	3	cα−curvature	cα−curvature	NOUN
ejpam-5864	167	4	and	and	CCONJ
ejpam-5864	167	5	τα(s	τα(s	PUNCT
ejpam-5864	167	6	)	)	PUNCT
ejpam-5864	167	7	=	=	SYM
ejpam-5864	167	8	⟨dαe2(s	⟨dαe2(s	NOUN
ejpam-5864	167	9	)	)	PUNCT
ejpam-5864	167	10	,	,	PUNCT
ejpam-5864	167	11	e3(s)⟩	e3(s)⟩	NOUN
ejpam-5864	167	12	cα−torsion	cα−torsion	NOUN
ejpam-5864	167	13	.	.	PUNCT
ejpam-5864	168	1	the	the	DET
ejpam-5864	168	2	cα−frame	cα−frame	PROPN
ejpam-5864	168	3	formulae	formulae	NOUN
ejpam-5864	168	4	are	be	AUX
ejpam-5864	168	5	now	now	ADV
ejpam-5864	168	6	[	[	X
ejpam-5864	169	1	36]dαe1	36]dαe1	NUM
ejpam-5864	169	2	dαe2	dαe2	NOUN
ejpam-5864	169	3	dαe3	dαe3	NOUN
ejpam-5864	169	4			NOUN
ejpam-5864	169	5	=	=	PUNCT
ejpam-5864	169	6			NOUN
ejpam-5864	169	7	0	0	NUM
ejpam-5864	170	1	κα	κα	INTJ
ejpam-5864	170	2	0	0	NUM
ejpam-5864	170	3	−κα	−κα	NOUN
ejpam-5864	170	4	0	0	NUM
ejpam-5864	170	5	τα	τα	PROPN
ejpam-5864	170	6	0	0	NUM
ejpam-5864	170	7	−τα	−τα	SYM
ejpam-5864	170	8	0	0	NUM
ejpam-5864	170	9	e1	e1	NUM
ejpam-5864	170	10	e2	e2	VERB
ejpam-5864	170	11	e3	e3	NOUN
ejpam-5864	170	12			NOUN
ejpam-5864	170	13	.	.	PUNCT
ejpam-5864	171	1	(	(	PUNCT
ejpam-5864	171	2	6	6	X
ejpam-5864	171	3	)	)	PUNCT
ejpam-5864	171	4	conclusion	conclusion	NOUN
ejpam-5864	171	5	1	1	NUM
ejpam-5864	171	6	.	.	PUNCT
ejpam-5864	172	1	(	(	PUNCT
ejpam-5864	172	2	what	what	PRON
ejpam-5864	172	3	is	be	AUX
ejpam-5864	172	4	the	the	DET
ejpam-5864	172	5	advantage	advantage	NOUN
ejpam-5864	172	6	of	of	ADP
ejpam-5864	172	7	cα−frame	cα−frame	NOUN
ejpam-5864	172	8	?	?	PUNCT
ejpam-5864	172	9	)	)	PUNCT
ejpam-5864	173	1	the	the	DET
ejpam-5864	173	2	concept	concept	NOUN
ejpam-5864	173	3	of	of	ADP
ejpam-5864	173	4	α	α	NOUN
ejpam-5864	173	5	-	-	NOUN
ejpam-5864	173	6	differentiability	differentiability	NOUN
ejpam-5864	173	7	offers	offer	VERB
ejpam-5864	173	8	a	a	DET
ejpam-5864	173	9	distinctive	distinctive	ADJ
ejpam-5864	173	10	perspective	perspective	NOUN
ejpam-5864	173	11	where	where	SCONJ
ejpam-5864	173	12	functions	function	NOUN
ejpam-5864	173	13	exhibit	exhibit	VERB
ejpam-5864	173	14	α	α	NOUN
ejpam-5864	173	15	-	-	NOUN
ejpam-5864	173	16	differentiability	differentiability	NOUN
ejpam-5864	173	17	at	at	ADP
ejpam-5864	173	18	points	point	NOUN
ejpam-5864	173	19	where	where	SCONJ
ejpam-5864	173	20	classical	classical	ADJ
ejpam-5864	173	21	differentiability	differentiability	NOUN
ejpam-5864	173	22	fails	fail	VERB
ejpam-5864	173	23	.	.	PUNCT
ejpam-5864	174	1	for	for	ADP
ejpam-5864	174	2	instance	instance	NOUN
ejpam-5864	174	3	,	,	PUNCT
ejpam-5864	174	4	consider	consider	VERB
ejpam-5864	174	5	a.	a.	NOUN
ejpam-5864	174	6	has	have	VERB
ejpam-5864	174	7	,	,	PUNCT
ejpam-5864	174	8	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	174	9	,	,	PUNCT
ejpam-5864	174	10	t.	t.	PROPN
ejpam-5864	174	11	abdeljawad	abdeljawad	PROPN
ejpam-5864	174	12	/	/	SYM
ejpam-5864	174	13	eur	eur	PROPN
ejpam-5864	174	14	.	.	PUNCT
ejpam-5864	175	1	j.	j.	PROPN
ejpam-5864	175	2	pure	pure	PROPN
ejpam-5864	175	3	appl	appl	PROPN
ejpam-5864	175	4	.	.	PROPN
ejpam-5864	175	5	math	math	PROPN
ejpam-5864	175	6	,	,	PUNCT
ejpam-5864	175	7	18	18	NUM
ejpam-5864	175	8	(	(	PUNCT
ejpam-5864	175	9	2	2	NUM
ejpam-5864	175	10	)	)	PUNCT
ejpam-5864	175	11	(	(	PUNCT
ejpam-5864	175	12	2025	2025	NUM
ejpam-5864	175	13	)	)	PUNCT
ejpam-5864	175	14	,	,	PUNCT
ejpam-5864	175	15	5864	5864	NUM
ejpam-5864	175	16	8	8	NUM
ejpam-5864	175	17	of	of	ADP
ejpam-5864	175	18	14	14	NUM
ejpam-5864	175	19	the	the	DET
ejpam-5864	175	20	function	function	NOUN
ejpam-5864	175	21	f(t	f(t	NOUN
ejpam-5864	175	22	)	)	PUNCT
ejpam-5864	175	23	=	=	SYM
ejpam-5864	175	24	2	2	NUM
ejpam-5864	175	25	√	√	NOUN
ejpam-5864	175	26	t.	t.	NOUN
ejpam-5864	175	27	at	at	ADP
ejpam-5864	175	28	t	t	PROPN
ejpam-5864	175	29	=	=	SYM
ejpam-5864	175	30	0	0	PROPN
ejpam-5864	175	31	,	,	PUNCT
ejpam-5864	175	32	the	the	DET
ejpam-5864	175	33	classical	classical	ADJ
ejpam-5864	175	34	derivative	derivative	ADJ
ejpam-5864	175	35	f	f	PROPN
ejpam-5864	175	36	′(0	′(0	PROPN
ejpam-5864	175	37	)	)	PUNCT
ejpam-5864	175	38	does	do	AUX
ejpam-5864	175	39	n’t	not	PART
ejpam-5864	175	40	exist	exist	VERB
ejpam-5864	175	41	.	.	PUNCT
ejpam-5864	176	1	however	however	ADV
ejpam-5864	176	2	,	,	PUNCT
ejpam-5864	176	3	employing	employ	VERB
ejpam-5864	176	4	the	the	DET
ejpam-5864	176	5	conformable	conformable	ADJ
ejpam-5864	176	6	fractional	fractional	ADJ
ejpam-5864	176	7	derivative	derivative	ADJ
ejpam-5864	176	8	yields	yield	NOUN
ejpam-5864	176	9	the	the	DET
ejpam-5864	176	10	result	result	NOUN
ejpam-5864	176	11	d	d	NOUN
ejpam-5864	176	12	1	1	NUM
ejpam-5864	176	13	2	2	NUM
ejpam-5864	176	14	f(0	f(0	NOUN
ejpam-5864	176	15	)	)	PUNCT
ejpam-5864	176	16	=	=	SYM
ejpam-5864	176	17	1	1	NUM
ejpam-5864	176	18	quite	quite	ADV
ejpam-5864	176	19	straightforwardly	straightforwardly	ADV
ejpam-5864	176	20	.	.	PUNCT
ejpam-5864	177	1	in	in	ADP
ejpam-5864	177	2	this	this	DET
ejpam-5864	177	3	example	example	NOUN
ejpam-5864	177	4	,	,	PUNCT
ejpam-5864	177	5	function	function	NOUN
ejpam-5864	177	6	f	f	PROPN
ejpam-5864	177	7	lacks	lack	VERB
ejpam-5864	177	8	a	a	DET
ejpam-5864	177	9	classical	classical	ADJ
ejpam-5864	177	10	tangent	tangent	NOUN
ejpam-5864	177	11	at	at	ADP
ejpam-5864	177	12	the	the	DET
ejpam-5864	177	13	point	point	NOUN
ejpam-5864	177	14	t	t	NOUN
ejpam-5864	177	15	=	=	SYM
ejpam-5864	177	16	0	0	NUM
ejpam-5864	177	17	,	,	PUNCT
ejpam-5864	177	18	but	but	CCONJ
ejpam-5864	177	19	an	an	DET
ejpam-5864	177	20	approximation	approximation	NOUN
ejpam-5864	177	21	to	to	ADP
ejpam-5864	177	22	this	this	DET
ejpam-5864	177	23	tangent	tangent	NOUN
ejpam-5864	177	24	is	be	AUX
ejpam-5864	177	25	achievable	achievable	ADJ
ejpam-5864	177	26	through	through	ADP
ejpam-5864	177	27	the	the	DET
ejpam-5864	177	28	conformable	conformable	ADJ
ejpam-5864	177	29	fractional	fractional	ADJ
ejpam-5864	177	30	derivative	derivative	NOUN
ejpam-5864	177	31	.	.	PUNCT
ejpam-5864	178	1	the	the	DET
ejpam-5864	178	2	frenet	frenet	ADJ
ejpam-5864	178	3	frame	frame	NOUN
ejpam-5864	178	4	of	of	ADP
ejpam-5864	178	5	a	a	DET
ejpam-5864	178	6	curve	curve	NOUN
ejpam-5864	178	7	heavily	heavily	ADV
ejpam-5864	178	8	relies	rely	VERB
ejpam-5864	178	9	on	on	ADP
ejpam-5864	178	10	the	the	DET
ejpam-5864	178	11	existence	existence	NOUN
ejpam-5864	178	12	of	of	ADP
ejpam-5864	178	13	the	the	DET
ejpam-5864	178	14	curve	curve	NOUN
ejpam-5864	178	15	’s	’s	PART
ejpam-5864	178	16	tangent	tangent	NOUN
ejpam-5864	178	17	at	at	ADP
ejpam-5864	178	18	a	a	DET
ejpam-5864	178	19	given	give	VERB
ejpam-5864	178	20	point	point	NOUN
ejpam-5864	178	21	.	.	PUNCT
ejpam-5864	179	1	yet	yet	ADV
ejpam-5864	179	2	,	,	PUNCT
ejpam-5864	179	3	the	the	DET
ejpam-5864	179	4	cα	cα	NOUN
ejpam-5864	179	5	-	-	PUNCT
ejpam-5864	179	6	frame	frame	NOUN
ejpam-5864	179	7	resolves	resolve	NOUN
ejpam-5864	179	8	this	this	DET
ejpam-5864	179	9	issue	issue	NOUN
ejpam-5864	179	10	.	.	PUNCT
ejpam-5864	180	1	in	in	ADP
ejpam-5864	180	2	points	point	NOUN
ejpam-5864	180	3	within	within	ADP
ejpam-5864	180	4	the	the	DET
ejpam-5864	180	5	cα	cα	NOUN
ejpam-5864	180	6	-	-	PUNCT
ejpam-5864	180	7	frame	frame	NOUN
ejpam-5864	180	8	where	where	SCONJ
ejpam-5864	180	9	the	the	DET
ejpam-5864	180	10	curve	curve	NOUN
ejpam-5864	180	11	’s	’s	PART
ejpam-5864	180	12	tangent	tangent	NOUN
ejpam-5864	180	13	is	be	AUX
ejpam-5864	180	14	absent	absent	ADJ
ejpam-5864	180	15	,	,	PUNCT
ejpam-5864	180	16	fractional	fractional	ADJ
ejpam-5864	180	17	values	value	NOUN
ejpam-5864	180	18	are	be	AUX
ejpam-5864	180	19	assigned	assign	VERB
ejpam-5864	180	20	to	to	PART
ejpam-5864	180	21	approximate	approximate	VERB
ejpam-5864	180	22	the	the	DET
ejpam-5864	180	23	tangent	tangent	NOUN
ejpam-5864	180	24	at	at	ADP
ejpam-5864	180	25	that	that	DET
ejpam-5864	180	26	specific	specific	ADJ
ejpam-5864	180	27	point	point	NOUN
ejpam-5864	180	28	.	.	PUNCT
ejpam-5864	181	1	moreover	moreover	ADV
ejpam-5864	181	2	,	,	PUNCT
ejpam-5864	181	3	when	when	SCONJ
ejpam-5864	181	4	α	α	X
ejpam-5864	181	5	→	→	SYM
ejpam-5864	181	6	1	1	NUM
ejpam-5864	181	7	,	,	PUNCT
ejpam-5864	181	8	the	the	DET
ejpam-5864	181	9	cα	cα	NOUN
ejpam-5864	181	10	-	-	PUNCT
ejpam-5864	181	11	frame	frame	NOUN
ejpam-5864	181	12	aligns	align	VERB
ejpam-5864	181	13	with	with	ADP
ejpam-5864	181	14	the	the	DET
ejpam-5864	181	15	frenet	frenet	ADJ
ejpam-5864	181	16	frame	frame	NOUN
ejpam-5864	181	17	.	.	PUNCT
ejpam-5864	182	1	in	in	ADP
ejpam-5864	182	2	such	such	ADJ
ejpam-5864	182	3	instances	instance	NOUN
ejpam-5864	182	4	,	,	PUNCT
ejpam-5864	182	5	the	the	DET
ejpam-5864	182	6	cα	cα	NOUN
ejpam-5864	182	7	-	-	PUNCT
ejpam-5864	182	8	frame	frame	NOUN
ejpam-5864	182	9	encompasses	encompass	VERB
ejpam-5864	182	10	the	the	DET
ejpam-5864	182	11	classical	classical	ADJ
ejpam-5864	182	12	frenet	frenet	ADJ
ejpam-5864	182	13	frame	frame	NOUN
ejpam-5864	182	14	while	while	SCONJ
ejpam-5864	182	15	extending	extend	VERB
ejpam-5864	182	16	advantages	advantage	NOUN
ejpam-5864	182	17	to	to	ADP
ejpam-5864	182	18	researchers	researcher	NOUN
ejpam-5864	182	19	dealing	deal	VERB
ejpam-5864	182	20	with	with	ADP
ejpam-5864	182	21	points	point	NOUN
ejpam-5864	182	22	where	where	SCONJ
ejpam-5864	182	23	the	the	DET
ejpam-5864	182	24	frenet	frenet	ADJ
ejpam-5864	182	25	frame	frame	NOUN
ejpam-5864	182	26	lacks	lack	VERB
ejpam-5864	182	27	definition	definition	NOUN
ejpam-5864	182	28	.	.	PUNCT
ejpam-5864	183	1	theorem	theorem	NOUN
ejpam-5864	183	2	2	2	NUM
ejpam-5864	183	3	.	.	PUNCT
ejpam-5864	184	1	[	[	X
ejpam-5864	184	2	36	36	NUM
ejpam-5864	184	3	]	]	PUNCT
ejpam-5864	184	4	let	let	VERB
ejpam-5864	184	5	x	x	SYM
ejpam-5864	184	6	=	=	SYM
ejpam-5864	184	7	x(s	x(s	PROPN
ejpam-5864	184	8	)	)	PUNCT
ejpam-5864	184	9	be	be	VERB
ejpam-5864	184	10	cα−naturally	cα−naturally	ADV
ejpam-5864	184	11	parametrized	parametrized	ADJ
ejpam-5864	184	12	curve	curve	NOUN
ejpam-5864	184	13	in	in	ADP
ejpam-5864	184	14	the	the	DET
ejpam-5864	184	15	euclidean	euclidean	ADJ
ejpam-5864	184	16	3−space	3−space	NUM
ejpam-5864	184	17	where	where	SCONJ
ejpam-5864	184	18	s	s	VERB
ejpam-5864	184	19	measures	measure	VERB
ejpam-5864	184	20	its	its	PRON
ejpam-5864	184	21	cα−arc	cα−arc	NOUN
ejpam-5864	184	22	length	length	NOUN
ejpam-5864	184	23	.	.	PUNCT
ejpam-5864	185	1	when	when	SCONJ
ejpam-5864	185	2	α	α	X
ejpam-5864	185	3	→	→	SYM
ejpam-5864	185	4	1	1	NUM
ejpam-5864	185	5	,	,	PUNCT
ejpam-5864	185	6	as	as	SCONJ
ejpam-5864	185	7	follows	follow	VERB
ejpam-5864	185	8	κα	κα	INTJ
ejpam-5864	185	9	=	=	SYM
ejpam-5864	185	10	s1−α	s1−α	PROPN
ejpam-5864	185	11	√	√	NUM
ejpam-5864	185	12	(	(	PUNCT
ejpam-5864	185	13	1−	1−	NUM
ejpam-5864	185	14	α)2s−2α	α)2s−2α	NUM
ejpam-5864	185	15	+	+	X
ejpam-5864	186	1	s2−2ακ2	s2−2ακ2	PROPN
ejpam-5864	186	2	.	.	PUNCT
ejpam-5864	187	1	(	(	PUNCT
ejpam-5864	187	2	7	7	NUM
ejpam-5864	187	3	)	)	PUNCT
ejpam-5864	187	4	and	and	CCONJ
ejpam-5864	187	5	τα	τα	NOUN
ejpam-5864	187	6	=	=	SYM
ejpam-5864	187	7	s5−5ακ2	s5−5ακ2	PROPN
ejpam-5864	187	8	κ2α	κ2α	PROPN
ejpam-5864	187	9	τ	τ	X
ejpam-5864	187	10	.	.	PUNCT
ejpam-5864	188	1	(	(	PUNCT
ejpam-5864	188	2	8)	8)	NUM
ejpam-5864	188	3	proposition	proposition	NOUN
ejpam-5864	188	4	1	1	NUM
ejpam-5864	188	5	.	.	PUNCT
ejpam-5864	189	1	let	let	VERB
ejpam-5864	189	2	the	the	DET
ejpam-5864	189	3	α−conforamable	α−conforamable	NUM
ejpam-5864	189	4	frame	frame	NOUN
ejpam-5864	189	5	of	of	ADP
ejpam-5864	189	6	a	a	DET
ejpam-5864	189	7	naturally	naturally	ADV
ejpam-5864	189	8	parameterized	parameterized	ADJ
ejpam-5864	189	9	α−conformable	α−conformable	NOUN
ejpam-5864	189	10	x	x	PRON
ejpam-5864	189	11	curve	curve	NOUN
ejpam-5864	189	12	be	be	AUX
ejpam-5864	189	13	{	{	PUNCT
ejpam-5864	189	14	e1	e1	PROPN
ejpam-5864	189	15	,	,	PUNCT
ejpam-5864	189	16	e2	e2	PROPN
ejpam-5864	189	17	,	,	PUNCT
ejpam-5864	189	18	e3	e3	NOUN
ejpam-5864	189	19	}	}	PUNCT
ejpam-5864	189	20	and	and	CCONJ
ejpam-5864	189	21	the	the	DET
ejpam-5864	189	22	α−conformable	α−conformable	ADJ
ejpam-5864	189	23	curvature	curvature	NOUN
ejpam-5864	189	24	and	and	CCONJ
ejpam-5864	189	25	torsion	torsion	NOUN
ejpam-5864	189	26	be	be	AUX
ejpam-5864	189	27	κα	κα	INTJ
ejpam-5864	189	28	and	and	CCONJ
ejpam-5864	189	29	τα	τα	NOUN
ejpam-5864	189	30	,	,	PUNCT
ejpam-5864	189	31	respectively	respectively	ADV
ejpam-5864	189	32	.	.	PUNCT
ejpam-5864	190	1	if	if	SCONJ
ejpam-5864	190	2	the	the	DET
ejpam-5864	190	3	α−conformable	α−conformable	ADJ
ejpam-5864	190	4	curve	curve	NOUN
ejpam-5864	190	5	x	x	PUNCT
ejpam-5864	190	6	lies	lie	VERB
ejpam-5864	190	7	on	on	ADP
ejpam-5864	190	8	the	the	DET
ejpam-5864	190	9	α−conformable	α−conformable	ADJ
ejpam-5864	190	10	sphere	sphere	NOUN
ejpam-5864	190	11	s2α(cα	s2α(cα	NOUN
ejpam-5864	190	12	,	,	PUNCT
ejpam-5864	190	13	rα	rα	ADJ
ejpam-5864	190	14	)	)	PUNCT
ejpam-5864	190	15	,	,	PUNCT
ejpam-5864	190	16	the	the	DET
ejpam-5864	190	17	curve	curve	NOUN
ejpam-5864	190	18	x	x	VERB
ejpam-5864	190	19	is	be	AUX
ejpam-5864	190	20	called	call	VERB
ejpam-5864	190	21	α−conformable	α−conformable	ADJ
ejpam-5864	190	22	spherical	spherical	ADJ
ejpam-5864	190	23	curve	curve	NOUN
ejpam-5864	190	24	.	.	PUNCT
ejpam-5864	191	1	then	then	ADV
ejpam-5864	191	2	⟨x	⟨x	VERB
ejpam-5864	191	3	,	,	PUNCT
ejpam-5864	191	4	e1⟩	e1⟩	PRON
ejpam-5864	191	5	=	=	SYM
ejpam-5864	191	6	0α	0α	PROPN
ejpam-5864	191	7	and	and	CCONJ
ejpam-5864	191	8	as	as	SCONJ
ejpam-5864	191	9	follows	follow	VERB
ejpam-5864	191	10	x(s	x(s	PROPN
ejpam-5864	191	11	)	)	PUNCT
ejpam-5864	192	1	=	=	PUNCT
ejpam-5864	193	1	cα	cα	ADP
ejpam-5864	193	2	+	+	NOUN
ejpam-5864	193	3	0αλ1	0αλ1	NUM
ejpam-5864	193	4	−	−	PROPN
ejpam-5864	193	5	1α	1α	NOUN
ejpam-5864	193	6	κα	κα	PROPN
ejpam-5864	193	7	e2	e2	PROPN
ejpam-5864	193	8	−	−	PROPN
ejpam-5864	193	9	1α	1α	NUM
ejpam-5864	193	10	τα	τα	NOUN
ejpam-5864	193	11	(	(	PUNCT
ejpam-5864	193	12	1α	1α	NUM
ejpam-5864	193	13	κα	κα	X
ejpam-5864	193	14	)	)	PUNCT
ejpam-5864	193	15	′	′	NUM
ejpam-5864	193	16	e3	e3	NOUN
ejpam-5864	193	17	.	.	PUNCT
ejpam-5864	193	18	example	example	NOUN
ejpam-5864	194	1	2	2	NUM
ejpam-5864	194	2	.	.	PUNCT
ejpam-5864	194	3	let	let	VERB
ejpam-5864	194	4	α−conformable	α−conformable	ADJ
ejpam-5864	194	5	spherical	spherical	ADJ
ejpam-5864	194	6	curve	curve	NOUN
ejpam-5864	194	7	be	be	AUX
ejpam-5864	194	8	y	y	PROPN
ejpam-5864	194	9	in	in	ADP
ejpam-5864	194	10	s2α	s2α	PROPN
ejpam-5864	194	11	for	for	ADP
ejpam-5864	194	12	rα	rα	ADJ
ejpam-5864	194	13	=	=	SYM
ejpam-5864	194	14	uα−1	uα−1	PROPN
ejpam-5864	194	15	,	,	PUNCT
ejpam-5864	194	16	cα	cα	ADP
ejpam-5864	194	17	=	=	SYM
ejpam-5864	194	18	(	(	PUNCT
ejpam-5864	194	19	0	0	NUM
ejpam-5864	194	20	,	,	PUNCT
ejpam-5864	194	21	0	0	NUM
ejpam-5864	194	22	,	,	PUNCT
ejpam-5864	194	23	0	0	NUM
ejpam-5864	194	24	)	)	PUNCT
ejpam-5864	194	25	given	give	VERB
ejpam-5864	194	26	by	by	ADP
ejpam-5864	194	27	the	the	DET
ejpam-5864	194	28	parametrization	parametrization	NOUN
ejpam-5864	194	29	y(s	y(s	PROPN
ejpam-5864	194	30	)	)	PUNCT
ejpam-5864	195	1	=	=	PRON
ejpam-5864	195	2	(	(	PUNCT
ejpam-5864	195	3	1	1	NUM
ejpam-5864	195	4	2	2	NUM
ejpam-5864	195	5	uα−1	uα−1	NOUN
ejpam-5864	195	6	cos	cos	ADP
ejpam-5864	195	7	2s	2s	NOUN
ejpam-5864	195	8	,	,	PUNCT
ejpam-5864	195	9	1	1	NUM
ejpam-5864	195	10	2	2	NUM
ejpam-5864	195	11	uα−1	uα−1	ADJ
ejpam-5864	195	12	sin	sin	NOUN
ejpam-5864	195	13	2s	2s	NOUN
ejpam-5864	195	14	,	,	PUNCT
ejpam-5864	195	15	√	√	NUM
ejpam-5864	195	16	3	3	NUM
ejpam-5864	195	17	2	2	NUM
ejpam-5864	195	18	uα−1	uα−1	ADV
ejpam-5864	195	19	)	)	PUNCT
ejpam-5864	195	20	.	.	PUNCT
ejpam-5864	196	1	(	(	PUNCT
ejpam-5864	196	2	9	9	X
ejpam-5864	196	3	)	)	PUNCT
ejpam-5864	196	4	in	in	ADP
ejpam-5864	196	5	figure	figure	NOUN
ejpam-5864	196	6	4	4	NUM
ejpam-5864	196	7	,	,	PUNCT
ejpam-5864	196	8	we	we	PRON
ejpam-5864	196	9	present	present	VERB
ejpam-5864	196	10	a	a	DET
ejpam-5864	196	11	figures	figure	NOUN
ejpam-5864	196	12	of	of	ADP
ejpam-5864	196	13	the	the	DET
ejpam-5864	196	14	α−conformable	α−conformable	ADJ
ejpam-5864	196	15	spherical	spherical	ADJ
ejpam-5864	196	16	curve	curve	NOUN
ejpam-5864	196	17	according	accord	VERB
ejpam-5864	196	18	to	to	ADP
ejpam-5864	196	19	different	different	ADJ
ejpam-5864	196	20	values	value	NOUN
ejpam-5864	196	21	of	of	ADP
ejpam-5864	196	22	α	α	PROPN
ejpam-5864	196	23	.	.	PUNCT
ejpam-5864	197	1	a.	a.	PROPN
ejpam-5864	197	2	has	have	VERB
ejpam-5864	197	3	,	,	PUNCT
ejpam-5864	197	4	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	197	5	,	,	PUNCT
ejpam-5864	197	6	t.	t.	PROPN
ejpam-5864	197	7	abdeljawad	abdeljawad	PROPN
ejpam-5864	197	8	/	/	SYM
ejpam-5864	197	9	eur	eur	PROPN
ejpam-5864	197	10	.	.	PUNCT
ejpam-5864	198	1	j.	j.	PROPN
ejpam-5864	198	2	pure	pure	PROPN
ejpam-5864	198	3	appl	appl	PROPN
ejpam-5864	198	4	.	.	PROPN
ejpam-5864	198	5	math	math	PROPN
ejpam-5864	198	6	,	,	PUNCT
ejpam-5864	198	7	18	18	NUM
ejpam-5864	198	8	(	(	PUNCT
ejpam-5864	198	9	2	2	NUM
ejpam-5864	198	10	)	)	PUNCT
ejpam-5864	198	11	(	(	PUNCT
ejpam-5864	198	12	2025	2025	NUM
ejpam-5864	198	13	)	)	PUNCT
ejpam-5864	198	14	,	,	PUNCT
ejpam-5864	198	15	5864	5864	NUM
ejpam-5864	198	16	9	9	NUM
ejpam-5864	198	17	of	of	ADP
ejpam-5864	198	18	14	14	NUM
ejpam-5864	198	19	figure	figure	NOUN
ejpam-5864	198	20	4	4	NUM
ejpam-5864	198	21	:	:	PUNCT
ejpam-5864	198	22	α−conformable	α−conformable	ADJ
ejpam-5864	198	23	spherical	spherical	ADJ
ejpam-5864	198	24	curve	curve	NOUN
ejpam-5864	198	25	y(s	y(s	PROPN
ejpam-5864	198	26	)	)	PUNCT
ejpam-5864	198	27	for	for	ADP
ejpam-5864	198	28	for	for	ADP
ejpam-5864	198	29	α	α	PRON
ejpam-5864	198	30	→	→	SYM
ejpam-5864	198	31	1	1	NUM
ejpam-5864	198	32	,	,	PUNCT
ejpam-5864	198	33	α	α	NOUN
ejpam-5864	198	34	=	=	SYM
ejpam-5864	198	35	0.9	0.9	NUM
ejpam-5864	198	36	,	,	PUNCT
ejpam-5864	198	37	α	α	NOUN
ejpam-5864	198	38	=	=	SYM
ejpam-5864	198	39	0.7	0.7	NUM
ejpam-5864	198	40	,	,	PUNCT
ejpam-5864	198	41	α	α	NOUN
ejpam-5864	198	42	=	=	SYM
ejpam-5864	198	43	0.5	0.5	NUM
ejpam-5864	198	44	,	,	PUNCT
ejpam-5864	198	45	α	α	NOUN
ejpam-5864	198	46	=	=	SYM
ejpam-5864	198	47	0.3	0.3	NUM
ejpam-5864	198	48	and	and	CCONJ
ejpam-5864	198	49	α	α	NOUN
ejpam-5864	198	50	=	=	NOUN
ejpam-5864	198	51	0.1	0.1	NUM
ejpam-5864	198	52	,	,	PUNCT
ejpam-5864	198	53	respectively	respectively	ADV
ejpam-5864	198	54	.	.	PUNCT
ejpam-5864	199	1	4	4	X
ejpam-5864	199	2	.	.	X
ejpam-5864	199	3	cα−rectifying	cα−rectifye	VERB
ejpam-5864	199	4	curves	curve	NOUN
ejpam-5864	199	5	let	let	VERB
ejpam-5864	199	6	x(s	x(s	PROPN
ejpam-5864	199	7	)	)	PUNCT
ejpam-5864	199	8	be	be	AUX
ejpam-5864	199	9	a	a	DET
ejpam-5864	199	10	cα−naturally	cα−naturally	ADV
ejpam-5864	199	11	parametrized	parametrized	ADJ
ejpam-5864	199	12	curve	curve	NOUN
ejpam-5864	199	13	in	in	ADP
ejpam-5864	199	14	e3	e3	NOUN
ejpam-5864	199	15	,	,	PUNCT
ejpam-5864	199	16	s	s	VERB
ejpam-5864	199	17	∈	∈	X
ejpam-5864	200	1	i	i	PRON
ejpam-5864	200	2	⊂	⊂	PROPN
ejpam-5864	200	3	r	r	NOUN
ejpam-5864	200	4	and	and	CCONJ
ejpam-5864	200	5	{	{	PUNCT
ejpam-5864	200	6	e1(s	e1(s	PROPN
ejpam-5864	200	7	)	)	PUNCT
ejpam-5864	200	8	,	,	PUNCT
ejpam-5864	200	9	e2(s	e2(s	NOUN
ejpam-5864	200	10	)	)	PUNCT
ejpam-5864	200	11	,	,	PUNCT
ejpam-5864	200	12	e3(s	e3(s	PROPN
ejpam-5864	200	13	)	)	PUNCT
ejpam-5864	200	14	}	}	PUNCT
ejpam-5864	200	15	denotes	denote	VERB
ejpam-5864	200	16	the	the	DET
ejpam-5864	200	17	cα−frame	cα−frame	NOUN
ejpam-5864	200	18	.	.	PUNCT
ejpam-5864	201	1	suppose	suppose	VERB
ejpam-5864	201	2	that	that	SCONJ
ejpam-5864	201	3	cα−biregular	cα−biregular	PROPN
ejpam-5864	201	4	.	.	PUNCT
ejpam-5864	202	1	we	we	PRON
ejpam-5864	202	2	call	call	VERB
ejpam-5864	202	3	x(s	x(s	PROPN
ejpam-5864	202	4	)	)	PUNCT
ejpam-5864	202	5	cα−rectifying	cα−rectifye	VERB
ejpam-5864	202	6	curve	curve	NOUN
ejpam-5864	202	7	if	if	SCONJ
ejpam-5864	202	8	there	there	PRON
ejpam-5864	202	9	is	be	VERB
ejpam-5864	202	10	a	a	DET
ejpam-5864	202	11	linear	linear	ADJ
ejpam-5864	202	12	relation	relation	NOUN
ejpam-5864	202	13	as	as	ADP
ejpam-5864	202	14	x(s	x(s	PROPN
ejpam-5864	202	15	)	)	PUNCT
ejpam-5864	203	1	=	=	PUNCT
ejpam-5864	203	2	λ(s)e1(s	λ(s)e1(s	PROPN
ejpam-5864	203	3	)	)	PUNCT
ejpam-5864	203	4	+	+	NUM
ejpam-5864	203	5	µ(s)e3(s	µ(s)e3(	NOUN
ejpam-5864	203	6	)	)	PUNCT
ejpam-5864	203	7	.	.	PUNCT
ejpam-5864	204	1	(	(	PUNCT
ejpam-5864	204	2	10	10	NUM
ejpam-5864	204	3	)	)	PUNCT
ejpam-5864	204	4	here	here	ADV
ejpam-5864	204	5	the	the	DET
ejpam-5864	204	6	functions	function	NOUN
ejpam-5864	204	7	λ(s	λ(s	PROPN
ejpam-5864	204	8	)	)	PUNCT
ejpam-5864	204	9	and	and	CCONJ
ejpam-5864	204	10	µ(s	µ(	NOUN
ejpam-5864	204	11	)	)	PUNCT
ejpam-5864	204	12	are	be	AUX
ejpam-5864	204	13	of	of	ADP
ejpam-5864	204	14	class	class	NOUN
ejpam-5864	204	15	cn	cn	PROPN
ejpam-5864	204	16	on	on	ADP
ejpam-5864	204	17	i	i	PRON
ejpam-5864	204	18	called	call	VERB
ejpam-5864	204	19	cα−tangential	cα−tangential	ADJ
ejpam-5864	204	20	and	and	CCONJ
ejpam-5864	204	21	cα−binormal	cα−binormal	ADJ
ejpam-5864	204	22	components	component	NOUN
ejpam-5864	204	23	of	of	ADP
ejpam-5864	204	24	x(s	x(s	PROPN
ejpam-5864	204	25	)	)	PUNCT
ejpam-5864	204	26	,	,	PUNCT
ejpam-5864	204	27	respectively	respectively	ADV
ejpam-5864	204	28	.	.	PUNCT
ejpam-5864	205	1	hence	hence	ADV
ejpam-5864	205	2	,	,	PUNCT
ejpam-5864	205	3	λ(s	λ(s	PROPN
ejpam-5864	205	4	)	)	PUNCT
ejpam-5864	205	5	=	=	PUNCT
ejpam-5864	206	1	⟨x(s	⟨x(s	PROPN
ejpam-5864	206	2	)	)	PUNCT
ejpam-5864	206	3	,	,	PUNCT
ejpam-5864	206	4	e1(s)⟩	e1(s)⟩	NOUN
ejpam-5864	206	5	and	and	CCONJ
ejpam-5864	206	6	µ(s	µ(	NOUN
ejpam-5864	206	7	)	)	PUNCT
ejpam-5864	206	8	=	=	SYM
ejpam-5864	207	1	⟨x(s	⟨x(s	PROPN
ejpam-5864	207	2	)	)	PUNCT
ejpam-5864	207	3	,	,	PUNCT
ejpam-5864	207	4	e3(s)⟩.	e3(s)⟩.	VERB
ejpam-5864	207	5	remark	remark	NOUN
ejpam-5864	207	6	also	also	ADV
ejpam-5864	207	7	that	that	SCONJ
ejpam-5864	207	8	cα−rectifying	cα−rectifye	VERB
ejpam-5864	207	9	curve	curve	NOUN
ejpam-5864	207	10	x(s	x(s	PROPN
ejpam-5864	207	11	)	)	PUNCT
ejpam-5864	207	12	holds	hold	VERB
ejpam-5864	207	13	⟨x(s	⟨x(s	PROPN
ejpam-5864	207	14	)	)	PUNCT
ejpam-5864	207	15	,	,	PUNCT
ejpam-5864	208	1	e2(s)⟩	e2(s)⟩	NOUN
ejpam-5864	208	2	=	=	SYM
ejpam-5864	208	3	0	0	NUM
ejpam-5864	208	4	for	for	ADP
ejpam-5864	208	5	each	each	DET
ejpam-5864	208	6	s	s	PROPN
ejpam-5864	208	7	∈	∈	PROPN
ejpam-5864	208	8	i.	i.	NOUN
ejpam-5864	208	9	taking	take	VERB
ejpam-5864	208	10	a	a	DET
ejpam-5864	208	11	conformable	conformable	ADJ
ejpam-5864	208	12	differentiation	differentiation	NOUN
ejpam-5864	208	13	in	in	ADP
ejpam-5864	208	14	eq	eq	ADP
ejpam-5864	208	15	.	.	PUNCT
ejpam-5864	209	1	(	(	PUNCT
ejpam-5864	209	2	10	10	NUM
ejpam-5864	209	3	)	)	PUNCT
ejpam-5864	209	4	together	together	ADV
ejpam-5864	209	5	with	with	ADP
ejpam-5864	209	6	considering	consider	VERB
ejpam-5864	209	7	cα−frame	cα−frame	NOUN
ejpam-5864	209	8	formulae	formulae	NOUN
ejpam-5864	209	9	,	,	PUNCT
ejpam-5864	209	10	we	we	PRON
ejpam-5864	209	11	have	have	VERB
ejpam-5864	209	12	(	(	PUNCT
ejpam-5864	209	13	dαλ−	dαλ−	PROPN
ejpam-5864	209	14	1)e1	1)e1	PROPN
ejpam-5864	210	1	+	+	CCONJ
ejpam-5864	210	2	(	(	PUNCT
ejpam-5864	210	3	λκα	λκα	X
ejpam-5864	210	4	−	−	PROPN
ejpam-5864	210	5	µτα)e2	µτα)e2	PUNCT
ejpam-5864	210	6	+	+	NOUN
ejpam-5864	210	7	dαµe3	dαµe3	NOUN
ejpam-5864	210	8	=	=	SYM
ejpam-5864	210	9	0	0	X
ejpam-5864	210	10	.	.	PUNCT
ejpam-5864	211	1	(	(	PUNCT
ejpam-5864	211	2	11	11	NUM
ejpam-5864	211	3	)	)	PUNCT
ejpam-5864	211	4	according	accord	VERB
ejpam-5864	211	5	to	to	ADP
ejpam-5864	211	6	this	this	DET
ejpam-5864	211	7	equation	equation	NOUN
ejpam-5864	211	8	,	,	PUNCT
ejpam-5864	211	9	the	the	DET
ejpam-5864	211	10	following	follow	VERB
ejpam-5864	211	11	results	result	NOUN
ejpam-5864	211	12	are	be	AUX
ejpam-5864	211	13	given	give	VERB
ejpam-5864	211	14	dαλ	dαλ	PROPN
ejpam-5864	211	15	=	=	SYM
ejpam-5864	211	16	1	1	NUM
ejpam-5864	211	17	,	,	PUNCT
ejpam-5864	211	18	(	(	PUNCT
ejpam-5864	211	19	12	12	NUM
ejpam-5864	211	20	)	)	PUNCT
ejpam-5864	211	21	τα	τα	NOUN
ejpam-5864	211	22	κα	κα	PROPN
ejpam-5864	211	23	=	=	SYM
ejpam-5864	211	24	λ	λ	X
ejpam-5864	211	25	µ	µ	X
ejpam-5864	211	26	,	,	PUNCT
ejpam-5864	211	27	(	(	PUNCT
ejpam-5864	211	28	13	13	NUM
ejpam-5864	211	29	)	)	PUNCT
ejpam-5864	211	30	dαµ	dαµ	NOUN
ejpam-5864	211	31	=	=	NOUN
ejpam-5864	211	32	0	0	X
ejpam-5864	211	33	.	.	PUNCT
ejpam-5864	212	1	(	(	PUNCT
ejpam-5864	212	2	14	14	NUM
ejpam-5864	212	3	)	)	PUNCT
ejpam-5864	212	4	a.	a.	NOUN
ejpam-5864	212	5	has	have	VERB
ejpam-5864	212	6	,	,	PUNCT
ejpam-5864	212	7	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	212	8	,	,	PUNCT
ejpam-5864	212	9	t.	t.	PROPN
ejpam-5864	212	10	abdeljawad	abdeljawad	PROPN
ejpam-5864	212	11	/	/	SYM
ejpam-5864	212	12	eur	eur	PROPN
ejpam-5864	212	13	.	.	PUNCT
ejpam-5864	213	1	j.	j.	PROPN
ejpam-5864	213	2	pure	pure	PROPN
ejpam-5864	213	3	appl	appl	PROPN
ejpam-5864	213	4	.	.	PROPN
ejpam-5864	213	5	math	math	PROPN
ejpam-5864	213	6	,	,	PUNCT
ejpam-5864	213	7	18	18	NUM
ejpam-5864	213	8	(	(	PUNCT
ejpam-5864	213	9	2	2	NUM
ejpam-5864	213	10	)	)	PUNCT
ejpam-5864	213	11	(	(	PUNCT
ejpam-5864	213	12	2025	2025	NUM
ejpam-5864	213	13	)	)	PUNCT
ejpam-5864	213	14	,	,	PUNCT
ejpam-5864	213	15	5864	5864	NUM
ejpam-5864	213	16	10	10	NUM
ejpam-5864	213	17	of	of	ADP
ejpam-5864	213	18	14	14	NUM
ejpam-5864	213	19	conclusion	conclusion	NOUN
ejpam-5864	213	20	2	2	NUM
ejpam-5864	213	21	.	.	PUNCT
ejpam-5864	213	22	from	from	ADP
ejpam-5864	213	23	eqs	eqs	PROPN
ejpam-5864	213	24	.	.	PUNCT
ejpam-5864	214	1	(	(	PUNCT
ejpam-5864	214	2	12	12	NUM
ejpam-5864	214	3	)	)	PUNCT
ejpam-5864	214	4	and	and	CCONJ
ejpam-5864	214	5	(	(	PUNCT
ejpam-5864	214	6	14	14	NUM
ejpam-5864	214	7	)	)	PUNCT
ejpam-5864	214	8	one	one	PRON
ejpam-5864	214	9	concludes	conclude	VERB
ejpam-5864	214	10	that	that	SCONJ
ejpam-5864	214	11	λ(s	λ(s	PROPN
ejpam-5864	214	12	)	)	PUNCT
ejpam-5864	214	13	=	=	PUNCT
ejpam-5864	215	1	sα	sα	PROPN
ejpam-5864	215	2	α	α	PROPN
ejpam-5864	215	3	+	+	CCONJ
ejpam-5864	215	4	c1	c1	PROPN
ejpam-5864	215	5	and	and	CCONJ
ejpam-5864	215	6	µ(s	µ(s	PROPN
ejpam-5864	215	7	)	)	PUNCT
ejpam-5864	215	8	=	=	SYM
ejpam-5864	215	9	c2	c2	PROPN
ejpam-5864	215	10	for	for	ADP
ejpam-5864	215	11	c1	c1	PROPN
ejpam-5864	215	12	,	,	PUNCT
ejpam-5864	215	13	c2	c2	PROPN
ejpam-5864	215	14	∈	∈	PROPN
ejpam-5864	215	15	r.	r.	PROPN
ejpam-5864	215	16	notice	notice	NOUN
ejpam-5864	215	17	here	here	ADV
ejpam-5864	215	18	that	that	SCONJ
ejpam-5864	215	19	c2	c2	PROPN
ejpam-5864	215	20	̸=	̸=	PROPN
ejpam-5864	215	21	0	0	NUM
ejpam-5864	215	22	because	because	SCONJ
ejpam-5864	215	23	otherwise	otherwise	ADV
ejpam-5864	215	24	one	one	NUM
ejpam-5864	215	25	derives	derive	VERB
ejpam-5864	215	26	from	from	ADP
ejpam-5864	215	27	in	in	ADP
ejpam-5864	215	28	eq	eq	ADP
ejpam-5864	215	29	.	.	PUNCT
ejpam-5864	216	1	(	(	PUNCT
ejpam-5864	216	2	13	13	NUM
ejpam-5864	216	3	)	)	PUNCT
ejpam-5864	216	4	that	that	PRON
ejpam-5864	216	5	κα(s	κα(s	X
ejpam-5864	216	6	)	)	PUNCT
ejpam-5864	216	7	is	be	AUX
ejpam-5864	216	8	0	0	NUM
ejpam-5864	216	9	.	.	PUNCT
ejpam-5864	217	1	this	this	PRON
ejpam-5864	217	2	contradicts	contradict	VERB
ejpam-5864	217	3	with	with	ADP
ejpam-5864	217	4	biregularity	biregularity	NOUN
ejpam-5864	217	5	of	of	ADP
ejpam-5864	217	6	x(s	x(s	PROPN
ejpam-5864	217	7	)	)	PUNCT
ejpam-5864	217	8	.	.	PUNCT
ejpam-5864	218	1	analogously	analogously	ADV
ejpam-5864	218	2	,	,	PUNCT
ejpam-5864	218	3	τα(s	τα(s	NUM
ejpam-5864	218	4	)	)	PUNCT
ejpam-5864	218	5	is	be	AUX
ejpam-5864	218	6	nowhere	nowhere	ADV
ejpam-5864	218	7	0	0	NUM
ejpam-5864	218	8	.	.	PUNCT
ejpam-5864	219	1	in	in	ADP
ejpam-5864	219	2	conclusion	conclusion	NOUN
ejpam-5864	219	3	,	,	PUNCT
ejpam-5864	219	4	we	we	PRON
ejpam-5864	219	5	deduce	deduce	VERB
ejpam-5864	219	6	that	that	SCONJ
ejpam-5864	219	7	a	a	DET
ejpam-5864	219	8	cα−rectifying	cα−rectifye	VERB
ejpam-5864	219	9	curve	curve	NOUN
ejpam-5864	219	10	has	have	VERB
ejpam-5864	219	11	to	to	PART
ejpam-5864	219	12	be	be	AUX
ejpam-5864	219	13	cα−twisted	cα−twiste	VERB
ejpam-5864	219	14	.	.	PUNCT
ejpam-5864	220	1	theorem	theorem	NOUN
ejpam-5864	220	2	3	3	X
ejpam-5864	220	3	.	.	PUNCT
ejpam-5864	221	1	let	let	VERB
ejpam-5864	221	2	x(s	x(s	PROPN
ejpam-5864	221	3	)	)	PUNCT
ejpam-5864	222	1	⊂	⊂	PRON
ejpam-5864	222	2	e3	e3	VERB
ejpam-5864	222	3	be	be	AUX
ejpam-5864	222	4	a	a	DET
ejpam-5864	222	5	cα−rectifying	cα−rectifye	VERB
ejpam-5864	222	6	curve	curve	NOUN
ejpam-5864	222	7	and	and	CCONJ
ejpam-5864	222	8	κα	κα	INTJ
ejpam-5864	222	9	̸=	̸=	PROPN
ejpam-5864	222	10	0	0	NUM
ejpam-5864	223	1	and	and	CCONJ
ejpam-5864	223	2	τα	τα	NOUN
ejpam-5864	223	3	is	be	AUX
ejpam-5864	223	4	nowhere	nowhere	ADP
ejpam-5864	223	5	0α	0α	PROPN
ejpam-5864	223	6	.	.	PUNCT
ejpam-5864	224	1	then	then	ADV
ejpam-5864	224	2	ρ2(s	ρ2(s	NUM
ejpam-5864	224	3	)	)	PUNCT
ejpam-5864	224	4	=	=	SYM
ejpam-5864	225	1	1α(s	1α(s	NUM
ejpam-5864	225	2	2α	2α	NOUN
ejpam-5864	225	3	+	+	CCONJ
ejpam-5864	225	4	csα	csα	NOUN
ejpam-5864	225	5	+	+	CCONJ
ejpam-5864	225	6	d	d	NOUN
ejpam-5864	225	7	)	)	PUNCT
ejpam-5864	225	8	(	(	PUNCT
ejpam-5864	225	9	15	15	NUM
ejpam-5864	225	10	)	)	PUNCT
ejpam-5864	225	11	where	where	SCONJ
ejpam-5864	225	12	ρ(s	ρ(s	NOUN
ejpam-5864	225	13	)	)	PUNCT
ejpam-5864	226	1	=	=	PRON
ejpam-5864	226	2	∥x(s)∥	∥x(s)∥	PROPN
ejpam-5864	226	3	is	be	AUX
ejpam-5864	226	4	the	the	DET
ejpam-5864	226	5	distance	distance	NOUN
ejpam-5864	226	6	function	function	NOUN
ejpam-5864	226	7	,	,	PUNCT
ejpam-5864	226	8	c	c	PROPN
ejpam-5864	226	9	and	and	CCONJ
ejpam-5864	226	10	d	d	ADP
ejpam-5864	226	11	real	real	ADJ
ejpam-5864	226	12	numbers	number	NOUN
ejpam-5864	226	13	.	.	PUNCT
ejpam-5864	227	1	proof	proof	NOUN
ejpam-5864	227	2	.	.	PUNCT
ejpam-5864	228	1	consider	consider	VERB
ejpam-5864	228	2	the	the	DET
ejpam-5864	228	3	a	a	DET
ejpam-5864	228	4	cα−rectifying	cα−rectifying	ADJ
ejpam-5864	228	5	curve	curve	NOUN
ejpam-5864	228	6	x(s	x(s	PROPN
ejpam-5864	228	7	)	)	PUNCT
ejpam-5864	228	8	in	in	ADP
ejpam-5864	228	9	eq	eq	ADP
ejpam-5864	228	10	.	.	PUNCT
ejpam-5864	229	1	(	(	PUNCT
ejpam-5864	229	2	10	10	NUM
ejpam-5864	229	3	)	)	PUNCT
ejpam-5864	229	4	,	,	PUNCT
ejpam-5864	229	5	so	so	CCONJ
ejpam-5864	229	6	the	the	DET
ejpam-5864	229	7	following	follow	VERB
ejpam-5864	229	8	equation	equation	NOUN
ejpam-5864	229	9	exists	exist	VERB
ejpam-5864	229	10	ρ2(s	ρ2(s	NOUN
ejpam-5864	229	11	)	)	PUNCT
ejpam-5864	229	12	=	=	SYM
ejpam-5864	229	13	⟨x(s),x(s)⟩	⟨x(s),x(s)⟩	NOUN
ejpam-5864	229	14	=	=	SYM
ejpam-5864	229	15	∥e1∥λ2(s	∥e1∥λ2(s	PROPN
ejpam-5864	229	16	)	)	PUNCT
ejpam-5864	230	1	+	+	CCONJ
ejpam-5864	231	1	∥e3∥µ2(s	∥e3∥µ2(s	X
ejpam-5864	231	2	)	)	PUNCT
ejpam-5864	231	3	where	where	SCONJ
ejpam-5864	231	4	e1	e1	NOUN
ejpam-5864	231	5	and	and	CCONJ
ejpam-5864	231	6	e3	e3	NOUN
ejpam-5864	231	7	are	be	AUX
ejpam-5864	231	8	cα−unit	cα−unit	NOUN
ejpam-5864	231	9	speed	speed	NOUN
ejpam-5864	231	10	vectors	vector	NOUN
ejpam-5864	231	11	.	.	PUNCT
ejpam-5864	232	1	so	so	ADV
ejpam-5864	232	2	this	this	DET
ejpam-5864	232	3	equation	equation	NOUN
ejpam-5864	232	4	is	be	AUX
ejpam-5864	232	5	edited	edit	VERB
ejpam-5864	232	6	ρ2(s	ρ2(s	NUM
ejpam-5864	232	7	)	)	PUNCT
ejpam-5864	232	8	=	=	SYM
ejpam-5864	233	1	1α	1α	NOUN
ejpam-5864	233	2	(	(	PUNCT
ejpam-5864	233	3	s2α	s2α	ADP
ejpam-5864	233	4	α2	α2	PROPN
ejpam-5864	233	5	+	+	CCONJ
ejpam-5864	233	6	2c1	2c1	NUM
ejpam-5864	233	7	sα	sα	ADV
ejpam-5864	233	8	α	α	PROPN
ejpam-5864	233	9	+	+	PROPN
ejpam-5864	233	10	c22	c22	NOUN
ejpam-5864	233	11	)	)	PUNCT
ejpam-5864	233	12	(	(	PUNCT
ejpam-5864	233	13	16	16	NUM
ejpam-5864	233	14	)	)	PUNCT
ejpam-5864	233	15	or	or	CCONJ
ejpam-5864	233	16	ρ2(s	ρ2(s	NUM
ejpam-5864	233	17	)	)	PUNCT
ejpam-5864	233	18	=	=	SYM
ejpam-5864	233	19	1α	1α	NUM
ejpam-5864	233	20	α2	α2	PROPN
ejpam-5864	233	21	(	(	PUNCT
ejpam-5864	233	22	s2α	s2α	PROPN
ejpam-5864	233	23	+	+	CCONJ
ejpam-5864	233	24	2c1αs	2c1αs	NUM
ejpam-5864	233	25	α	α	NOUN
ejpam-5864	233	26	+	+	CCONJ
ejpam-5864	233	27	c22α	c22α	VERB
ejpam-5864	233	28	2	2	NUM
ejpam-5864	233	29	)	)	PUNCT
ejpam-5864	233	30	.	.	PUNCT
ejpam-5864	234	1	(	(	PUNCT
ejpam-5864	234	2	17	17	NUM
ejpam-5864	234	3	)	)	PUNCT
ejpam-5864	234	4	here	here	ADV
ejpam-5864	234	5	,	,	PUNCT
ejpam-5864	234	6	when	when	SCONJ
ejpam-5864	234	7	α	α	X
ejpam-5864	234	8	→	→	SYM
ejpam-5864	234	9	1	1	NUM
ejpam-5864	234	10	,	,	PUNCT
ejpam-5864	234	11	since	since	SCONJ
ejpam-5864	234	12	1α	1α	NUM
ejpam-5864	234	13	α2	α2	NOUN
ejpam-5864	234	14	=	=	SYM
ejpam-5864	234	15	1	1	NUM
ejpam-5864	234	16	is	be	AUX
ejpam-5864	234	17	1α	1α	NUM
ejpam-5864	234	18	α2	α2	NOUN
ejpam-5864	234	19	=	=	SYM
ejpam-5864	234	20	1α	1α	NOUN
ejpam-5864	234	21	can	can	AUX
ejpam-5864	234	22	be	be	AUX
ejpam-5864	234	23	written	write	VERB
ejpam-5864	234	24	.	.	PUNCT
ejpam-5864	235	1	also	also	ADV
ejpam-5864	235	2	,	,	PUNCT
ejpam-5864	235	3	since	since	SCONJ
ejpam-5864	235	4	α	α	PRON
ejpam-5864	235	5	is	be	AUX
ejpam-5864	235	6	a	a	DET
ejpam-5864	235	7	real	real	ADJ
ejpam-5864	235	8	number	number	NOUN
ejpam-5864	235	9	,	,	PUNCT
ejpam-5864	235	10	if	if	SCONJ
ejpam-5864	235	11	2c1α	2c1α	NUM
ejpam-5864	235	12	=	=	SYM
ejpam-5864	235	13	c	c	PROPN
ejpam-5864	235	14	and	and	CCONJ
ejpam-5864	235	15	c22α	c22α	VERB
ejpam-5864	235	16	2	2	NUM
ejpam-5864	235	17	=	=	SYM
ejpam-5864	235	18	d	d	NOUN
ejpam-5864	235	19	are	be	AUX
ejpam-5864	235	20	selected	select	VERB
ejpam-5864	235	21	,	,	PUNCT
ejpam-5864	235	22	we	we	PRON
ejpam-5864	235	23	get	get	VERB
ejpam-5864	235	24	the	the	DET
ejpam-5864	235	25	following	following	ADJ
ejpam-5864	235	26	ρ2(s	ρ2(s	NOUN
ejpam-5864	235	27	)	)	PUNCT
ejpam-5864	235	28	=	=	SYM
ejpam-5864	235	29	1α(s	1α(s	NUM
ejpam-5864	235	30	2α	2α	NOUN
ejpam-5864	235	31	+	+	CCONJ
ejpam-5864	235	32	csα	csα	NOUN
ejpam-5864	235	33	+	+	CCONJ
ejpam-5864	235	34	d	d	NOUN
ejpam-5864	235	35	)	)	PUNCT
ejpam-5864	235	36	.	.	PUNCT
ejpam-5864	236	1	(	(	PUNCT
ejpam-5864	236	2	18	18	NUM
ejpam-5864	236	3	)	)	PUNCT
ejpam-5864	236	4	theorem	theorem	NOUN
ejpam-5864	236	5	4	4	NUM
ejpam-5864	236	6	.	.	PUNCT
ejpam-5864	237	1	let	let	VERB
ejpam-5864	237	2	x(s	x(s	PROPN
ejpam-5864	237	3	)	)	PUNCT
ejpam-5864	238	1	⊂	⊂	PRON
ejpam-5864	238	2	e3	e3	VERB
ejpam-5864	238	3	be	be	AUX
ejpam-5864	238	4	a	a	DET
ejpam-5864	238	5	cα−rectifying	cα−rectifye	VERB
ejpam-5864	238	6	curve	curve	NOUN
ejpam-5864	238	7	.	.	PUNCT
ejpam-5864	239	1	then	then	ADV
ejpam-5864	239	2	the	the	DET
ejpam-5864	239	3	ratio	ratio	NOUN
ejpam-5864	239	4	of	of	ADP
ejpam-5864	239	5	the	the	DET
ejpam-5864	239	6	conformable	conformable	ADJ
ejpam-5864	239	7	curvatures	curvature	NOUN
ejpam-5864	239	8	is	be	AUX
ejpam-5864	239	9	for	for	ADP
ejpam-5864	239	10	a	a	DET
ejpam-5864	239	11	,	,	PUNCT
ejpam-5864	239	12	b	b	X
ejpam-5864	239	13	∈	∈	PROPN
ejpam-5864	239	14	r	r	NOUN
ejpam-5864	239	15	τα	τα	NOUN
ejpam-5864	239	16	κα	κα	PROPN
ejpam-5864	239	17	=	=	PUNCT
ejpam-5864	239	18	asα	asα	PROPN
ejpam-5864	239	19	+	+	CCONJ
ejpam-5864	239	20	b.	b.	NOUN
ejpam-5864	239	21	proof	proof	NOUN
ejpam-5864	239	22	.	.	PUNCT
ejpam-5864	240	1	from	from	ADP
ejpam-5864	240	2	eq	eq	ADP
ejpam-5864	240	3	.	.	PUNCT
ejpam-5864	241	1	(	(	PUNCT
ejpam-5864	241	2	13	13	NUM
ejpam-5864	241	3	)	)	PUNCT
ejpam-5864	241	4	,	,	PUNCT
ejpam-5864	241	5	we	we	PRON
ejpam-5864	241	6	know	know	VERB
ejpam-5864	241	7	the	the	DET
ejpam-5864	241	8	following	follow	VERB
ejpam-5864	241	9	equation	equation	NOUN
ejpam-5864	241	10	τα	τα	NOUN
ejpam-5864	241	11	κα	κα	PROPN
ejpam-5864	241	12	=	=	SYM
ejpam-5864	241	13	λ	λ	X
ejpam-5864	241	14	µ	µ	NOUN
ejpam-5864	241	15	.	.	PUNCT
ejpam-5864	242	1	now	now	ADV
ejpam-5864	242	2	,	,	PUNCT
ejpam-5864	242	3	if	if	SCONJ
ejpam-5864	242	4	we	we	PRON
ejpam-5864	242	5	use	use	VERB
ejpam-5864	242	6	the	the	DET
ejpam-5864	242	7	results	result	NOUN
ejpam-5864	242	8	of	of	ADP
ejpam-5864	242	9	the	the	DET
ejpam-5864	242	10	λ	λ	PROPN
ejpam-5864	242	11	and	and	CCONJ
ejpam-5864	242	12	µ	µ	DET
ejpam-5864	242	13	conformable	conformable	ADJ
ejpam-5864	242	14	differentiable	differentiable	ADJ
ejpam-5864	242	15	equations	equation	NOUN
ejpam-5864	242	16	available	available	ADJ
ejpam-5864	242	17	in	in	ADP
ejpam-5864	242	18	conclusion	conclusion	NOUN
ejpam-5864	242	19	2	2	NUM
ejpam-5864	242	20	in	in	ADP
ejpam-5864	242	21	the	the	DET
ejpam-5864	242	22	above	above	ADJ
ejpam-5864	242	23	equation	equation	NOUN
ejpam-5864	242	24	,	,	PUNCT
ejpam-5864	242	25	we	we	PRON
ejpam-5864	242	26	get	get	VERB
ejpam-5864	242	27	τα	τα	NOUN
ejpam-5864	243	1	κα	κα	PROPN
ejpam-5864	244	1	=	=	NOUN
ejpam-5864	244	2	sα	sα	ADJ
ejpam-5864	244	3	α	α	PROPN
ejpam-5864	244	4	+	+	CCONJ
ejpam-5864	244	5	c1	c1	PROPN
ejpam-5864	244	6	c2	c2	PROPN
ejpam-5864	244	7	.	.	PUNCT
ejpam-5864	245	1	or	or	CCONJ
ejpam-5864	245	2	τα	τα	NOUN
ejpam-5864	246	1	κα	κα	INTJ
ejpam-5864	246	2	=	=	PRON
ejpam-5864	246	3	sα	sα	ADJ
ejpam-5864	246	4	αc2	αc2	PROPN
ejpam-5864	246	5	+	+	CCONJ
ejpam-5864	246	6	c1	c1	PROPN
ejpam-5864	246	7	c2	c2	PROPN
ejpam-5864	246	8	since	since	SCONJ
ejpam-5864	246	9	c1	c1	PROPN
ejpam-5864	246	10	,	,	PUNCT
ejpam-5864	246	11	c2	c2	PROPN
ejpam-5864	246	12	and	and	CCONJ
ejpam-5864	246	13	α	α	PROPN
ejpam-5864	246	14	are	be	AUX
ejpam-5864	246	15	real	real	ADJ
ejpam-5864	246	16	numbers	number	NOUN
ejpam-5864	246	17	,	,	PUNCT
ejpam-5864	246	18	if	if	SCONJ
ejpam-5864	246	19	we	we	PRON
ejpam-5864	246	20	select	select	VERB
ejpam-5864	246	21	new	new	ADJ
ejpam-5864	246	22	real	real	ADJ
ejpam-5864	246	23	numbers	number	NOUN
ejpam-5864	246	24	as	as	ADP
ejpam-5864	246	25	1	1	NUM
ejpam-5864	246	26	αc2	αc2	NOUN
ejpam-5864	246	27	=	=	SYM
ejpam-5864	246	28	a	a	PROPN
ejpam-5864	246	29	and	and	CCONJ
ejpam-5864	246	30	c1	c1	PROPN
ejpam-5864	246	31	c2	c2	PROPN
ejpam-5864	246	32	=	=	SYM
ejpam-5864	246	33	b	b	PROPN
ejpam-5864	246	34	,	,	PUNCT
ejpam-5864	246	35	it	it	PRON
ejpam-5864	246	36	can	can	AUX
ejpam-5864	246	37	be	be	AUX
ejpam-5864	246	38	easily	easily	ADV
ejpam-5864	246	39	seen	see	VERB
ejpam-5864	246	40	that	that	SCONJ
ejpam-5864	246	41	the	the	DET
ejpam-5864	246	42	following	follow	VERB
ejpam-5864	246	43	equation	equation	NOUN
ejpam-5864	246	44	is	be	AUX
ejpam-5864	246	45	achieved	achieve	VERB
ejpam-5864	246	46	τα	τα	NOUN
ejpam-5864	246	47	κα	κα	INTJ
ejpam-5864	246	48	=	=	PUNCT
ejpam-5864	246	49	asα	asα	PROPN
ejpam-5864	246	50	+	+	CCONJ
ejpam-5864	246	51	b.	b.	PROPN
ejpam-5864	246	52	a.	a.	NOUN
ejpam-5864	246	53	has	have	VERB
ejpam-5864	246	54	,	,	PUNCT
ejpam-5864	246	55	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	246	56	,	,	PUNCT
ejpam-5864	246	57	t.	t.	PROPN
ejpam-5864	246	58	abdeljawad	abdeljawad	PROPN
ejpam-5864	246	59	/	/	SYM
ejpam-5864	246	60	eur	eur	PROPN
ejpam-5864	246	61	.	.	PUNCT
ejpam-5864	247	1	j.	j.	PROPN
ejpam-5864	247	2	pure	pure	PROPN
ejpam-5864	247	3	appl	appl	PROPN
ejpam-5864	247	4	.	.	PROPN
ejpam-5864	247	5	math	math	PROPN
ejpam-5864	247	6	,	,	PUNCT
ejpam-5864	247	7	18	18	NUM
ejpam-5864	247	8	(	(	PUNCT
ejpam-5864	247	9	2	2	NUM
ejpam-5864	247	10	)	)	PUNCT
ejpam-5864	247	11	(	(	PUNCT
ejpam-5864	247	12	2025	2025	NUM
ejpam-5864	247	13	)	)	PUNCT
ejpam-5864	247	14	,	,	PUNCT
ejpam-5864	247	15	5864	5864	NUM
ejpam-5864	247	16	11	11	NUM
ejpam-5864	247	17	of	of	ADP
ejpam-5864	247	18	14	14	NUM
ejpam-5864	247	19	theorem	theorem	NOUN
ejpam-5864	247	20	5	5	NUM
ejpam-5864	247	21	.	.	PUNCT
ejpam-5864	248	1	let	let	VERB
ejpam-5864	248	2	x	x	PRON
ejpam-5864	248	3	:	:	PUNCT
ejpam-5864	248	4	i	i	PRON
ejpam-5864	248	5	⊂	⊂	VERB
ejpam-5864	248	6	r	r	X
ejpam-5864	248	7	→	→	PUNCT
ejpam-5864	248	8	e3	e3	NOUN
ejpam-5864	248	9	be	be	AUX
ejpam-5864	248	10	a	a	DET
ejpam-5864	248	11	cα−rectifying	cα−rectifye	VERB
ejpam-5864	248	12	curve	curve	NOUN
ejpam-5864	248	13	e3	e3	NOUN
ejpam-5864	248	14	with	with	ADP
ejpam-5864	248	15	κα	κα	INTJ
ejpam-5864	248	16	̸=	̸=	PROPN
ejpam-5864	248	17	0α	0α	NUM
ejpam-5864	248	18	.	.	PUNCT
ejpam-5864	249	1	in	in	ADP
ejpam-5864	249	2	this	this	DET
ejpam-5864	249	3	case	case	NOUN
ejpam-5864	249	4	,	,	PUNCT
ejpam-5864	249	5	the	the	DET
ejpam-5864	249	6	following	follow	VERB
ejpam-5864	249	7	result	result	NOUN
ejpam-5864	249	8	applies	apply	VERB
ejpam-5864	249	9	x(s	x(s	PROPN
ejpam-5864	249	10	)	)	PUNCT
ejpam-5864	250	1	=	=	SYM
ejpam-5864	250	2	1α	1α	NUM
ejpam-5864	250	3	√	√	NUM
ejpam-5864	250	4	f(t)2α	f(t)2α	PUNCT
ejpam-5864	251	1	+	+	PUNCT
ejpam-5864	251	2	n2αy(s	n2αy(	NOUN
ejpam-5864	251	3	)	)	PUNCT
ejpam-5864	251	4	,	,	PUNCT
ejpam-5864	251	5	(	(	PUNCT
ejpam-5864	251	6	19	19	NUM
ejpam-5864	251	7	)	)	PUNCT
ejpam-5864	251	8	where	where	SCONJ
ejpam-5864	251	9	f(t	f(t	NOUN
ejpam-5864	251	10	)	)	PUNCT
ejpam-5864	251	11	is	be	AUX
ejpam-5864	251	12	a	a	DET
ejpam-5864	251	13	conformable	conformable	ADJ
ejpam-5864	251	14	differentiable	differentiable	ADJ
ejpam-5864	251	15	function	function	NOUN
ejpam-5864	251	16	and	and	CCONJ
ejpam-5864	251	17	n	n	PRON
ejpam-5864	251	18	is	be	AUX
ejpam-5864	251	19	a	a	DET
ejpam-5864	251	20	positive	positive	ADJ
ejpam-5864	251	21	number	number	NOUN
ejpam-5864	251	22	and	and	CCONJ
ejpam-5864	251	23	y	y	NOUN
ejpam-5864	251	24	=	=	SYM
ejpam-5864	251	25	y(s	y(s	PROPN
ejpam-5864	251	26	)	)	PUNCT
ejpam-5864	251	27	is	be	AUX
ejpam-5864	251	28	a	a	DET
ejpam-5864	251	29	cα−unit	cα−unit	NOUN
ejpam-5864	251	30	speed	speed	NOUN
ejpam-5864	251	31	spherical	spherical	ADJ
ejpam-5864	251	32	curve	curve	NOUN
ejpam-5864	251	33	in	in	ADP
ejpam-5864	251	34	s2	s2	PROPN
ejpam-5864	251	35	α	α	NOUN
ejpam-5864	251	36	.	.	PUNCT
ejpam-5864	252	1	proof	proof	NOUN
ejpam-5864	252	2	.	.	PUNCT
ejpam-5864	253	1	let	let	VERB
ejpam-5864	253	2	x(s	x(s	PROPN
ejpam-5864	253	3	)	)	PUNCT
ejpam-5864	254	1	⊂	⊂	PRON
ejpam-5864	254	2	e3	e3	VERB
ejpam-5864	254	3	be	be	AUX
ejpam-5864	254	4	a	a	DET
ejpam-5864	254	5	cα−rectifying	cα−rectifye	VERB
ejpam-5864	254	6	curve	curve	NOUN
ejpam-5864	254	7	with	with	ADP
ejpam-5864	254	8	κα	κα	INTJ
ejpam-5864	254	9	̸=	̸=	PROPN
ejpam-5864	254	10	0α	0α	NUM
ejpam-5864	254	11	.	.	PUNCT
ejpam-5864	255	1	suppose	suppose	VERB
ejpam-5864	255	2	that	that	SCONJ
ejpam-5864	255	3	0α	0α	PROPN
ejpam-5864	255	4	lies	lie	VERB
ejpam-5864	255	5	in	in	ADP
ejpam-5864	255	6	i	i	PRON
ejpam-5864	255	7	and	and	CCONJ
ejpam-5864	255	8	x	x	NOUN
ejpam-5864	255	9	=	=	SYM
ejpam-5864	255	10	x(s	x(s	PROPN
ejpam-5864	255	11	)	)	PUNCT
ejpam-5864	255	12	is	be	AUX
ejpam-5864	255	13	cα−unit	cα−unit	NOUN
ejpam-5864	255	14	speed	speed	NOUN
ejpam-5864	255	15	curve	curve	NOUN
ejpam-5864	255	16	.	.	PUNCT
ejpam-5864	256	1	by	by	ADP
ejpam-5864	256	2	the	the	DET
ejpam-5864	256	3	eq	eq	NOUN
ejpam-5864	256	4	.	.	PUNCT
ejpam-5864	257	1	(	(	PUNCT
ejpam-5864	257	2	18	18	NUM
ejpam-5864	257	3	)	)	PUNCT
ejpam-5864	257	4	,	,	PUNCT
ejpam-5864	257	5	the	the	DET
ejpam-5864	257	6	distance	distance	NOUN
ejpam-5864	257	7	function	function	NOUN
ejpam-5864	257	8	ρ	ρ	NOUN
ejpam-5864	257	9	=	=	SYM
ejpam-5864	257	10	∥x∥	∥x∥	NOUN
ejpam-5864	257	11	of	of	ADP
ejpam-5864	257	12	the	the	DET
ejpam-5864	257	13	curve	curve	NOUN
ejpam-5864	257	14	satisfies	satisfie	NOUN
ejpam-5864	257	15	ρ2(s	ρ2(s	NUM
ejpam-5864	257	16	)	)	PUNCT
ejpam-5864	257	17	=	=	SYM
ejpam-5864	257	18	1α(s	1α(s	NUM
ejpam-5864	257	19	2α+csα+d	2α+csα+d	NUM
ejpam-5864	257	20	)	)	PUNCT
ejpam-5864	257	21	for	for	ADP
ejpam-5864	257	22	some	some	DET
ejpam-5864	257	23	constant	constant	ADJ
ejpam-5864	257	24	c	c	NOUN
ejpam-5864	257	25	and	and	CCONJ
ejpam-5864	257	26	d.	d.	PROPN
ejpam-5864	257	27	after	after	ADP
ejpam-5864	257	28	a	a	DET
ejpam-5864	257	29	conformable	conformable	ADJ
ejpam-5864	257	30	translation	translation	NOUN
ejpam-5864	257	31	in	in	ADP
ejpam-5864	257	32	s	s	PROPN
ejpam-5864	257	33	,	,	PUNCT
ejpam-5864	257	34	we	we	PRON
ejpam-5864	257	35	may	may	AUX
ejpam-5864	257	36	take	take	VERB
ejpam-5864	257	37	ρ2(s	ρ2(s	NOUN
ejpam-5864	257	38	)	)	PUNCT
ejpam-5864	257	39	=	=	SYM
ejpam-5864	258	1	1α(s	1α(s	NUM
ejpam-5864	258	2	2α	2α	NOUN
ejpam-5864	258	3	+	+	X
ejpam-5864	258	4	m	m	NOUN
ejpam-5864	258	5	)	)	PUNCT
ejpam-5864	258	6	,	,	PUNCT
ejpam-5864	258	7	for	for	ADP
ejpam-5864	258	8	some	some	DET
ejpam-5864	258	9	constant	constant	ADJ
ejpam-5864	258	10	m.	m.	NOUN
ejpam-5864	258	11	since	since	SCONJ
ejpam-5864	258	12	0α	0α	PROPN
ejpam-5864	258	13	∈	∈	PROPN
ejpam-5864	259	1	i	i	PRON
ejpam-5864	259	2	,	,	PUNCT
ejpam-5864	259	3	m	m	VERB
ejpam-5864	259	4	>	>	X
ejpam-5864	259	5	0α	0α	PROPN
ejpam-5864	259	6	.	.	PUNCT
ejpam-5864	260	1	therefore	therefore	ADV
ejpam-5864	260	2	,	,	PUNCT
ejpam-5864	260	3	we	we	PRON
ejpam-5864	260	4	may	may	AUX
ejpam-5864	260	5	put	put	VERB
ejpam-5864	260	6	m	m	NOUN
ejpam-5864	260	7	=	=	NOUN
ejpam-5864	260	8	n2α	n2α	PROPN
ejpam-5864	260	9	for	for	ADP
ejpam-5864	260	10	n	n	DET
ejpam-5864	260	11	∈	∈	PROPN
ejpam-5864	260	12	r+	r+	NOUN
ejpam-5864	260	13	.	.	PUNCT
ejpam-5864	261	1	introduce	introduce	VERB
ejpam-5864	261	2	a	a	DET
ejpam-5864	261	3	spherical	spherical	ADJ
ejpam-5864	261	4	curve	curve	NOUN
ejpam-5864	261	5	y(s	y(s	PROPN
ejpam-5864	261	6	)	)	PUNCT
ejpam-5864	261	7	as	as	ADP
ejpam-5864	261	8	x(s	x(s	PROPN
ejpam-5864	261	9	)	)	PUNCT
ejpam-5864	262	1	=	=	PUNCT
ejpam-5864	263	1	1α	1α	NOUN
ejpam-5864	263	2	√	√	INTJ
ejpam-5864	263	3	s2α	s2α	PROPN
ejpam-5864	263	4	+	+	CCONJ
ejpam-5864	263	5	n2αy(s	n2αy(s	PROPN
ejpam-5864	263	6	)	)	PUNCT
ejpam-5864	263	7	.	.	PUNCT
ejpam-5864	264	1	(	(	PUNCT
ejpam-5864	264	2	20	20	NUM
ejpam-5864	264	3	)	)	PUNCT
ejpam-5864	264	4	by	by	ADP
ejpam-5864	264	5	taking	take	VERB
ejpam-5864	264	6	the	the	DET
ejpam-5864	264	7	conformable	conformable	ADJ
ejpam-5864	264	8	derivative	derivative	NOUN
ejpam-5864	264	9	of	of	ADP
ejpam-5864	264	10	this	this	DET
ejpam-5864	264	11	equation	equation	NOUN
ejpam-5864	264	12	according	accord	VERB
ejpam-5864	264	13	to	to	ADP
ejpam-5864	264	14	s	s	PROPN
ejpam-5864	264	15	,	,	PUNCT
ejpam-5864	264	16	we	we	PRON
ejpam-5864	264	17	get	get	VERB
ejpam-5864	264	18	dαx	dαx	NOUN
ejpam-5864	264	19	=	=	PUNCT
ejpam-5864	264	20	(	(	PUNCT
ejpam-5864	264	21	0α	0α	NOUN
ejpam-5864	265	1	√	√	VERB
ejpam-5864	265	2	s2α	s2α	PUNCT
ejpam-5864	266	1	+	+	CCONJ
ejpam-5864	266	2	n2α	n2α	PROPN
ejpam-5864	266	3	+	+	CCONJ
ejpam-5864	266	4	1ααs	1ααs	NUM
ejpam-5864	266	5	α	α	NOUN
ejpam-5864	266	6	√	√	NUM
ejpam-5864	266	7	s2α	s2α	PUNCT
ejpam-5864	267	1	+	+	CCONJ
ejpam-5864	267	2	n2α	n2α	PROPN
ejpam-5864	267	3	)	)	PUNCT
ejpam-5864	268	1	y	y	PROPN
ejpam-5864	269	1	+	+	NOUN
ejpam-5864	269	2	1α	1α	NUM
ejpam-5864	269	3	√	√	INTJ
ejpam-5864	269	4	s2α	s2α	PUNCT
ejpam-5864	270	1	+	+	CCONJ
ejpam-5864	270	2	n2αdαy	n2αdαy	PROPN
ejpam-5864	270	3	(	(	PUNCT
ejpam-5864	270	4	21	21	NUM
ejpam-5864	270	5	)	)	PUNCT
ejpam-5864	270	6	note	note	NOUN
ejpam-5864	270	7	that	that	SCONJ
ejpam-5864	270	8	the	the	DET
ejpam-5864	270	9	conformable	conformable	ADJ
ejpam-5864	270	10	derivative	derivative	NOUN
ejpam-5864	270	11	of	of	ADP
ejpam-5864	270	12	dα1α	dα1α	PROPN
ejpam-5864	270	13	=	=	SYM
ejpam-5864	270	14	0α	0α	PROPN
ejpam-5864	270	15	.	.	PUNCT
ejpam-5864	271	1	also	also	ADV
ejpam-5864	271	2	,	,	PUNCT
ejpam-5864	271	3	since	since	SCONJ
ejpam-5864	271	4	y	y	PROPN
ejpam-5864	271	5	is	be	AUX
ejpam-5864	271	6	cα−unit	cα−unit	PROPN
ejpam-5864	271	7	and	and	CCONJ
ejpam-5864	271	8	y	y	PROPN
ejpam-5864	271	9	and	and	CCONJ
ejpam-5864	271	10	dαy	dαy	PROPN
ejpam-5864	271	11	are	be	AUX
ejpam-5864	271	12	cα−orthogonal	cα−orthogonal	ADJ
ejpam-5864	271	13	,	,	PUNCT
ejpam-5864	271	14	from	from	ADP
ejpam-5864	271	15	eq	eq	ADP
ejpam-5864	271	16	.	.	PUNCT
ejpam-5864	272	1	(	(	PUNCT
ejpam-5864	272	2	21	21	NUM
ejpam-5864	272	3	)	)	PUNCT
ejpam-5864	272	4	the	the	DET
ejpam-5864	272	5	following	follow	VERB
ejpam-5864	272	6	equation	equation	NOUN
ejpam-5864	272	7	is	be	AUX
ejpam-5864	272	8	obtained	obtain	VERB
ejpam-5864	272	9	∥dαy∥	∥dαy∥	NOUN
ejpam-5864	272	10	=	=	PUNCT
ejpam-5864	272	11	√	√	PROPN
ejpam-5864	272	12	1αs2α(1−	1αs2α(1−	NUM
ejpam-5864	272	13	α2	α2	ADJ
ejpam-5864	272	14	)	)	PUNCT
ejpam-5864	273	1	+	+	CCONJ
ejpam-5864	273	2	n2α	n2α	PROPN
ejpam-5864	273	3	(	(	PUNCT
ejpam-5864	273	4	s2α	s2α	PROPN
ejpam-5864	273	5	+	+	PROPN
ejpam-5864	273	6	n2α)2	n2α)2	PROPN
ejpam-5864	273	7	where	where	SCONJ
ejpam-5864	273	8	it	it	PRON
ejpam-5864	273	9	is	be	AUX
ejpam-5864	273	10	clear	clear	ADJ
ejpam-5864	273	11	that	that	SCONJ
ejpam-5864	273	12	∥dαy∥	∥dαy∥	PROPN
ejpam-5864	273	13	is	be	AUX
ejpam-5864	273	14	the	the	DET
ejpam-5864	273	15	cα−velocity	cα−velocity	NOUN
ejpam-5864	273	16	of	of	ADP
ejpam-5864	273	17	the	the	DET
ejpam-5864	273	18	cα−spherical	cα−spherical	ADJ
ejpam-5864	273	19	curve	curve	NOUN
ejpam-5864	273	20	y.	y.	PROPN
ejpam-5864	274	1	then	then	ADV
ejpam-5864	274	2	t	t	PROPN
ejpam-5864	274	3	=	=	PUNCT
ejpam-5864	274	4	is0	is0	NOUN
ejpam-5864	274	5	√	√	ADV
ejpam-5864	274	6	1αs2α(1−	1αs2α(1−	NUM
ejpam-5864	274	7	α2	α2	ADJ
ejpam-5864	274	8	)	)	PUNCT
ejpam-5864	275	1	+	+	CCONJ
ejpam-5864	275	2	n2α	n2α	PROPN
ejpam-5864	275	3	(	(	PUNCT
ejpam-5864	275	4	s2α	s2α	PROPN
ejpam-5864	275	5	+	+	NUM
ejpam-5864	275	6	n2α)2	n2α)2	PROPN
ejpam-5864	275	7	=	=	SYM
ejpam-5864	275	8	f−1(s	f−1(s	PROPN
ejpam-5864	275	9	)	)	PUNCT
ejpam-5864	275	10	.	.	PUNCT
ejpam-5864	276	1	so	so	ADV
ejpam-5864	276	2	,	,	PUNCT
ejpam-5864	276	3	s	s	NOUN
ejpam-5864	276	4	=	=	ADJ
ejpam-5864	276	5	f(t	f(t	NOUN
ejpam-5864	276	6	)	)	PUNCT
ejpam-5864	276	7	is	be	AUX
ejpam-5864	276	8	obtained	obtain	VERB
ejpam-5864	276	9	.	.	PUNCT
ejpam-5864	277	1	here	here	ADV
ejpam-5864	277	2	f(t	f(t	PROPN
ejpam-5864	277	3	)	)	PUNCT
ejpam-5864	277	4	is	be	AUX
ejpam-5864	277	5	a	a	DET
ejpam-5864	277	6	function	function	NOUN
ejpam-5864	277	7	that	that	PRON
ejpam-5864	277	8	gives	give	VERB
ejpam-5864	277	9	the	the	DET
ejpam-5864	277	10	result	result	NOUN
ejpam-5864	277	11	n.tant	n.tant	ADP
ejpam-5864	277	12	when	when	SCONJ
ejpam-5864	277	13	α	α	PROPN
ejpam-5864	277	14	→	→	SYM
ejpam-5864	277	15	1	1	NUM
ejpam-5864	277	16	.	.	PUNCT
ejpam-5864	277	17	if	if	SCONJ
ejpam-5864	277	18	this	this	DET
ejpam-5864	277	19	result	result	NOUN
ejpam-5864	277	20	is	be	AUX
ejpam-5864	277	21	written	write	VERB
ejpam-5864	277	22	in	in	ADP
ejpam-5864	277	23	eq	eq	NOUN
ejpam-5864	277	24	(	(	PUNCT
ejpam-5864	277	25	20	20	NUM
ejpam-5864	277	26	)	)	PUNCT
ejpam-5864	277	27	,	,	PUNCT
ejpam-5864	277	28	we	we	PRON
ejpam-5864	277	29	get	get	VERB
ejpam-5864	277	30	x(s	x(s	PROPN
ejpam-5864	277	31	)	)	PUNCT
ejpam-5864	278	1	=	=	SYM
ejpam-5864	278	2	1α	1α	NUM
ejpam-5864	278	3	√	√	NUM
ejpam-5864	278	4	f(t)2α	f(t)2α	PUNCT
ejpam-5864	279	1	+	+	CCONJ
ejpam-5864	279	2	n2αy(s	n2αy(	NOUN
ejpam-5864	279	3	)	)	PUNCT
ejpam-5864	279	4	.	.	PUNCT
ejpam-5864	280	1	(	(	PUNCT
ejpam-5864	280	2	22	22	NUM
ejpam-5864	280	3	)	)	PUNCT
ejpam-5864	280	4	5	5	NUM
ejpam-5864	280	5	.	.	PUNCT
ejpam-5864	280	6	conclusion	conclusion	NOUN
ejpam-5864	280	7	while	while	SCONJ
ejpam-5864	280	8	ordinary	ordinary	ADJ
ejpam-5864	280	9	analysis	analysis	NOUN
ejpam-5864	280	10	and	and	CCONJ
ejpam-5864	280	11	the	the	DET
ejpam-5864	280	12	differential	differential	ADJ
ejpam-5864	280	13	geometry	geometry	NOUN
ejpam-5864	280	14	are	be	AUX
ejpam-5864	280	15	related	relate	VERB
ejpam-5864	280	16	to	to	ADP
ejpam-5864	280	17	ordinary	ordinary	ADJ
ejpam-5864	280	18	derivatives	derivative	NOUN
ejpam-5864	280	19	,	,	PUNCT
ejpam-5864	280	20	fractional	fractional	ADJ
ejpam-5864	280	21	calculus	calculus	NOUN
ejpam-5864	280	22	provides	provide	VERB
ejpam-5864	280	23	us	we	PRON
ejpam-5864	280	24	with	with	ADP
ejpam-5864	280	25	the	the	DET
ejpam-5864	280	26	more	more	ADV
ejpam-5864	280	27	fractional	fractional	ADJ
ejpam-5864	280	28	analysis	analysis	NOUN
ejpam-5864	280	29	which	which	PRON
ejpam-5864	280	30	depends	depend	VERB
ejpam-5864	280	31	on	on	ADP
ejpam-5864	280	32	differentiation	differentiation	NOUN
ejpam-5864	280	33	and	and	CCONJ
ejpam-5864	280	34	integration	integration	NOUN
ejpam-5864	280	35	with	with	ADP
ejpam-5864	280	36	respect	respect	NOUN
ejpam-5864	280	37	to	to	ADP
ejpam-5864	280	38	arbitrary	arbitrary	ADJ
ejpam-5864	280	39	order	order	NOUN
ejpam-5864	280	40	.	.	PUNCT
ejpam-5864	281	1	in	in	ADP
ejpam-5864	281	2	the	the	DET
ejpam-5864	281	3	last	last	ADJ
ejpam-5864	281	4	few	few	ADJ
ejpam-5864	281	5	decades	decade	NOUN
ejpam-5864	281	6	,	,	PUNCT
ejpam-5864	281	7	fractional	fractional	ADJ
ejpam-5864	281	8	analysis	analysis	NOUN
ejpam-5864	281	9	has	have	AUX
ejpam-5864	281	10	been	be	AUX
ejpam-5864	281	11	used	use	VERB
ejpam-5864	281	12	extensively	extensively	ADV
ejpam-5864	281	13	in	in	ADP
ejpam-5864	281	14	almost	almost	ADV
ejpam-5864	281	15	all	all	PRON
ejpam-5864	281	16	basic	basic	ADJ
ejpam-5864	281	17	sciences	science	NOUN
ejpam-5864	281	18	,	,	PUNCT
ejpam-5864	281	19	especially	especially	ADV
ejpam-5864	281	20	in	in	ADP
ejpam-5864	281	21	physics	physics	NOUN
ejpam-5864	281	22	,	,	PUNCT
ejpam-5864	281	23	chemistry	chemistry	NOUN
ejpam-5864	281	24	and	and	CCONJ
ejpam-5864	281	25	engineering	engineering	NOUN
ejpam-5864	281	26	.	.	PUNCT
ejpam-5864	282	1	it	it	PRON
ejpam-5864	282	2	is	be	AUX
ejpam-5864	282	3	claimed	claim	VERB
ejpam-5864	282	4	that	that	SCONJ
ejpam-5864	282	5	fractional	fractional	ADJ
ejpam-5864	282	6	analysis	analysis	NOUN
ejpam-5864	282	7	gives	give	VERB
ejpam-5864	282	8	more	more	ADJ
ejpam-5864	282	9	numerical	numerical	ADJ
ejpam-5864	282	10	results	result	NOUN
ejpam-5864	282	11	than	than	ADP
ejpam-5864	282	12	classical	classical	ADJ
ejpam-5864	282	13	analysis	analysis	NOUN
ejpam-5864	282	14	.	.	PUNCT
ejpam-5864	283	1	this	this	PRON
ejpam-5864	283	2	makes	make	VERB
ejpam-5864	283	3	fractional	fractional	ADJ
ejpam-5864	283	4	analysis	analysis	NOUN
ejpam-5864	283	5	more	more	ADV
ejpam-5864	283	6	advantageous	advantageous	ADJ
ejpam-5864	283	7	.	.	PUNCT
ejpam-5864	284	1	a.	a.	PROPN
ejpam-5864	284	2	has	have	VERB
ejpam-5864	284	3	,	,	PUNCT
ejpam-5864	284	4	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	284	5	,	,	PUNCT
ejpam-5864	284	6	t.	t.	PROPN
ejpam-5864	284	7	abdeljawad	abdeljawad	PROPN
ejpam-5864	284	8	/	/	SYM
ejpam-5864	284	9	eur	eur	PROPN
ejpam-5864	284	10	.	.	PUNCT
ejpam-5864	285	1	j.	j.	PROPN
ejpam-5864	285	2	pure	pure	PROPN
ejpam-5864	285	3	appl	appl	PROPN
ejpam-5864	285	4	.	.	PROPN
ejpam-5864	285	5	math	math	PROPN
ejpam-5864	285	6	,	,	PUNCT
ejpam-5864	285	7	18	18	NUM
ejpam-5864	285	8	(	(	PUNCT
ejpam-5864	285	9	2	2	NUM
ejpam-5864	285	10	)	)	PUNCT
ejpam-5864	285	11	(	(	PUNCT
ejpam-5864	285	12	2025	2025	NUM
ejpam-5864	285	13	)	)	PUNCT
ejpam-5864	285	14	,	,	PUNCT
ejpam-5864	285	15	5864	5864	NUM
ejpam-5864	285	16	12	12	NUM
ejpam-5864	285	17	of	of	ADP
ejpam-5864	285	18	14	14	NUM
ejpam-5864	285	19	since	since	SCONJ
ejpam-5864	285	20	conformable	conformable	ADJ
ejpam-5864	285	21	derivatives	derivative	NOUN
ejpam-5864	285	22	have	have	VERB
ejpam-5864	285	23	several	several	ADJ
ejpam-5864	285	24	well	well	ADV
ejpam-5864	285	25	-	-	PUNCT
ejpam-5864	285	26	behaved	behave	VERB
ejpam-5864	285	27	properties	property	NOUN
ejpam-5864	285	28	like	like	ADP
ejpam-5864	285	29	ordinary	ordinary	ADJ
ejpam-5864	285	30	derivatives	derivative	NOUN
ejpam-5864	285	31	,	,	PUNCT
ejpam-5864	285	32	in	in	ADP
ejpam-5864	285	33	this	this	DET
ejpam-5864	285	34	work	work	NOUN
ejpam-5864	285	35	the	the	DET
ejpam-5864	285	36	basic	basic	ADJ
ejpam-5864	285	37	concepts	concept	NOUN
ejpam-5864	285	38	of	of	ADP
ejpam-5864	285	39	geometry	geometry	NOUN
ejpam-5864	285	40	have	have	AUX
ejpam-5864	285	41	been	be	AUX
ejpam-5864	285	42	re	re	VERB
ejpam-5864	285	43	-	-	VERB
ejpam-5864	285	44	examined	examine	VERB
ejpam-5864	285	45	and	and	CCONJ
ejpam-5864	285	46	studied	study	VERB
ejpam-5864	285	47	in	in	ADP
ejpam-5864	285	48	the	the	DET
ejpam-5864	285	49	frame	frame	NOUN
ejpam-5864	285	50	of	of	ADP
ejpam-5864	285	51	conformable	conformable	ADJ
ejpam-5864	285	52	fractional	fractional	ADJ
ejpam-5864	285	53	analysis	analysis	NOUN
ejpam-5864	285	54	.	.	PUNCT
ejpam-5864	286	1	our	our	PRON
ejpam-5864	286	2	new	new	ADJ
ejpam-5864	286	3	differential	differential	NOUN
ejpam-5864	286	4	geometry	geometry	NOUN
ejpam-5864	286	5	concepts	concept	NOUN
ejpam-5864	286	6	we	we	PRON
ejpam-5864	286	7	have	have	AUX
ejpam-5864	286	8	studied	study	VERB
ejpam-5864	286	9	give	give	VERB
ejpam-5864	286	10	the	the	DET
ejpam-5864	286	11	readers	reader	NOUN
ejpam-5864	286	12	a	a	DET
ejpam-5864	286	13	more	more	ADV
ejpam-5864	286	14	general	general	ADJ
ejpam-5864	286	15	approach	approach	NOUN
ejpam-5864	286	16	to	to	PART
ejpam-5864	286	17	deal	deal	VERB
ejpam-5864	286	18	with	with	ADP
ejpam-5864	286	19	.	.	PUNCT
ejpam-5864	287	1	the	the	DET
ejpam-5864	287	2	limiting	limit	VERB
ejpam-5864	287	3	case	case	NOUN
ejpam-5864	287	4	α	α	X
ejpam-5864	287	5	→	→	SYM
ejpam-5864	287	6	1	1	NUM
ejpam-5864	287	7	sends	send	VERB
ejpam-5864	287	8	us	we	PRON
ejpam-5864	287	9	back	back	ADV
ejpam-5864	287	10	to	to	ADP
ejpam-5864	287	11	the	the	DET
ejpam-5864	287	12	classical	classical	ADJ
ejpam-5864	287	13	geometry	geometry	NOUN
ejpam-5864	287	14	.	.	PUNCT
ejpam-5864	288	1	•	•	NUM
ejpam-5864	288	2	the	the	DET
ejpam-5864	288	3	cα−	cα−	NUM
ejpam-5864	288	4	frame	frame	NOUN
ejpam-5864	288	5	has	have	AUX
ejpam-5864	288	6	been	be	AUX
ejpam-5864	288	7	constructed	construct	VERB
ejpam-5864	288	8	differently	differently	ADV
ejpam-5864	288	9	from	from	ADP
ejpam-5864	288	10	previous	previous	ADJ
ejpam-5864	288	11	similar	similar	ADJ
ejpam-5864	288	12	studies	study	NOUN
ejpam-5864	288	13	and	and	CCONJ
ejpam-5864	288	14	the	the	DET
ejpam-5864	288	15	classical	classical	ADJ
ejpam-5864	288	16	frenet	frenet	ADJ
ejpam-5864	288	17	frame	frame	NOUN
ejpam-5864	288	18	.	.	PUNCT
ejpam-5864	289	1	the	the	DET
ejpam-5864	289	2	advantage	advantage	NOUN
ejpam-5864	289	3	of	of	ADP
ejpam-5864	289	4	this	this	DET
ejpam-5864	289	5	frame	frame	NOUN
ejpam-5864	289	6	is	be	AUX
ejpam-5864	289	7	that	that	SCONJ
ejpam-5864	289	8	when	when	SCONJ
ejpam-5864	289	9	α	α	PRON
ejpam-5864	289	10	→	→	SYM
ejpam-5864	289	11	1	1	NUM
ejpam-5864	289	12	it	it	PRON
ejpam-5864	289	13	gives	give	VERB
ejpam-5864	289	14	the	the	DET
ejpam-5864	289	15	classical	classical	ADJ
ejpam-5864	289	16	frenet	frenet	ADJ
ejpam-5864	289	17	frame	frame	NOUN
ejpam-5864	289	18	,	,	PUNCT
ejpam-5864	289	19	it	it	PRON
ejpam-5864	289	20	also	also	ADV
ejpam-5864	289	21	gives	give	VERB
ejpam-5864	289	22	the	the	DET
ejpam-5864	289	23	opportunity	opportunity	NOUN
ejpam-5864	289	24	to	to	PART
ejpam-5864	289	25	examine	examine	VERB
ejpam-5864	289	26	the	the	DET
ejpam-5864	289	27	frame	frame	NOUN
ejpam-5864	289	28	of	of	ADP
ejpam-5864	289	29	the	the	DET
ejpam-5864	289	30	curve	curve	NOUN
ejpam-5864	289	31	for	for	ADP
ejpam-5864	289	32	all	all	DET
ejpam-5864	289	33	cases	case	NOUN
ejpam-5864	289	34	in	in	ADP
ejpam-5864	289	35	the	the	DET
ejpam-5864	289	36	range	range	NOUN
ejpam-5864	289	37	of	of	ADP
ejpam-5864	289	38	0	0	NUM
ejpam-5864	289	39	<	<	X
ejpam-5864	289	40	α	α	X
ejpam-5864	289	41	<	<	X
ejpam-5864	289	42	1	1	NUM
ejpam-5864	289	43	.	.	PUNCT
ejpam-5864	290	1	in	in	ADP
ejpam-5864	290	2	other	other	ADJ
ejpam-5864	290	3	words	word	NOUN
ejpam-5864	290	4	,	,	PUNCT
ejpam-5864	290	5	it	it	PRON
ejpam-5864	290	6	exhibits	exhibit	VERB
ejpam-5864	290	7	a	a	DET
ejpam-5864	290	8	more	more	ADV
ejpam-5864	290	9	general	general	ADJ
ejpam-5864	290	10	situation	situation	NOUN
ejpam-5864	290	11	compared	compare	VERB
ejpam-5864	290	12	to	to	ADP
ejpam-5864	290	13	the	the	DET
ejpam-5864	290	14	classical	classical	ADJ
ejpam-5864	290	15	frenet	frenet	ADJ
ejpam-5864	290	16	frame	frame	NOUN
ejpam-5864	290	17	.	.	PUNCT
ejpam-5864	291	1	•	•	NUM
ejpam-5864	291	2	curves	curve	NOUN
ejpam-5864	291	3	defined	define	VERB
ejpam-5864	291	4	according	accord	VERB
ejpam-5864	291	5	to	to	ADP
ejpam-5864	291	6	the	the	DET
ejpam-5864	291	7	cα−frame	cα−frame	NOUN
ejpam-5864	291	8	take	take	VERB
ejpam-5864	291	9	on	on	ADP
ejpam-5864	291	10	a	a	DET
ejpam-5864	291	11	different	different	ADJ
ejpam-5864	291	12	variation	variation	NOUN
ejpam-5864	291	13	of	of	ADP
ejpam-5864	291	14	the	the	DET
ejpam-5864	291	15	curve	curve	NOUN
ejpam-5864	291	16	for	for	ADP
ejpam-5864	291	17	each	each	DET
ejpam-5864	291	18	α	α	NOUN
ejpam-5864	291	19	value	value	NOUN
ejpam-5864	291	20	.	.	PUNCT
ejpam-5864	292	1	•	•	NUM
ejpam-5864	292	2	an	an	DET
ejpam-5864	292	3	example	example	NOUN
ejpam-5864	292	4	of	of	ADP
ejpam-5864	292	5	this	this	PRON
ejpam-5864	292	6	can	can	AUX
ejpam-5864	292	7	be	be	AUX
ejpam-5864	292	8	seen	see	VERB
ejpam-5864	292	9	very	very	ADV
ejpam-5864	292	10	well	well	ADV
ejpam-5864	292	11	in	in	ADP
ejpam-5864	292	12	eq	eq	ADP
ejpam-5864	292	13	.	.	PUNCT
ejpam-5864	293	1	(	(	PUNCT
ejpam-5864	293	2	22	22	NUM
ejpam-5864	293	3	)	)	PUNCT
ejpam-5864	293	4	.	.	PUNCT
ejpam-5864	294	1	for	for	ADP
ejpam-5864	294	2	each	each	DET
ejpam-5864	294	3	α	α	NOUN
ejpam-5864	294	4	value	value	NOUN
ejpam-5864	294	5	in	in	ADP
ejpam-5864	294	6	this	this	DET
ejpam-5864	294	7	equation	equation	NOUN
ejpam-5864	294	8	,	,	PUNCT
ejpam-5864	294	9	the	the	DET
ejpam-5864	294	10	function	function	NOUN
ejpam-5864	294	11	f(t	f(t	PROPN
ejpam-5864	294	12	)	)	PUNCT
ejpam-5864	294	13	will	will	AUX
ejpam-5864	294	14	give	give	VERB
ejpam-5864	294	15	a	a	DET
ejpam-5864	294	16	different	different	ADJ
ejpam-5864	294	17	result	result	NOUN
ejpam-5864	294	18	.	.	PUNCT
ejpam-5864	295	1	thus	thus	ADV
ejpam-5864	295	2	,	,	PUNCT
ejpam-5864	295	3	the	the	DET
ejpam-5864	295	4	x	x	NOUN
ejpam-5864	295	5	curve	curve	NOUN
ejpam-5864	295	6	will	will	AUX
ejpam-5864	295	7	turn	turn	VERB
ejpam-5864	295	8	into	into	ADP
ejpam-5864	295	9	a	a	DET
ejpam-5864	295	10	different	different	ADJ
ejpam-5864	295	11	a	a	DET
ejpam-5864	295	12	cα−rectifying	cα−rectifye	VERB
ejpam-5864	295	13	curve	curve	NOUN
ejpam-5864	295	14	in	in	ADP
ejpam-5864	295	15	a	a	DET
ejpam-5864	295	16	conformable	conformable	ADJ
ejpam-5864	295	17	sense	sense	NOUN
ejpam-5864	295	18	according	accord	VERB
ejpam-5864	295	19	to	to	ADP
ejpam-5864	295	20	each	each	DET
ejpam-5864	295	21	α	α	NOUN
ejpam-5864	295	22	value	value	NOUN
ejpam-5864	295	23	,	,	PUNCT
ejpam-5864	295	24	and	and	CCONJ
ejpam-5864	295	25	when	when	SCONJ
ejpam-5864	295	26	α	α	X
ejpam-5864	295	27	→	→	SYM
ejpam-5864	295	28	1	1	NUM
ejpam-5864	295	29	it	it	PRON
ejpam-5864	295	30	will	will	AUX
ejpam-5864	295	31	turn	turn	VERB
ejpam-5864	295	32	into	into	ADP
ejpam-5864	295	33	a	a	DET
ejpam-5864	295	34	classical	classical	ADJ
ejpam-5864	295	35	rectifying	rectifying	NOUN
ejpam-5864	295	36	curve	curve	NOUN
ejpam-5864	295	37	.	.	PUNCT
ejpam-5864	296	1	•	•	NUM
ejpam-5864	296	2	the	the	DET
ejpam-5864	296	3	variation	variation	NOUN
ejpam-5864	296	4	of	of	ADP
ejpam-5864	296	5	the	the	DET
ejpam-5864	296	6	cα−frame	cα−frame	NOUN
ejpam-5864	296	7	at	at	ADP
ejpam-5864	296	8	any	any	DET
ejpam-5864	296	9	point	point	NOUN
ejpam-5864	296	10	of	of	ADP
ejpam-5864	296	11	the	the	DET
ejpam-5864	296	12	cα−curve	cα−curve	NOUN
ejpam-5864	296	13	and	and	CCONJ
ejpam-5864	296	14	of	of	ADP
ejpam-5864	296	15	each	each	DET
ejpam-5864	296	16	defined	define	VERB
ejpam-5864	296	17	curve	curve	NOUN
ejpam-5864	296	18	depending	depend	VERB
ejpam-5864	296	19	on	on	ADP
ejpam-5864	296	20	this	this	DET
ejpam-5864	296	21	frame	frame	NOUN
ejpam-5864	296	22	within	within	ADP
ejpam-5864	296	23	the	the	DET
ejpam-5864	296	24	range	range	NOUN
ejpam-5864	296	25	of	of	ADP
ejpam-5864	296	26	0	0	NUM
ejpam-5864	296	27	<	<	X
ejpam-5864	296	28	α	α	X
ejpam-5864	296	29	<	<	X
ejpam-5864	296	30	1	1	NUM
ejpam-5864	296	31	can	can	AUX
ejpam-5864	296	32	be	be	AUX
ejpam-5864	296	33	examined	examine	VERB
ejpam-5864	296	34	.	.	PUNCT
ejpam-5864	297	1	in	in	ADP
ejpam-5864	297	2	addition	addition	NOUN
ejpam-5864	297	3	,	,	PUNCT
ejpam-5864	297	4	a	a	DET
ejpam-5864	297	5	curve	curve	NOUN
ejpam-5864	297	6	can	can	AUX
ejpam-5864	297	7	be	be	AUX
ejpam-5864	297	8	generated	generate	VERB
ejpam-5864	297	9	for	for	ADP
ejpam-5864	297	10	the	the	DET
ejpam-5864	297	11	resulting	result	VERB
ejpam-5864	297	12	cα−frame	cα−frame	NOUN
ejpam-5864	297	13	for	for	ADP
ejpam-5864	297	14	each	each	DET
ejpam-5864	297	15	α	α	NOUN
ejpam-5864	297	16	value	value	NOUN
ejpam-5864	297	17	.	.	PUNCT
ejpam-5864	298	1	acknowledgements	acknowledgement	VERB
ejpam-5864	298	2	the	the	DET
ejpam-5864	298	3	author	author	NOUN
ejpam-5864	298	4	t.abdeljawad	t.abdeljawad	NOUN
ejpam-5864	298	5	would	would	AUX
ejpam-5864	298	6	like	like	VERB
ejpam-5864	298	7	to	to	PART
ejpam-5864	298	8	thank	thank	VERB
ejpam-5864	298	9	prince	prince	PROPN
ejpam-5864	298	10	sultan	sultan	PROPN
ejpam-5864	298	11	university	university	PROPN
ejpam-5864	298	12	for	for	ADP
ejpam-5864	298	13	paying	pay	VERB
ejpam-5864	298	14	the	the	DET
ejpam-5864	298	15	apc	apc	NOUN
ejpam-5864	298	16	and	and	CCONJ
ejpam-5864	298	17	for	for	ADP
ejpam-5864	298	18	the	the	DET
ejpam-5864	298	19	support	support	NOUN
ejpam-5864	298	20	through	through	ADP
ejpam-5864	298	21	tas	tas	PROPN
ejpam-5864	298	22	research	research	NOUN
ejpam-5864	298	23	lab	lab	NOUN
ejpam-5864	298	24	.	.	PUNCT
ejpam-5864	299	1	references	reference	NOUN
ejpam-5864	299	2	[	[	X
ejpam-5864	299	3	1	1	NUM
ejpam-5864	299	4	]	]	PUNCT
ejpam-5864	299	5	m.	m.	NOUN
ejpam-5864	299	6	barros	barros	PROPN
ejpam-5864	299	7	,	,	PUNCT
ejpam-5864	299	8	j.	j.	PROPN
ejpam-5864	299	9	l.	l.	PROPN
ejpam-5864	299	10	cabrerizo	cabrerizo	PROPN
ejpam-5864	299	11	,	,	PUNCT
ejpam-5864	299	12	m.	m.	NOUN
ejpam-5864	299	13	fernández	fernández	PROPN
ejpam-5864	299	14	,	,	PUNCT
ejpam-5864	299	15	and	and	CCONJ
ejpam-5864	299	16	a.	a.	PROPN
ejpam-5864	299	17	romero	romero	PROPN
ejpam-5864	299	18	.	.	PUNCT
ejpam-5864	300	1	magnetic	magnetic	ADJ
ejpam-5864	300	2	vortex	vortex	NOUN
ejpam-5864	300	3	filament	filament	NOUN
ejpam-5864	300	4	flows	flow	VERB
ejpam-5864	300	5	.	.	PUNCT
ejpam-5864	301	1	journal	journal	PROPN
ejpam-5864	301	2	of	of	ADP
ejpam-5864	301	3	mathematical	mathematical	ADJ
ejpam-5864	301	4	physics	physics	NOUN
ejpam-5864	301	5	,	,	PUNCT
ejpam-5864	301	6	48(8):082904	48(8):082904	NUM
ejpam-5864	301	7	,	,	PUNCT
ejpam-5864	301	8	2007	2007	NUM
ejpam-5864	301	9	.	.	PUNCT
ejpam-5864	302	1	[	[	X
ejpam-5864	302	2	2	2	X
ejpam-5864	302	3	]	]	PUNCT
ejpam-5864	302	4	z.	z.	PROPN
ejpam-5864	302	5	b.	b.	PROPN
ejpam-5864	302	6	ozdemir	ozdemir	PROPN
ejpam-5864	302	7	,	,	PUNCT
ejpam-5864	302	8	i.	i.	PROPN
ejpam-5864	302	9	gok	gok	PROPN
ejpam-5864	302	10	,	,	PUNCT
ejpam-5864	302	11	y.	y.	PROPN
ejpam-5864	302	12	yayli	yayli	PROPN
ejpam-5864	302	13	,	,	PUNCT
ejpam-5864	302	14	and	and	CCONJ
ejpam-5864	302	15	n.	n.	PROPN
ejpam-5864	302	16	ekmekci	ekmekci	PROPN
ejpam-5864	302	17	.	.	PUNCT
ejpam-5864	303	1	notes	note	NOUN
ejpam-5864	303	2	on	on	ADP
ejpam-5864	303	3	magnetic	magnetic	ADJ
ejpam-5864	303	4	curves	curve	NOUN
ejpam-5864	303	5	in	in	ADP
ejpam-5864	303	6	3d	3d	NUM
ejpam-5864	303	7	semi	semi	ADJ
ejpam-5864	303	8	-	-	ADJ
ejpam-5864	303	9	riemannian	riemannian	ADJ
ejpam-5864	303	10	manifolds	manifold	NOUN
ejpam-5864	303	11	.	.	PUNCT
ejpam-5864	304	1	turkish	turkish	ADJ
ejpam-5864	304	2	journal	journal	NOUN
ejpam-5864	304	3	of	of	ADP
ejpam-5864	304	4	mathematics	mathematic	NOUN
ejpam-5864	304	5	,	,	PUNCT
ejpam-5864	304	6	39(3):412–426	39(3):412–426	NUM
ejpam-5864	304	7	,	,	PUNCT
ejpam-5864	304	8	2015	2015	NUM
ejpam-5864	304	9	.	.	PUNCT
ejpam-5864	305	1	[	[	X
ejpam-5864	305	2	3	3	NUM
ejpam-5864	305	3	]	]	X
ejpam-5864	305	4	m.	m.	NOUN
ejpam-5864	305	5	shareduwan	shareduwan	PROPN
ejpam-5864	305	6	,	,	PUNCT
ejpam-5864	305	7	m.	m.	PROPN
ejpam-5864	305	8	kasihmuddin	kasihmuddin	PROPN
ejpam-5864	305	9	,	,	PUNCT
ejpam-5864	305	10	m.	m.	NOUN
ejpam-5864	305	11	a.	a.	PROPN
ejpam-5864	305	12	mansor	mansor	PROPN
ejpam-5864	305	13	,	,	PUNCT
ejpam-5864	305	14	and	and	CCONJ
ejpam-5864	305	15	s.	s.	PROPN
ejpam-5864	305	16	sathasivam	sathasivam	VERB
ejpam-5864	305	17	.	.	PUNCT
ejpam-5864	306	1	bezier	bezier	NOUN
ejpam-5864	306	2	curves	curve	NOUN
ejpam-5864	306	3	satisfiability	satisfiability	NOUN
ejpam-5864	306	4	model	model	NOUN
ejpam-5864	306	5	in	in	ADP
ejpam-5864	306	6	enhanced	enhanced	ADJ
ejpam-5864	306	7	hopfield	hopfield	ADJ
ejpam-5864	306	8	network	network	NOUN
ejpam-5864	306	9	.	.	PUNCT
ejpam-5864	307	1	international	international	ADJ
ejpam-5864	307	2	journal	journal	NOUN
ejpam-5864	307	3	of	of	ADP
ejpam-5864	307	4	intelligent	intelligent	ADJ
ejpam-5864	307	5	systems	system	NOUN
ejpam-5864	307	6	and	and	CCONJ
ejpam-5864	307	7	applications	application	NOUN
ejpam-5864	307	8	,	,	PUNCT
ejpam-5864	307	9	8(12):9–17	8(12):9–17	NOUN
ejpam-5864	307	10	,	,	PUNCT
ejpam-5864	307	11	2016	2016	NUM
ejpam-5864	307	12	.	.	PUNCT
ejpam-5864	308	1	[	[	X
ejpam-5864	308	2	4	4	NUM
ejpam-5864	308	3	]	]	X
ejpam-5864	308	4	n.	n.	PROPN
ejpam-5864	308	5	k.	k.	PROPN
ejpam-5864	308	6	razali	razali	PROPN
ejpam-5864	308	7	.	.	PUNCT
ejpam-5864	309	1	rational	rational	ADJ
ejpam-5864	309	2	cubic	cubic	NOUN
ejpam-5864	309	3	of	of	ADP
ejpam-5864	309	4	timmer	timmer	PROPN
ejpam-5864	309	5	and	and	CCONJ
ejpam-5864	309	6	bezier	bezier	NOUN
ejpam-5864	309	7	curve	curve	NOUN
ejpam-5864	309	8	with	with	ADP
ejpam-5864	309	9	application	application	NOUN
ejpam-5864	309	10	in	in	ADP
ejpam-5864	309	11	arabic	arabic	ADJ
ejpam-5864	309	12	calligraphy	calligraphy	NOUN
ejpam-5864	309	13	design	design	NOUN
ejpam-5864	309	14	.	.	PUNCT
ejpam-5864	310	1	international	international	ADJ
ejpam-5864	310	2	journal	journal	NOUN
ejpam-5864	310	3	of	of	ADP
ejpam-5864	310	4	advanced	advanced	ADJ
ejpam-5864	310	5	trends	trend	NOUN
ejpam-5864	310	6	in	in	ADP
ejpam-5864	310	7	computer	computer	NOUN
ejpam-5864	310	8	science	science	NOUN
ejpam-5864	310	9	and	and	CCONJ
ejpam-5864	310	10	engineering	engineering	NOUN
ejpam-5864	310	11	,	,	PUNCT
ejpam-5864	310	12	8(1.5):40–43	8(1.5):40–43	NUM
ejpam-5864	310	13	,	,	PUNCT
ejpam-5864	310	14	2019	2019	NUM
ejpam-5864	310	15	.	.	PUNCT
ejpam-5864	311	1	[	[	X
ejpam-5864	311	2	5	5	X
ejpam-5864	311	3	]	]	PUNCT
ejpam-5864	311	4	b.	b.	PROPN
ejpam-5864	311	5	y.	y.	PROPN
ejpam-5864	311	6	chen	chen	PROPN
ejpam-5864	311	7	.	.	PUNCT
ejpam-5864	312	1	when	when	SCONJ
ejpam-5864	312	2	does	do	AUX
ejpam-5864	312	3	the	the	DET
ejpam-5864	312	4	position	position	NOUN
ejpam-5864	312	5	vector	vector	NOUN
ejpam-5864	312	6	of	of	ADP
ejpam-5864	312	7	a	a	DET
ejpam-5864	312	8	space	space	NOUN
ejpam-5864	312	9	curve	curve	NOUN
ejpam-5864	312	10	always	always	ADV
ejpam-5864	312	11	lie	lie	VERB
ejpam-5864	312	12	in	in	ADP
ejpam-5864	312	13	its	its	PRON
ejpam-5864	312	14	rectifying	rectifying	NOUN
ejpam-5864	312	15	plane	plane	NOUN
ejpam-5864	312	16	?	?	PUNCT
ejpam-5864	313	1	the	the	DET
ejpam-5864	313	2	american	american	PROPN
ejpam-5864	313	3	mathematical	mathematical	PROPN
ejpam-5864	313	4	monthly	monthly	ADV
ejpam-5864	313	5	,	,	PUNCT
ejpam-5864	313	6	110(2):147–152	110(2):147–152	PROPN
ejpam-5864	313	7	,	,	PUNCT
ejpam-5864	313	8	2003	2003	NUM
ejpam-5864	313	9	.	.	PUNCT
ejpam-5864	314	1	a.	a.	PROPN
ejpam-5864	314	2	has	have	VERB
ejpam-5864	314	3	,	,	PUNCT
ejpam-5864	314	4	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	314	5	,	,	PUNCT
ejpam-5864	314	6	t.	t.	PROPN
ejpam-5864	314	7	abdeljawad	abdeljawad	PROPN
ejpam-5864	314	8	/	/	SYM
ejpam-5864	314	9	eur	eur	PROPN
ejpam-5864	314	10	.	.	PUNCT
ejpam-5864	315	1	j.	j.	PROPN
ejpam-5864	315	2	pure	pure	PROPN
ejpam-5864	315	3	appl	appl	PROPN
ejpam-5864	315	4	.	.	PROPN
ejpam-5864	315	5	math	math	PROPN
ejpam-5864	315	6	,	,	PUNCT
ejpam-5864	315	7	18	18	NUM
ejpam-5864	315	8	(	(	PUNCT
ejpam-5864	315	9	2	2	NUM
ejpam-5864	315	10	)	)	PUNCT
ejpam-5864	315	11	(	(	PUNCT
ejpam-5864	315	12	2025	2025	NUM
ejpam-5864	315	13	)	)	PUNCT
ejpam-5864	315	14	,	,	PUNCT
ejpam-5864	315	15	5864	5864	NUM
ejpam-5864	315	16	13	13	NUM
ejpam-5864	315	17	of	of	ADP
ejpam-5864	315	18	14	14	NUM
ejpam-5864	315	19	[	[	SYM
ejpam-5864	315	20	6	6	NUM
ejpam-5864	315	21	]	]	PUNCT
ejpam-5864	315	22	s.	s.	PROPN
ejpam-5864	315	23	d.	d.	PROPN
ejpam-5864	315	24	gertzbein	gertzbein	PROPN
ejpam-5864	315	25	,	,	PUNCT
ejpam-5864	315	26	j.	j.	PROPN
ejpam-5864	315	27	seligman	seligman	PROPN
ejpam-5864	315	28	,	,	PUNCT
ejpam-5864	315	29	r.	r.	PROPN
ejpam-5864	315	30	holtby	holtby	PROPN
ejpam-5864	315	31	,	,	PUNCT
ejpam-5864	315	32	k.	k.	PROPN
ejpam-5864	315	33	w.	w.	PROPN
ejpam-5864	315	34	chan	chan	PROPN
ejpam-5864	315	35	,	,	PUNCT
ejpam-5864	315	36	n.	n.	PROPN
ejpam-5864	315	37	ogston	ogston	PROPN
ejpam-5864	315	38	,	,	PUNCT
ejpam-5864	315	39	a.	a.	PROPN
ejpam-5864	315	40	kapasouri	kapasouri	PROPN
ejpam-5864	315	41	,	,	PUNCT
ejpam-5864	315	42	m.	m.	NOUN
ejpam-5864	315	43	tile	tile	NOUN
ejpam-5864	315	44	,	,	PUNCT
ejpam-5864	315	45	and	and	CCONJ
ejpam-5864	315	46	b.	b.	PROPN
ejpam-5864	315	47	cruickshank	cruickshank	PROPN
ejpam-5864	315	48	.	.	PUNCT
ejpam-5864	316	1	centrode	centrode	NOUN
ejpam-5864	316	2	patterns	pattern	NOUN
ejpam-5864	316	3	and	and	CCONJ
ejpam-5864	316	4	segmental	segmental	ADJ
ejpam-5864	316	5	instability	instability	NOUN
ejpam-5864	316	6	in	in	ADP
ejpam-5864	316	7	degenerative	degenerative	ADJ
ejpam-5864	316	8	disk	disk	NOUN
ejpam-5864	316	9	disease	disease	NOUN
ejpam-5864	316	10	.	.	PUNCT
ejpam-5864	317	1	spine	spine	PROPN
ejpam-5864	317	2	,	,	PUNCT
ejpam-5864	317	3	10(3):257–261	10(3):257–261	NUM
ejpam-5864	317	4	,	,	PUNCT
ejpam-5864	317	5	1985	1985	NUM
ejpam-5864	317	6	.	.	PUNCT
ejpam-5864	318	1	[	[	X
ejpam-5864	318	2	7	7	X
ejpam-5864	318	3	]	]	X
ejpam-5864	318	4	p.	p.	NOUN
ejpam-5864	318	5	j.	j.	PROPN
ejpam-5864	318	6	weiler	weiler	PROPN
ejpam-5864	318	7	and	and	CCONJ
ejpam-5864	318	8	e.	e.	PROPN
ejpam-5864	318	9	r.	r.	PROPN
ejpam-5864	318	10	bogoch	bogoch	PROPN
ejpam-5864	318	11	.	.	PUNCT
ejpam-5864	319	1	kinematics	kinematic	NOUN
ejpam-5864	319	2	of	of	ADP
ejpam-5864	319	3	the	the	DET
ejpam-5864	319	4	distal	distal	ADJ
ejpam-5864	319	5	radioulnar	radioulnar	ADJ
ejpam-5864	319	6	joint	joint	NOUN
ejpam-5864	319	7	in	in	ADP
ejpam-5864	319	8	rheumatoid	rheumatoid	NOUN
ejpam-5864	319	9	arthritis	arthritis	NOUN
ejpam-5864	319	10	:	:	PUNCT
ejpam-5864	319	11	an	an	DET
ejpam-5864	319	12	in	in	ADP
ejpam-5864	319	13	vivo	vivo	NOUN
ejpam-5864	319	14	study	study	NOUN
ejpam-5864	319	15	using	use	VERB
ejpam-5864	319	16	centrode	centrode	NOUN
ejpam-5864	319	17	analysis	analysis	NOUN
ejpam-5864	319	18	.	.	PUNCT
ejpam-5864	320	1	the	the	DET
ejpam-5864	320	2	journal	journal	NOUN
ejpam-5864	320	3	of	of	ADP
ejpam-5864	320	4	hand	hand	NOUN
ejpam-5864	320	5	surgery	surgery	NOUN
ejpam-5864	320	6	,	,	PUNCT
ejpam-5864	320	7	20(6):937–943	20(6):937–943	NUM
ejpam-5864	320	8	,	,	PUNCT
ejpam-5864	320	9	1995	1995	NUM
ejpam-5864	320	10	.	.	PUNCT
ejpam-5864	321	1	[	[	X
ejpam-5864	321	2	8	8	NUM
ejpam-5864	321	3	]	]	PUNCT
ejpam-5864	321	4	b.	b.	PROPN
ejpam-5864	321	5	y.	y.	PROPN
ejpam-5864	321	6	chen	chen	PROPN
ejpam-5864	321	7	and	and	CCONJ
ejpam-5864	321	8	f.	f.	PROPN
ejpam-5864	321	9	dillen	dillen	PROPN
ejpam-5864	321	10	.	.	PUNCT
ejpam-5864	322	1	rectifying	rectifying	NOUN
ejpam-5864	322	2	curves	curve	NOUN
ejpam-5864	322	3	as	as	ADP
ejpam-5864	322	4	centrodes	centrode	NOUN
ejpam-5864	322	5	and	and	CCONJ
ejpam-5864	322	6	extremal	extremal	ADJ
ejpam-5864	322	7	curves	curve	NOUN
ejpam-5864	322	8	.	.	PUNCT
ejpam-5864	323	1	bulletin	bulletin	NOUN
ejpam-5864	323	2	of	of	ADP
ejpam-5864	323	3	the	the	DET
ejpam-5864	323	4	institute	institute	PROPN
ejpam-5864	323	5	of	of	ADP
ejpam-5864	323	6	mathematics	mathematics	PROPN
ejpam-5864	323	7	academia	academia	PROPN
ejpam-5864	323	8	sinica	sinica	PROPN
ejpam-5864	323	9	,	,	PUNCT
ejpam-5864	323	10	33(2):77–90	33(2):77–90	NUM
ejpam-5864	323	11	,	,	PUNCT
ejpam-5864	323	12	2005	2005	NUM
ejpam-5864	323	13	.	.	PUNCT
ejpam-5864	324	1	[	[	X
ejpam-5864	324	2	9	9	NUM
ejpam-5864	324	3	]	]	PUNCT
ejpam-5864	324	4	k.	k.	X
ejpam-5864	324	5	ilarslan	ilarslan	PROPN
ejpam-5864	324	6	and	and	CCONJ
ejpam-5864	324	7	e.	e.	PROPN
ejpam-5864	324	8	nesovic	nesovic	PROPN
ejpam-5864	324	9	.	.	PUNCT
ejpam-5864	325	1	some	some	DET
ejpam-5864	325	2	characterizations	characterization	NOUN
ejpam-5864	325	3	of	of	ADP
ejpam-5864	325	4	rectifying	rectifying	NOUN
ejpam-5864	325	5	curves	curve	NOUN
ejpam-5864	325	6	in	in	ADP
ejpam-5864	325	7	the	the	DET
ejpam-5864	325	8	euclidean	euclidean	ADJ
ejpam-5864	325	9	space	space	NOUN
ejpam-5864	325	10	e4	e4	PROPN
ejpam-5864	325	11	.	.	PUNCT
ejpam-5864	326	1	turkish	turkish	ADJ
ejpam-5864	326	2	journal	journal	NOUN
ejpam-5864	326	3	of	of	ADP
ejpam-5864	326	4	mathematics	mathematic	NOUN
ejpam-5864	326	5	,	,	PUNCT
ejpam-5864	326	6	32:21–30	32:21–30	NUM
ejpam-5864	326	7	,	,	PUNCT
ejpam-5864	326	8	2008	2008	NUM
ejpam-5864	326	9	.	.	PUNCT
ejpam-5864	327	1	[	[	X
ejpam-5864	327	2	10	10	NUM
ejpam-5864	327	3	]	]	PUNCT
ejpam-5864	327	4	t.	t.	NOUN
ejpam-5864	327	5	turhan	turhan	NOUN
ejpam-5864	327	6	.	.	PUNCT
ejpam-5864	328	1	on	on	ADP
ejpam-5864	328	2	rectifying	rectify	VERB
ejpam-5864	328	3	curves	curve	NOUN
ejpam-5864	328	4	and	and	CCONJ
ejpam-5864	328	5	their	their	PRON
ejpam-5864	328	6	characterization	characterization	NOUN
ejpam-5864	328	7	in	in	ADP
ejpam-5864	328	8	lorentz	lorentz	PROPN
ejpam-5864	328	9	n	n	CCONJ
ejpam-5864	328	10	-	-	PUNCT
ejpam-5864	328	11	space	space	NOUN
ejpam-5864	328	12	.	.	PUNCT
ejpam-5864	329	1	international	international	ADJ
ejpam-5864	329	2	electronic	electronic	ADJ
ejpam-5864	329	3	journal	journal	NOUN
ejpam-5864	329	4	of	of	ADP
ejpam-5864	329	5	geometry	geometry	NOUN
ejpam-5864	329	6	,	,	PUNCT
ejpam-5864	329	7	11(1):26–36	11(1):26–36	NUM
ejpam-5864	329	8	,	,	PUNCT
ejpam-5864	329	9	2018	2018	NUM
ejpam-5864	329	10	.	.	PUNCT
ejpam-5864	330	1	[	[	X
ejpam-5864	330	2	11	11	NUM
ejpam-5864	330	3	]	]	PUNCT
ejpam-5864	330	4	b.	b.	PROPN
ejpam-5864	330	5	yılmaz	yılmaz	PROPN
ejpam-5864	330	6	,	,	PUNCT
ejpam-5864	330	7	i.	i.	PROPN
ejpam-5864	330	8	gok	gok	PROPN
ejpam-5864	330	9	,	,	PUNCT
ejpam-5864	330	10	and	and	CCONJ
ejpam-5864	330	11	y.	y.	PROPN
ejpam-5864	330	12	yayli	yayli	PROPN
ejpam-5864	330	13	.	.	PUNCT
ejpam-5864	331	1	extended	extend	VERB
ejpam-5864	331	2	rectifying	rectifying	NOUN
ejpam-5864	331	3	curves	curve	NOUN
ejpam-5864	331	4	in	in	ADP
ejpam-5864	331	5	minkowski	minkowski	ADJ
ejpam-5864	331	6	3	3	NUM
ejpam-5864	331	7	-	-	PUNCT
ejpam-5864	331	8	space	space	NOUN
ejpam-5864	331	9	.	.	PUNCT
ejpam-5864	332	1	advances	advance	NOUN
ejpam-5864	332	2	in	in	ADP
ejpam-5864	332	3	applied	apply	VERB
ejpam-5864	332	4	clifford	clifford	PROPN
ejpam-5864	332	5	algebras	algebras	PROPN
ejpam-5864	332	6	,	,	PUNCT
ejpam-5864	332	7	26:861–872	26:861–872	PROPN
ejpam-5864	332	8	,	,	PUNCT
ejpam-5864	332	9	2016	2016	NUM
ejpam-5864	332	10	.	.	PUNCT
ejpam-5864	333	1	[	[	X
ejpam-5864	333	2	12	12	NUM
ejpam-5864	333	3	]	]	PUNCT
ejpam-5864	333	4	b.	b.	PROPN
ejpam-5864	333	5	yılmaz	yılmaz	PROPN
ejpam-5864	333	6	,	,	PUNCT
ejpam-5864	333	7	i.	i.	PROPN
ejpam-5864	333	8	gok	gok	PROPN
ejpam-5864	333	9	,	,	PUNCT
ejpam-5864	333	10	and	and	CCONJ
ejpam-5864	333	11	y.	y.	PROPN
ejpam-5864	333	12	yayli	yayli	PROPN
ejpam-5864	333	13	.	.	PUNCT
ejpam-5864	334	1	differential	differential	ADJ
ejpam-5864	334	2	equations	equation	NOUN
ejpam-5864	334	3	of	of	ADP
ejpam-5864	334	4	rectifying	rectifying	NOUN
ejpam-5864	334	5	curves	curve	NOUN
ejpam-5864	334	6	and	and	CCONJ
ejpam-5864	334	7	focal	focal	ADJ
ejpam-5864	334	8	curves	curve	NOUN
ejpam-5864	334	9	in	in	ADP
ejpam-5864	334	10	en	en	PROPN
ejpam-5864	334	11	.	.	PROPN
ejpam-5864	334	12	journal	journal	PROPN
ejpam-5864	334	13	of	of	ADP
ejpam-5864	334	14	mathematical	mathematical	ADJ
ejpam-5864	334	15	sciences	science	NOUN
ejpam-5864	334	16	and	and	CCONJ
ejpam-5864	334	17	modelling	modelling	NOUN
ejpam-5864	334	18	,	,	PUNCT
ejpam-5864	334	19	5(1):8–15	5(1):8–15	NUM
ejpam-5864	334	20	,	,	PUNCT
ejpam-5864	334	21	2022	2022	NUM
ejpam-5864	334	22	.	.	PUNCT
ejpam-5864	335	1	[	[	X
ejpam-5864	335	2	13	13	NUM
ejpam-5864	335	3	]	]	PUNCT
ejpam-5864	335	4	s.	s.	PROPN
ejpam-5864	335	5	yanan	yanan	PROPN
ejpam-5864	335	6	.	.	PUNCT
ejpam-5864	336	1	conformal	conformal	ADJ
ejpam-5864	336	2	quasi	quasi	PROPN
ejpam-5864	336	3	-	-	ADJ
ejpam-5864	336	4	hemi	hemi	NOUN
ejpam-5864	336	5	-	-	PUNCT
ejpam-5864	336	6	slant	slant	ADJ
ejpam-5864	336	7	riemannian	riemannian	ADJ
ejpam-5864	336	8	maps	map	NOUN
ejpam-5864	336	9	.	.	PUNCT
ejpam-5864	337	1	communications	communication	NOUN
ejpam-5864	337	2	in	in	ADP
ejpam-5864	337	3	advanced	advanced	ADJ
ejpam-5864	337	4	mathematical	mathematical	ADJ
ejpam-5864	337	5	sciences	science	NOUN
ejpam-5864	337	6	,	,	PUNCT
ejpam-5864	337	7	5(2):99–113	5(2):99–113	NUM
ejpam-5864	337	8	,	,	PUNCT
ejpam-5864	337	9	2022	2022	NUM
ejpam-5864	337	10	.	.	PUNCT
ejpam-5864	338	1	[	[	X
ejpam-5864	338	2	14	14	NUM
ejpam-5864	338	3	]	]	PUNCT
ejpam-5864	338	4	i.	i.	NOUN
ejpam-5864	338	5	podlubny	podlubny	PROPN
ejpam-5864	338	6	.	.	PUNCT
ejpam-5864	339	1	fractional	fractional	ADJ
ejpam-5864	339	2	differential	differential	ADJ
ejpam-5864	339	3	equations	equation	NOUN
ejpam-5864	339	4	.	.	PUNCT
ejpam-5864	340	1	academic	academic	ADJ
ejpam-5864	340	2	press	press	NOUN
ejpam-5864	340	3	,	,	PUNCT
ejpam-5864	340	4	new	new	PROPN
ejpam-5864	340	5	york	york	PROPN
ejpam-5864	340	6	,	,	PUNCT
ejpam-5864	340	7	1999	1999	NUM
ejpam-5864	340	8	.	.	PUNCT
ejpam-5864	341	1	[	[	X
ejpam-5864	341	2	15	15	NUM
ejpam-5864	341	3	]	]	PUNCT
ejpam-5864	341	4	k.	k.	PROPN
ejpam-5864	341	5	b.	b.	PROPN
ejpam-5864	341	6	oldham	oldham	PROPN
ejpam-5864	341	7	and	and	CCONJ
ejpam-5864	341	8	j.	j.	PROPN
ejpam-5864	341	9	spanier	spanier	PROPN
ejpam-5864	341	10	.	.	PUNCT
ejpam-5864	342	1	the	the	DET
ejpam-5864	342	2	fractional	fractional	ADJ
ejpam-5864	342	3	calculus	calculus	NOUN
ejpam-5864	342	4	.	.	PUNCT
ejpam-5864	343	1	academic	academic	ADJ
ejpam-5864	343	2	press	press	NOUN
ejpam-5864	343	3	,	,	PUNCT
ejpam-5864	343	4	new	new	PROPN
ejpam-5864	343	5	york	york	PROPN
ejpam-5864	343	6	,	,	PUNCT
ejpam-5864	343	7	1974	1974	NUM
ejpam-5864	343	8	.	.	PUNCT
ejpam-5864	344	1	[	[	X
ejpam-5864	344	2	16	16	NUM
ejpam-5864	344	3	]	]	PUNCT
ejpam-5864	344	4	k.	k.	PROPN
ejpam-5864	344	5	s.	s.	PROPN
ejpam-5864	344	6	miller	miller	PROPN
ejpam-5864	344	7	and	and	CCONJ
ejpam-5864	344	8	b.	b.	PROPN
ejpam-5864	344	9	ross	ross	PROPN
ejpam-5864	344	10	.	.	PUNCT
ejpam-5864	345	1	an	an	DET
ejpam-5864	345	2	introduction	introduction	NOUN
ejpam-5864	345	3	to	to	ADP
ejpam-5864	345	4	the	the	DET
ejpam-5864	345	5	fractional	fractional	ADJ
ejpam-5864	345	6	calculus	calculus	NOUN
ejpam-5864	345	7	and	and	CCONJ
ejpam-5864	345	8	fractional	fractional	ADJ
ejpam-5864	345	9	differential	differential	ADJ
ejpam-5864	345	10	equations	equation	NOUN
ejpam-5864	345	11	.	.	PUNCT
ejpam-5864	346	1	wiley	wiley	PROPN
ejpam-5864	346	2	,	,	PUNCT
ejpam-5864	346	3	new	new	PROPN
ejpam-5864	346	4	york	york	PROPN
ejpam-5864	346	5	,	,	PUNCT
ejpam-5864	346	6	1993	1993	NUM
ejpam-5864	346	7	.	.	PUNCT
ejpam-5864	347	1	[	[	X
ejpam-5864	347	2	17	17	NUM
ejpam-5864	347	3	]	]	PUNCT
ejpam-5864	347	4	m.	m.	NOUN
ejpam-5864	347	5	caputo	caputo	PROPN
ejpam-5864	347	6	and	and	CCONJ
ejpam-5864	347	7	f.	f.	PROPN
ejpam-5864	347	8	mainardi	mainardi	PROPN
ejpam-5864	347	9	.	.	PUNCT
ejpam-5864	348	1	linear	linear	ADJ
ejpam-5864	348	2	models	model	NOUN
ejpam-5864	348	3	of	of	ADP
ejpam-5864	348	4	dissipation	dissipation	NOUN
ejpam-5864	348	5	in	in	ADP
ejpam-5864	348	6	anelastic	anelastic	ADJ
ejpam-5864	348	7	solids	solid	NOUN
ejpam-5864	348	8	.	.	PUNCT
ejpam-5864	349	1	la	la	PROPN
ejpam-5864	349	2	rivista	rivista	PROPN
ejpam-5864	349	3	del	del	PROPN
ejpam-5864	349	4	nuovo	nuovo	PROPN
ejpam-5864	349	5	cimento	cimento	PROPN
ejpam-5864	349	6	,	,	PUNCT
ejpam-5864	349	7	1(2):161–198	1(2):161–198	NUM
ejpam-5864	349	8	,	,	PUNCT
ejpam-5864	349	9	1971	1971	NUM
ejpam-5864	349	10	.	.	PUNCT
ejpam-5864	350	1	[	[	X
ejpam-5864	350	2	18	18	NUM
ejpam-5864	350	3	]	]	X
ejpam-5864	350	4	r.	r.	PROPN
ejpam-5864	350	5	almeida	almeida	PROPN
ejpam-5864	350	6	,	,	PUNCT
ejpam-5864	350	7	m.	m.	NOUN
ejpam-5864	350	8	guzowska	guzowska	PROPN
ejpam-5864	350	9	,	,	PUNCT
ejpam-5864	350	10	and	and	CCONJ
ejpam-5864	350	11	t.	t.	PROPN
ejpam-5864	350	12	odzijewicz	odzijewicz	NOUN
ejpam-5864	350	13	.	.	PUNCT
ejpam-5864	351	1	a	a	DET
ejpam-5864	351	2	remark	remark	NOUN
ejpam-5864	351	3	on	on	ADP
ejpam-5864	351	4	local	local	ADJ
ejpam-5864	351	5	fractional	fractional	ADJ
ejpam-5864	351	6	calculus	calculus	NOUN
ejpam-5864	351	7	and	and	CCONJ
ejpam-5864	351	8	ordinary	ordinary	ADJ
ejpam-5864	351	9	derivatives	derivative	NOUN
ejpam-5864	351	10	.	.	PUNCT
ejpam-5864	352	1	open	open	ADJ
ejpam-5864	352	2	mathematics	mathematic	NOUN
ejpam-5864	352	3	,	,	PUNCT
ejpam-5864	352	4	14:1122–1124	14:1122–1124	NUM
ejpam-5864	352	5	,	,	PUNCT
ejpam-5864	352	6	2016	2016	NUM
ejpam-5864	352	7	.	.	PUNCT
ejpam-5864	353	1	[	[	X
ejpam-5864	353	2	19	19	NUM
ejpam-5864	353	3	]	]	X
ejpam-5864	353	4	r.	r.	PROPN
ejpam-5864	353	5	khalil	khalil	PROPN
ejpam-5864	353	6	,	,	PUNCT
ejpam-5864	353	7	m.	m.	NOUN
ejpam-5864	353	8	horani	horani	PROPN
ejpam-5864	353	9	,	,	PUNCT
ejpam-5864	353	10	a.	a.	NOUN
ejpam-5864	353	11	yousef	yousef	PROPN
ejpam-5864	353	12	,	,	PUNCT
ejpam-5864	353	13	and	and	CCONJ
ejpam-5864	353	14	m.	m.	NOUN
ejpam-5864	353	15	sababheh	sababheh	NOUN
ejpam-5864	353	16	.	.	PUNCT
ejpam-5864	354	1	a	a	DET
ejpam-5864	354	2	new	new	ADJ
ejpam-5864	354	3	definition	definition	NOUN
ejpam-5864	354	4	of	of	ADP
ejpam-5864	354	5	fractional	fractional	ADJ
ejpam-5864	354	6	derivative	derivative	NOUN
ejpam-5864	354	7	.	.	PUNCT
ejpam-5864	355	1	journal	journal	PROPN
ejpam-5864	355	2	of	of	ADP
ejpam-5864	355	3	computational	computational	ADJ
ejpam-5864	355	4	and	and	CCONJ
ejpam-5864	355	5	applied	applied	ADJ
ejpam-5864	355	6	mathematics	mathematic	NOUN
ejpam-5864	355	7	,	,	PUNCT
ejpam-5864	355	8	264:65–70	264:65–70	NUM
ejpam-5864	355	9	,	,	PUNCT
ejpam-5864	355	10	2014	2014	NUM
ejpam-5864	355	11	.	.	PUNCT
ejpam-5864	356	1	[	[	X
ejpam-5864	356	2	20	20	NUM
ejpam-5864	356	3	]	]	PUNCT
ejpam-5864	356	4	u.	u.	PROPN
ejpam-5864	356	5	n.	n.	PROPN
ejpam-5864	356	6	katugampola	katugampola	PROPN
ejpam-5864	356	7	.	.	PUNCT
ejpam-5864	357	1	a	a	DET
ejpam-5864	357	2	new	new	ADJ
ejpam-5864	357	3	fractional	fractional	ADJ
ejpam-5864	357	4	derivative	derivative	NOUN
ejpam-5864	357	5	with	with	ADP
ejpam-5864	357	6	classical	classical	ADJ
ejpam-5864	357	7	properties	property	NOUN
ejpam-5864	357	8	.	.	PUNCT
ejpam-5864	358	1	arxiv:1410.6535v2	arxiv:1410.6535v2	ADP
ejpam-5864	358	2	,	,	PUNCT
ejpam-5864	358	3	2014	2014	NUM
ejpam-5864	358	4	.	.	PUNCT
ejpam-5864	359	1	[	[	X
ejpam-5864	359	2	21	21	NUM
ejpam-5864	359	3	]	]	X
ejpam-5864	359	4	j.	j.	PROPN
ejpam-5864	359	5	v.	v.	PROPN
ejpam-5864	359	6	c.	c.	PROPN
ejpam-5864	359	7	sousa	sousa	PROPN
ejpam-5864	359	8	and	and	CCONJ
ejpam-5864	359	9	j.	j.	PROPN
ejpam-5864	359	10	e.	e.	PROPN
ejpam-5864	359	11	c.	c.	PROPN
ejpam-5864	359	12	de	de	PROPN
ejpam-5864	359	13	oliveira	oliveira	PROPN
ejpam-5864	359	14	.	.	PUNCT
ejpam-5864	360	1	mittag	mittag	ADJ
ejpam-5864	360	2	-	-	PUNCT
ejpam-5864	360	3	leffler	leffler	NOUN
ejpam-5864	360	4	functions	function	NOUN
ejpam-5864	360	5	and	and	CCONJ
ejpam-5864	360	6	the	the	DET
ejpam-5864	360	7	truncated	truncated	ADJ
ejpam-5864	360	8	v	v	NOUN
ejpam-5864	360	9	-	-	PUNCT
ejpam-5864	360	10	fractional	fractional	ADJ
ejpam-5864	360	11	derivative	derivative	NOUN
ejpam-5864	360	12	.	.	PUNCT
ejpam-5864	361	1	mediterranean	mediterranean	PROPN
ejpam-5864	361	2	journal	journal	PROPN
ejpam-5864	361	3	of	of	ADP
ejpam-5864	361	4	mathematics	mathematics	PROPN
ejpam-5864	361	5	,	,	PUNCT
ejpam-5864	361	6	14(6):244	14(6):244	PROPN
ejpam-5864	361	7	,	,	PUNCT
ejpam-5864	361	8	2017	2017	NUM
ejpam-5864	361	9	.	.	PUNCT
ejpam-5864	362	1	[	[	X
ejpam-5864	362	2	22	22	NUM
ejpam-5864	362	3	]	]	PUNCT
ejpam-5864	362	4	j.	j.	PROPN
ejpam-5864	362	5	v.	v.	PROPN
ejpam-5864	362	6	c.	c.	PROPN
ejpam-5864	362	7	sousa	sousa	PROPN
ejpam-5864	362	8	and	and	CCONJ
ejpam-5864	362	9	j.	j.	PROPN
ejpam-5864	362	10	e.	e.	PROPN
ejpam-5864	362	11	c.	c.	PROPN
ejpam-5864	362	12	de	de	PROPN
ejpam-5864	362	13	oliveira	oliveira	PROPN
ejpam-5864	362	14	.	.	PUNCT
ejpam-5864	363	1	on	on	ADP
ejpam-5864	363	2	the	the	DET
ejpam-5864	363	3	local	local	ADJ
ejpam-5864	363	4	m	m	NOUN
ejpam-5864	363	5	-	-	ADJ
ejpam-5864	363	6	derivative	derivative	ADJ
ejpam-5864	363	7	.	.	PUNCT
ejpam-5864	364	1	progress	progress	NOUN
ejpam-5864	364	2	in	in	ADP
ejpam-5864	364	3	fractional	fractional	ADJ
ejpam-5864	364	4	differentiation	differentiation	NOUN
ejpam-5864	364	5	and	and	CCONJ
ejpam-5864	364	6	applications	application	NOUN
ejpam-5864	364	7	,	,	PUNCT
ejpam-5864	364	8	4(4):479–492	4(4):479–492	NOUN
ejpam-5864	364	9	,	,	PUNCT
ejpam-5864	364	10	2018	2018	NUM
ejpam-5864	364	11	.	.	PUNCT
ejpam-5864	365	1	[	[	X
ejpam-5864	365	2	23	23	NUM
ejpam-5864	365	3	]	]	PUNCT
ejpam-5864	365	4	t.	t.	PROPN
ejpam-5864	365	5	abdeljawad	abdeljawad	NOUN
ejpam-5864	365	6	.	.	PUNCT
ejpam-5864	366	1	on	on	ADP
ejpam-5864	366	2	conformable	conformable	ADJ
ejpam-5864	366	3	fractional	fractional	ADJ
ejpam-5864	366	4	calculus	calculus	NOUN
ejpam-5864	366	5	.	.	PUNCT
ejpam-5864	367	1	journal	journal	PROPN
ejpam-5864	367	2	of	of	ADP
ejpam-5864	367	3	computational	computational	ADJ
ejpam-5864	367	4	and	and	CCONJ
ejpam-5864	367	5	applied	applied	ADJ
ejpam-5864	367	6	mathematics	mathematic	NOUN
ejpam-5864	367	7	,	,	PUNCT
ejpam-5864	367	8	279(1):57–66	279(1):57–66	NOUN
ejpam-5864	367	9	,	,	PUNCT
ejpam-5864	367	10	2015	2015	NUM
ejpam-5864	367	11	.	.	PUNCT
ejpam-5864	368	1	[	[	X
ejpam-5864	368	2	24	24	NUM
ejpam-5864	368	3	]	]	PUNCT
ejpam-5864	368	4	t.	t.	PROPN
ejpam-5864	368	5	yajima	yajima	PROPN
ejpam-5864	368	6	and	and	CCONJ
ejpam-5864	368	7	k.	k.	PROPN
ejpam-5864	368	8	yamasaki	yamasaki	PROPN
ejpam-5864	368	9	.	.	PUNCT
ejpam-5864	369	1	geometry	geometry	NOUN
ejpam-5864	369	2	of	of	ADP
ejpam-5864	369	3	surfaces	surface	NOUN
ejpam-5864	369	4	with	with	ADP
ejpam-5864	369	5	caputo	caputo	PROPN
ejpam-5864	369	6	fractional	fractional	ADJ
ejpam-5864	369	7	derivatives	derivative	NOUN
ejpam-5864	369	8	and	and	CCONJ
ejpam-5864	369	9	applications	application	NOUN
ejpam-5864	369	10	to	to	PART
ejpam-5864	369	11	incompressible	incompressible	ADJ
ejpam-5864	369	12	two	two	NUM
ejpam-5864	369	13	-	-	PUNCT
ejpam-5864	369	14	dimensional	dimensional	ADJ
ejpam-5864	369	15	flows	flow	NOUN
ejpam-5864	369	16	.	.	PUNCT
ejpam-5864	370	1	journal	journal	PROPN
ejpam-5864	370	2	of	of	ADP
ejpam-5864	370	3	physics	physics	PROPN
ejpam-5864	370	4	a	a	PRON
ejpam-5864	370	5	:	:	PUNCT
ejpam-5864	370	6	mathematical	mathematical	ADJ
ejpam-5864	370	7	and	and	CCONJ
ejpam-5864	370	8	theoretical	theoretical	ADJ
ejpam-5864	370	9	,	,	PUNCT
ejpam-5864	370	10	45:065201	45:065201	NUM
ejpam-5864	370	11	,	,	PUNCT
ejpam-5864	370	12	2012	2012	NUM
ejpam-5864	370	13	.	.	PUNCT
ejpam-5864	371	1	[	[	X
ejpam-5864	371	2	25	25	NUM
ejpam-5864	371	3	]	]	PUNCT
ejpam-5864	371	4	t.	t.	PROPN
ejpam-5864	371	5	yajima	yajima	PROPN
ejpam-5864	371	6	,	,	PUNCT
ejpam-5864	371	7	s.	s.	PROPN
ejpam-5864	371	8	oiwa	oiwa	PROPN
ejpam-5864	371	9	,	,	PUNCT
ejpam-5864	371	10	and	and	CCONJ
ejpam-5864	371	11	k.	k.	PROPN
ejpam-5864	371	12	yamasaki	yamasaki	PROPN
ejpam-5864	371	13	.	.	PUNCT
ejpam-5864	372	1	geometry	geometry	NOUN
ejpam-5864	372	2	of	of	ADP
ejpam-5864	372	3	curves	curve	NOUN
ejpam-5864	372	4	with	with	ADP
ejpam-5864	372	5	fractional	fractional	ADJ
ejpam-5864	372	6	-	-	PUNCT
ejpam-5864	372	7	order	order	NOUN
ejpam-5864	372	8	tangent	tangent	NOUN
ejpam-5864	372	9	vector	vector	NOUN
ejpam-5864	372	10	and	and	CCONJ
ejpam-5864	372	11	frenet	frenet	NOUN
ejpam-5864	372	12	-	-	PUNCT
ejpam-5864	372	13	serret	serret	NOUN
ejpam-5864	372	14	formulas	formula	NOUN
ejpam-5864	372	15	.	.	PUNCT
ejpam-5864	373	1	fractional	fractional	ADJ
ejpam-5864	373	2	calculus	calculus	NOUN
ejpam-5864	373	3	and	and	CCONJ
ejpam-5864	373	4	applied	apply	VERB
ejpam-5864	373	5	analysis	analysis	NOUN
ejpam-5864	373	6	,	,	PUNCT
ejpam-5864	373	7	21(6):1493–1505	21(6):1493–1505	NUM
ejpam-5864	373	8	,	,	PUNCT
ejpam-5864	373	9	2018	2018	NUM
ejpam-5864	373	10	.	.	PUNCT
ejpam-5864	374	1	a.	a.	PROPN
ejpam-5864	374	2	has	have	VERB
ejpam-5864	374	3	,	,	PUNCT
ejpam-5864	374	4	b.yılmaz	b.yılmaz	NOUN
ejpam-5864	374	5	,	,	PUNCT
ejpam-5864	374	6	t.	t.	PROPN
ejpam-5864	374	7	abdeljawad	abdeljawad	PROPN
ejpam-5864	374	8	/	/	SYM
ejpam-5864	374	9	eur	eur	PROPN
ejpam-5864	374	10	.	.	PUNCT
ejpam-5864	375	1	j.	j.	PROPN
ejpam-5864	375	2	pure	pure	PROPN
ejpam-5864	375	3	appl	appl	PROPN
ejpam-5864	375	4	.	.	PROPN
ejpam-5864	375	5	math	math	PROPN
ejpam-5864	375	6	,	,	PUNCT
ejpam-5864	375	7	18	18	NUM
ejpam-5864	375	8	(	(	PUNCT
ejpam-5864	375	9	2	2	NUM
ejpam-5864	375	10	)	)	PUNCT
ejpam-5864	375	11	(	(	PUNCT
ejpam-5864	375	12	2025	2025	NUM
ejpam-5864	375	13	)	)	PUNCT
ejpam-5864	375	14	,	,	PUNCT
ejpam-5864	375	15	5864	5864	NUM
ejpam-5864	375	16	14	14	NUM
ejpam-5864	375	17	of	of	ADP
ejpam-5864	375	18	14	14	NUM
ejpam-5864	375	19	[	[	SYM
ejpam-5864	375	20	26	26	NUM
ejpam-5864	375	21	]	]	PUNCT
ejpam-5864	375	22	k.	k.	PROPN
ejpam-5864	375	23	a.	a.	PROPN
ejpam-5864	375	24	lazopoulos	lazopoulos	PROPN
ejpam-5864	375	25	and	and	CCONJ
ejpam-5864	375	26	a.	a.	PROPN
ejpam-5864	375	27	k.	k.	PROPN
ejpam-5864	375	28	lazopoulos	lazopoulos	PROPN
ejpam-5864	375	29	.	.	PUNCT
ejpam-5864	376	1	fractional	fractional	ADJ
ejpam-5864	376	2	differential	differential	ADJ
ejpam-5864	376	3	geometry	geometry	NOUN
ejpam-5864	376	4	of	of	ADP
ejpam-5864	376	5	curves	curve	NOUN
ejpam-5864	376	6	and	and	CCONJ
ejpam-5864	376	7	surfaces	surface	NOUN
ejpam-5864	376	8	.	.	PUNCT
ejpam-5864	377	1	progress	progress	NOUN
ejpam-5864	377	2	in	in	ADP
ejpam-5864	377	3	fractional	fractional	ADJ
ejpam-5864	377	4	differentiation	differentiation	NOUN
ejpam-5864	377	5	and	and	CCONJ
ejpam-5864	377	6	applications	application	NOUN
ejpam-5864	377	7	,	,	PUNCT
ejpam-5864	377	8	2(3):169–186	2(3):169–186	NUM
ejpam-5864	377	9	,	,	PUNCT
ejpam-5864	377	10	2016	2016	NUM
ejpam-5864	377	11	.	.	PUNCT
ejpam-5864	378	1	[	[	X
ejpam-5864	378	2	27	27	NUM
ejpam-5864	378	3	]	]	PUNCT
ejpam-5864	378	4	m.	m.	PROPN
ejpam-5864	378	5	e.	e.	PROPN
ejpam-5864	378	6	aydin	aydin	PROPN
ejpam-5864	378	7	,	,	PUNCT
ejpam-5864	378	8	a.	a.	NOUN
ejpam-5864	378	9	mihai	mihai	PROPN
ejpam-5864	378	10	,	,	PUNCT
ejpam-5864	378	11	and	and	CCONJ
ejpam-5864	378	12	a.	a.	NOUN
ejpam-5864	378	13	yokus	yokus	NOUN
ejpam-5864	378	14	.	.	PUNCT
ejpam-5864	379	1	applications	application	NOUN
ejpam-5864	379	2	of	of	ADP
ejpam-5864	379	3	fractional	fractional	ADJ
ejpam-5864	379	4	calculus	calculus	NOUN
ejpam-5864	379	5	in	in	ADP
ejpam-5864	379	6	equiaffine	equiaffine	NOUN
ejpam-5864	379	7	geometry	geometry	NOUN
ejpam-5864	379	8	:	:	PUNCT
ejpam-5864	379	9	plane	plane	NOUN
ejpam-5864	379	10	curves	curve	NOUN
ejpam-5864	379	11	with	with	ADP
ejpam-5864	379	12	fractional	fractional	ADJ
ejpam-5864	379	13	order	order	NOUN
ejpam-5864	379	14	.	.	PUNCT
ejpam-5864	380	1	mathematical	mathematical	ADJ
ejpam-5864	380	2	methods	method	NOUN
ejpam-5864	380	3	in	in	ADP
ejpam-5864	380	4	the	the	DET
ejpam-5864	380	5	applied	apply	VERB
ejpam-5864	380	6	sciences	science	NOUN
ejpam-5864	380	7	,	,	PUNCT
ejpam-5864	380	8	44(17):13659–13669	44(17):13659–13669	NUM
ejpam-5864	380	9	,	,	PUNCT
ejpam-5864	380	10	2021	2021	NUM
ejpam-5864	380	11	.	.	PUNCT
ejpam-5864	381	1	[	[	X
ejpam-5864	381	2	28	28	NUM
ejpam-5864	381	3	]	]	X
ejpam-5864	381	4	u.	u.	PROPN
ejpam-5864	381	5	gozutok	gozutok	PROPN
ejpam-5864	381	6	,	,	PUNCT
ejpam-5864	381	7	h.	h.	PROPN
ejpam-5864	381	8	a.	a.	NOUN
ejpam-5864	381	9	coban	coban	PROPN
ejpam-5864	381	10	,	,	PUNCT
ejpam-5864	381	11	and	and	CCONJ
ejpam-5864	381	12	y.	y.	PROPN
ejpam-5864	381	13	sagiroglu	sagiroglu	PROPN
ejpam-5864	381	14	.	.	PUNCT
ejpam-5864	382	1	frenet	frenet	ADJ
ejpam-5864	382	2	frame	frame	NOUN
ejpam-5864	382	3	with	with	ADP
ejpam-5864	382	4	respect	respect	NOUN
ejpam-5864	382	5	to	to	AUX
ejpam-5864	382	6	conformable	conformable	VERB
ejpam-5864	382	7	derivative	derivative	NOUN
ejpam-5864	382	8	.	.	PUNCT
ejpam-5864	383	1	filomat	filomat	PROPN
ejpam-5864	383	2	,	,	PUNCT
ejpam-5864	383	3	33(6):1541–1550	33(6):1541–1550	NUM
ejpam-5864	383	4	,	,	PUNCT
ejpam-5864	383	5	2019	2019	NUM
ejpam-5864	383	6	.	.	PUNCT
ejpam-5864	384	1	[	[	X
ejpam-5864	384	2	29	29	NUM
ejpam-5864	384	3	]	]	PUNCT
ejpam-5864	384	4	a.	a.	NOUN
ejpam-5864	384	5	has	have	VERB
ejpam-5864	384	6	and	and	CCONJ
ejpam-5864	384	7	b.	b.	PROPN
ejpam-5864	384	8	yılmaz	yılmaz	PROPN
ejpam-5864	384	9	.	.	PUNCT
ejpam-5864	385	1	special	special	ADJ
ejpam-5864	385	2	fractional	fractional	ADJ
ejpam-5864	385	3	curve	curve	NOUN
ejpam-5864	385	4	pairs	pair	NOUN
ejpam-5864	385	5	with	with	ADP
ejpam-5864	385	6	fractional	fractional	ADJ
ejpam-5864	385	7	calculus	calculus	NOUN
ejpam-5864	385	8	.	.	PUNCT
ejpam-5864	386	1	international	international	ADJ
ejpam-5864	386	2	electronic	electronic	ADJ
ejpam-5864	386	3	journal	journal	NOUN
ejpam-5864	386	4	of	of	ADP
ejpam-5864	386	5	geometry	geometry	NOUN
ejpam-5864	386	6	,	,	PUNCT
ejpam-5864	386	7	15(1):132–144	15(1):132–144	PROPN
ejpam-5864	386	8	,	,	PUNCT
ejpam-5864	386	9	2022	2022	NUM
ejpam-5864	386	10	.	.	PUNCT
ejpam-5864	387	1	[	[	X
ejpam-5864	387	2	30	30	NUM
ejpam-5864	387	3	]	]	PUNCT
ejpam-5864	387	4	a.	a.	NOUN
ejpam-5864	387	5	has	have	VERB
ejpam-5864	387	6	,	,	PUNCT
ejpam-5864	387	7	b.	b.	PROPN
ejpam-5864	387	8	yılmaz	yılmaz	PROPN
ejpam-5864	387	9	,	,	PUNCT
ejpam-5864	387	10	a.	a.	NOUN
ejpam-5864	387	11	akkurt	akkurt	PROPN
ejpam-5864	387	12	,	,	PUNCT
ejpam-5864	387	13	and	and	CCONJ
ejpam-5864	387	14	h.	h.	PROPN
ejpam-5864	387	15	yildirim	yildirim	PROPN
ejpam-5864	387	16	.	.	PUNCT
ejpam-5864	388	1	conformable	conformable	ADJ
ejpam-5864	388	2	special	special	ADJ
ejpam-5864	388	3	curves	curve	NOUN
ejpam-5864	388	4	in	in	ADP
ejpam-5864	388	5	euclidean	euclidean	ADJ
ejpam-5864	388	6	3	3	NUM
ejpam-5864	388	7	-	-	PUNCT
ejpam-5864	388	8	space	space	NOUN
ejpam-5864	388	9	.	.	PUNCT
ejpam-5864	389	1	filomat	filomat	NOUN
ejpam-5864	389	2	,	,	PUNCT
ejpam-5864	389	3	36(14):4687–4698	36(14):4687–4698	PROPN
ejpam-5864	389	4	,	,	PUNCT
ejpam-5864	389	5	2022	2022	NUM
ejpam-5864	389	6	.	.	PUNCT
ejpam-5864	390	1	[	[	X
ejpam-5864	390	2	31	31	NUM
ejpam-5864	390	3	]	]	PUNCT
ejpam-5864	390	4	a.	a.	NOUN
ejpam-5864	390	5	has	have	VERB
ejpam-5864	390	6	and	and	CCONJ
ejpam-5864	390	7	b.	b.	PROPN
ejpam-5864	390	8	yılmaz	yılmaz	PROPN
ejpam-5864	390	9	.	.	PUNCT
ejpam-5864	391	1	effect	effect	NOUN
ejpam-5864	391	2	of	of	ADP
ejpam-5864	391	3	fractional	fractional	ADJ
ejpam-5864	391	4	analysis	analysis	NOUN
ejpam-5864	391	5	on	on	ADP
ejpam-5864	391	6	magnetic	magnetic	ADJ
ejpam-5864	391	7	curves	curve	NOUN
ejpam-5864	391	8	.	.	PUNCT
ejpam-5864	392	1	revista	revista	PROPN
ejpam-5864	392	2	mexicana	mexicana	PROPN
ejpam-5864	392	3	de	de	PROPN
ejpam-5864	392	4	f́ısica	f́ısica	PROPN
ejpam-5864	392	5	,	,	PUNCT
ejpam-5864	392	6	68(4):1–15	68(4):1–15	NOUN
ejpam-5864	392	7	,	,	PUNCT
ejpam-5864	392	8	2022	2022	NUM
ejpam-5864	392	9	.	.	PUNCT
ejpam-5864	393	1	[	[	X
ejpam-5864	393	2	32	32	NUM
ejpam-5864	393	3	]	]	PUNCT
ejpam-5864	393	4	b.	b.	PROPN
ejpam-5864	393	5	yılmaz	yılmaz	PROPN
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ejpam-5864	393	7	a.	a.	NOUN
ejpam-5864	393	8	has	have	VERB
ejpam-5864	393	9	.	.	PUNCT
ejpam-5864	394	1	obtaining	obtain	VERB
ejpam-5864	394	2	fractional	fractional	ADJ
ejpam-5864	394	3	electromagnetic	electromagnetic	ADJ
ejpam-5864	394	4	curves	curve	NOUN
ejpam-5864	394	5	in	in	ADP
ejpam-5864	394	6	optical	optical	ADJ
ejpam-5864	394	7	fiber	fiber	NOUN
ejpam-5864	394	8	using	use	VERB
ejpam-5864	394	9	fractional	fractional	ADJ
ejpam-5864	394	10	alternative	alternative	ADJ
ejpam-5864	394	11	moving	move	VERB
ejpam-5864	394	12	frame	frame	NOUN
ejpam-5864	394	13	.	.	PUNCT
ejpam-5864	395	1	optik	optik	PROPN
ejpam-5864	395	2	international	international	PROPN
ejpam-5864	395	3	journal	journal	PROPN
ejpam-5864	395	4	for	for	ADP
ejpam-5864	395	5	light	light	NOUN
ejpam-5864	395	6	and	and	CCONJ
ejpam-5864	395	7	electron	electron	NOUN
ejpam-5864	395	8	optics	optic	NOUN
ejpam-5864	395	9	,	,	PUNCT
ejpam-5864	395	10	260(8):169067	260(8):169067	NUM
ejpam-5864	395	11	,	,	PUNCT
ejpam-5864	395	12	2022	2022	NUM
ejpam-5864	395	13	.	.	PUNCT
ejpam-5864	396	1	[	[	X
ejpam-5864	396	2	33	33	NUM
ejpam-5864	396	3	]	]	PUNCT
ejpam-5864	396	4	b.	b.	PROPN
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ejpam-5864	396	6	.	.	PUNCT
ejpam-5864	397	1	a	a	DET
ejpam-5864	397	2	new	new	ADJ
ejpam-5864	397	3	type	type	NOUN
ejpam-5864	397	4	electromagnetic	electromagnetic	ADJ
ejpam-5864	397	5	curves	curve	NOUN
ejpam-5864	397	6	in	in	ADP
ejpam-5864	397	7	optical	optical	ADJ
ejpam-5864	397	8	fiber	fiber	NOUN
ejpam-5864	397	9	and	and	CCONJ
ejpam-5864	397	10	rotation	rotation	NOUN
ejpam-5864	397	11	of	of	ADP
ejpam-5864	397	12	the	the	DET
ejpam-5864	397	13	polarization	polarization	NOUN
ejpam-5864	397	14	plane	plane	NOUN
ejpam-5864	397	15	using	use	VERB
ejpam-5864	397	16	fractional	fractional	ADJ
ejpam-5864	397	17	calculus	calculus	NOUN
ejpam-5864	397	18	.	.	PUNCT
ejpam-5864	398	1	optik	optik	PROPN
ejpam-5864	398	2	international	international	PROPN
ejpam-5864	398	3	journal	journal	PROPN
ejpam-5864	398	4	for	for	ADP
ejpam-5864	398	5	light	light	NOUN
ejpam-5864	398	6	and	and	CCONJ
ejpam-5864	398	7	electron	electron	NOUN
ejpam-5864	398	8	optics	optic	NOUN
ejpam-5864	398	9	,	,	PUNCT
ejpam-5864	398	10	247(30):168026	247(30):168026	PROPN
ejpam-5864	398	11	,	,	PUNCT
ejpam-5864	398	12	2021	2021	NUM
ejpam-5864	398	13	.	.	PUNCT
ejpam-5864	399	1	[	[	X
ejpam-5864	399	2	34	34	NUM
ejpam-5864	399	3	]	]	X
ejpam-5864	399	4	d.	d.	PROPN
ejpam-5864	399	5	j.	j.	PROPN
ejpam-5864	399	6	struik	struik	PROPN
ejpam-5864	399	7	.	.	PUNCT
ejpam-5864	400	1	lectures	lecture	NOUN
ejpam-5864	400	2	on	on	ADP
ejpam-5864	400	3	classical	classical	ADJ
ejpam-5864	400	4	differential	differential	NOUN
ejpam-5864	400	5	geometry	geometry	NOUN
ejpam-5864	400	6	.	.	PUNCT
ejpam-5864	401	1	dover	dover	PROPN
ejpam-5864	401	2	publications	publication	NOUN
ejpam-5864	401	3	,	,	PUNCT
ejpam-5864	401	4	new	new	PROPN
ejpam-5864	401	5	york	york	PROPN
ejpam-5864	401	6	,	,	PUNCT
ejpam-5864	401	7	1988	1988	NUM
ejpam-5864	401	8	.	.	PUNCT
ejpam-5864	402	1	[	[	X
ejpam-5864	402	2	35	35	NUM
ejpam-5864	402	3	]	]	X
ejpam-5864	402	4	n.	n.	PROPN
ejpam-5864	402	5	y.	y.	PROPN
ejpam-5864	402	6	gozutok	gozutok	PROPN
ejpam-5864	402	7	and	and	CCONJ
ejpam-5864	402	8	u.	u.	PROPN
ejpam-5864	402	9	gozutok	gozutok	PROPN
ejpam-5864	402	10	.	.	PUNCT
ejpam-5864	403	1	multivariable	multivariable	ADJ
ejpam-5864	403	2	conformable	conformable	ADJ
ejpam-5864	403	3	fractional	fractional	ADJ
ejpam-5864	403	4	calculus	calculus	NOUN
ejpam-5864	403	5	.	.	PUNCT
ejpam-5864	404	1	filomat	filomat	PROPN
ejpam-5864	404	2	,	,	PUNCT
ejpam-5864	404	3	32(2):45–53	32(2):45–53	NUM
ejpam-5864	404	4	,	,	PUNCT
ejpam-5864	404	5	2018	2018	NUM
ejpam-5864	404	6	.	.	PUNCT
ejpam-5864	405	1	[	[	X
ejpam-5864	405	2	36	36	NUM
ejpam-5864	405	3	]	]	PUNCT
ejpam-5864	405	4	a.	a.	NOUN
ejpam-5864	405	5	has	have	VERB
ejpam-5864	405	6	and	and	CCONJ
ejpam-5864	405	7	b.	b.	PROPN
ejpam-5864	405	8	yılmaz	yılmaz	PROPN
ejpam-5864	405	9	.	.	PUNCT
ejpam-5864	406	1	cα	cα	NOUN
ejpam-5864	406	2	-	-	PUNCT
ejpam-5864	406	3	curves	curve	NOUN
ejpam-5864	406	4	and	and	CCONJ
ejpam-5864	406	5	their	their	PRON
ejpam-5864	406	6	cα	cα	NOUN
ejpam-5864	406	7	-	-	PUNCT
ejpam-5864	406	8	frame	frame	NOUN
ejpam-5864	406	9	in	in	ADP
ejpam-5864	406	10	fractional	fractional	ADJ
ejpam-5864	406	11	differential	differential	NOUN
ejpam-5864	406	12	geometry	geometry	NOUN
ejpam-5864	406	13	.	.	PUNCT
ejpam-5864	407	1	journal	journal	PROPN
ejpam-5864	407	2	of	of	ADP
ejpam-5864	407	3	universal	universal	ADJ
ejpam-5864	407	4	mathematics	mathematic	NOUN
ejpam-5864	407	5	,	,	PUNCT
ejpam-5864	407	6	7(2):99–112	7(2):99–112	NUM
ejpam-5864	407	7	,	,	PUNCT
ejpam-5864	407	8	2024	2024	NUM
ejpam-5864	407	9	.	.	PUNCT