id	sid	tid	token	lemma	pos
ejpam-5478	1	1	european	european	PROPN
ejpam-5478	1	2	journal	journal	PROPN
ejpam-5478	1	3	of	of	ADP
ejpam-5478	1	4	pure	pure	ADJ
ejpam-5478	1	5	and	and	CCONJ
ejpam-5478	1	6	applied	applied	ADJ
ejpam-5478	1	7	mathematics	mathematic	NOUN
ejpam-5478	1	8	2025	2025	NUM
ejpam-5478	1	9	,	,	PUNCT
ejpam-5478	1	10	vol	vol	NOUN
ejpam-5478	1	11	.	.	PROPN
ejpam-5478	1	12	18	18	NUM
ejpam-5478	1	13	,	,	PUNCT
ejpam-5478	1	14	issue	issue	NOUN
ejpam-5478	1	15	1	1	NUM
ejpam-5478	1	16	,	,	PUNCT
ejpam-5478	1	17	article	article	NOUN
ejpam-5478	1	18	number	number	NOUN
ejpam-5478	1	19	5478	5478	NUM
ejpam-5478	1	20	issn	issn	VERB
ejpam-5478	1	21	1307	1307	NUM
ejpam-5478	1	22	-	-	SYM
ejpam-5478	1	23	5543	5543	NUM
ejpam-5478	1	24	–	–	PUNCT
ejpam-5478	1	25	ejpam.com	ejpam.com	X
ejpam-5478	1	26	published	publish	VERB
ejpam-5478	1	27	by	by	ADP
ejpam-5478	1	28	new	new	PROPN
ejpam-5478	1	29	york	york	PROPN
ejpam-5478	1	30	business	business	PROPN
ejpam-5478	1	31	global	global	ADJ
ejpam-5478	1	32	generalized	generalize	VERB
ejpam-5478	1	33	conformable	conformable	ADJ
ejpam-5478	1	34	hamiltonian	hamiltonian	ADJ
ejpam-5478	1	35	dynamics	dynamic	NOUN
ejpam-5478	1	36	with	with	ADP
ejpam-5478	1	37	higher	high	ADJ
ejpam-5478	1	38	-	-	PUNCT
ejpam-5478	1	39	order	order	NOUN
ejpam-5478	1	40	derivatives	derivative	NOUN
ejpam-5478	1	41	yazen	yazen	NOUN
ejpam-5478	1	42	.	.	PUNCT
ejpam-5478	1	43	m.	m.	PROPN
ejpam-5478	1	44	alawaideh1,∗	alawaideh1,∗	PROPN
ejpam-5478	1	45	,	,	PUNCT
ejpam-5478	1	46	aysel	aysel	PROPN
ejpam-5478	1	47	ramazanova2	ramazanova2	PROPN
ejpam-5478	1	48	,	,	PUNCT
ejpam-5478	1	49	hayat	hayat	PROPN
ejpam-5478	1	50	issaadi3	issaadi3	PROPN
ejpam-5478	1	51	,	,	PUNCT
ejpam-5478	1	52	bashar	bashar	PROPN
ejpam-5478	1	53	.	.	PUNCT
ejpam-5478	2	1	m.	m.	PROPN
ejpam-5478	2	2	al	al	PROPN
ejpam-5478	2	3	-	-	PUNCT
ejpam-5478	2	4	khamiseh1	khamiseh1	PROPN
ejpam-5478	2	5	,	,	PUNCT
ejpam-5478	2	6	muhammad	muhammad	PROPN
ejpam-5478	2	7	bilal4	bilal4	PROPN
ejpam-5478	2	8	,	,	PUNCT
ejpam-5478	2	9	dumitru	dumitru	ADJ
ejpam-5478	2	10	baleanu5	baleanu5	NOUN
ejpam-5478	2	11	1	1	NUM
ejpam-5478	2	12	meu	meu	PROPN
ejpam-5478	2	13	research	research	NOUN
ejpam-5478	2	14	unit	unit	NOUN
ejpam-5478	2	15	,	,	PUNCT
ejpam-5478	2	16	middle	middle	PROPN
ejpam-5478	2	17	east	east	PROPN
ejpam-5478	2	18	university	university	PROPN
ejpam-5478	2	19	,	,	PUNCT
ejpam-5478	2	20	amman	amman	PROPN
ejpam-5478	2	21	,	,	PUNCT
ejpam-5478	2	22	jordan	jordan	PROPN
ejpam-5478	2	23	2	2	NUM
ejpam-5478	2	24	university	university	NOUN
ejpam-5478	2	25	duisburg	duisburg	NOUN
ejpam-5478	2	26	-	-	PUNCT
ejpam-5478	2	27	essen	essen	VERB
ejpam-5478	2	28	3	3	NUM
ejpam-5478	2	29	usthb	usthb	ADJ
ejpam-5478	2	30	university	university	NOUN
ejpam-5478	2	31	,	,	PUNCT
ejpam-5478	2	32	operational	operational	ADJ
ejpam-5478	2	33	research	research	NOUN
ejpam-5478	2	34	department	department	PROPN
ejpam-5478	2	35	,	,	PUNCT
ejpam-5478	2	36	bp	bp	PROPN
ejpam-5478	2	37	32	32	NUM
ejpam-5478	2	38	el	el	PROPN
ejpam-5478	2	39	-	-	PUNCT
ejpam-5478	2	40	alia	alia	PROPN
ejpam-5478	2	41	,	,	PUNCT
ejpam-5478	2	42	bab	bab	PROPN
ejpam-5478	2	43	-	-	PUNCT
ejpam-5478	2	44	ezzouar	ezzouar	ADJ
ejpam-5478	2	45	,	,	PUNCT
ejpam-5478	2	46	16111	16111	NUM
ejpam-5478	2	47	,	,	PUNCT
ejpam-5478	2	48	algeria	algeria	PROPN
ejpam-5478	2	49	4	4	NUM
ejpam-5478	2	50	department	department	PROPN
ejpam-5478	2	51	of	of	ADP
ejpam-5478	2	52	physics	physics	PROPN
ejpam-5478	2	53	,	,	PUNCT
ejpam-5478	2	54	shanghai	shanghai	PROPN
ejpam-5478	2	55	university	university	PROPN
ejpam-5478	2	56	,	,	PUNCT
ejpam-5478	2	57	shanghai	shanghai	PROPN
ejpam-5478	2	58	200444	200444	NUM
ejpam-5478	2	59	,	,	PUNCT
ejpam-5478	2	60	china	china	PROPN
ejpam-5478	2	61	5	5	NUM
ejpam-5478	2	62	department	department	NOUN
ejpam-5478	2	63	of	of	ADP
ejpam-5478	2	64	computer	computer	NOUN
ejpam-5478	2	65	science	science	NOUN
ejpam-5478	2	66	and	and	CCONJ
ejpam-5478	2	67	mathematics	mathematic	NOUN
ejpam-5478	2	68	,	,	PUNCT
ejpam-5478	2	69	lebanese	lebanese	ADJ
ejpam-5478	2	70	american	american	PROPN
ejpam-5478	2	71	university	university	PROPN
ejpam-5478	2	72	,	,	PUNCT
ejpam-5478	2	73	beirut	beirut	PROPN
ejpam-5478	2	74	,	,	PUNCT
ejpam-5478	2	75	lebanon	lebanon	PROPN
ejpam-5478	2	76	abstract	abstract	NOUN
ejpam-5478	2	77	.	.	PUNCT
ejpam-5478	3	1	in	in	ADP
ejpam-5478	3	2	this	this	DET
ejpam-5478	3	3	paper	paper	NOUN
ejpam-5478	3	4	,	,	PUNCT
ejpam-5478	3	5	we	we	PRON
ejpam-5478	3	6	investigate	investigate	VERB
ejpam-5478	3	7	higher	high	ADJ
ejpam-5478	3	8	-	-	PUNCT
ejpam-5478	3	9	order	order	NOUN
ejpam-5478	3	10	calculus	calculus	NOUN
ejpam-5478	3	11	using	use	VERB
ejpam-5478	3	12	the	the	DET
ejpam-5478	3	13	conformable	conformable	ADJ
ejpam-5478	3	14	derivative	derivative	ADJ
ejpam-5478	3	15	and	and	CCONJ
ejpam-5478	3	16	integral	integral	ADJ
ejpam-5478	3	17	.	.	PUNCT
ejpam-5478	4	1	we	we	PRON
ejpam-5478	4	2	use	use	VERB
ejpam-5478	4	3	a	a	DET
ejpam-5478	4	4	fractional	fractional	ADJ
ejpam-5478	4	5	variant	variant	NOUN
ejpam-5478	4	6	of	of	ADP
ejpam-5478	4	7	the	the	DET
ejpam-5478	4	8	calculus	calculus	NOUN
ejpam-5478	4	9	of	of	ADP
ejpam-5478	4	10	variations	variation	NOUN
ejpam-5478	4	11	to	to	PART
ejpam-5478	4	12	obtain	obtain	VERB
ejpam-5478	4	13	the	the	DET
ejpam-5478	4	14	euler	euler	NOUN
ejpam-5478	4	15	-	-	PUNCT
ejpam-5478	4	16	lagrange	lagrange	NOUN
ejpam-5478	4	17	equation	equation	NOUN
ejpam-5478	4	18	.	.	PUNCT
ejpam-5478	5	1	our	our	PRON
ejpam-5478	5	2	route	route	NOUN
ejpam-5478	5	3	integral	integral	ADJ
ejpam-5478	5	4	quantization	quantization	NOUN
ejpam-5478	5	5	approach	approach	NOUN
ejpam-5478	5	6	streamlines	streamline	VERB
ejpam-5478	5	7	the	the	DET
ejpam-5478	5	8	procedure	procedure	NOUN
ejpam-5478	5	9	by	by	ADP
ejpam-5478	5	10	integrating	integrate	VERB
ejpam-5478	5	11	solely	solely	ADV
ejpam-5478	5	12	over	over	ADP
ejpam-5478	5	13	canonical	canonical	ADJ
ejpam-5478	5	14	coordinates	coordinate	NOUN
ejpam-5478	5	15	qi	qi	PROPN
ejpam-5478	5	16	,	,	PUNCT
ejpam-5478	5	17	eliminating	eliminate	VERB
ejpam-5478	5	18	the	the	DET
ejpam-5478	5	19	requirement	requirement	NOUN
ejpam-5478	5	20	to	to	PART
ejpam-5478	5	21	integrate	integrate	VERB
ejpam-5478	5	22	higher	high	ADJ
ejpam-5478	5	23	-	-	PUNCT
ejpam-5478	5	24	order	order	NOUN
ejpam-5478	5	25	derivatives	derivative	NOUN
ejpam-5478	5	26	(	(	PUNCT
ejpam-5478	5	27	qi	qi	NOUN
ejpam-5478	5	28	=	=	NOUN
ejpam-5478	5	29	dα	dα	NOUN
ejpam-5478	5	30	t	t	PROPN
ejpam-5478	5	31	qi	qi	PROPN
ejpam-5478	5	32	)	)	PUNCT
ejpam-5478	5	33	.	.	PUNCT
ejpam-5478	6	1	in	in	ADP
ejpam-5478	6	2	addition	addition	NOUN
ejpam-5478	6	3	,	,	PUNCT
ejpam-5478	6	4	we	we	PRON
ejpam-5478	6	5	employ	employ	VERB
ejpam-5478	6	6	the	the	DET
ejpam-5478	6	7	conformable	conformable	ADJ
ejpam-5478	6	8	derivative	derivative	NOUN
ejpam-5478	6	9	to	to	PART
ejpam-5478	6	10	develop	develop	VERB
ejpam-5478	6	11	canonical	canonical	ADJ
ejpam-5478	6	12	conserved	conserve	VERB
ejpam-5478	6	13	energy	energy	NOUN
ejpam-5478	6	14	-	-	PUNCT
ejpam-5478	6	15	momentum	momentum	NOUN
ejpam-5478	6	16	and	and	CCONJ
ejpam-5478	6	17	ostrogradsky	ostrogradsky	ADJ
ejpam-5478	6	18	’s	’s	PART
ejpam-5478	6	19	hamiltonian	hamiltonian	NOUN
ejpam-5478	6	20	.	.	PUNCT
ejpam-5478	7	1	furthermore	furthermore	ADV
ejpam-5478	7	2	,	,	PUNCT
ejpam-5478	7	3	we	we	PRON
ejpam-5478	7	4	generalized	generalize	VERB
ejpam-5478	7	5	the	the	DET
ejpam-5478	7	6	hamilton	hamilton	PROPN
ejpam-5478	7	7	formulation	formulation	NOUN
ejpam-5478	7	8	for	for	ADP
ejpam-5478	7	9	higher	high	ADJ
ejpam-5478	7	10	order	order	NOUN
ejpam-5478	7	11	derivatives	derivative	NOUN
ejpam-5478	7	12	and	and	CCONJ
ejpam-5478	7	13	applied	apply	VERB
ejpam-5478	7	14	this	this	DET
ejpam-5478	7	15	new	new	ADJ
ejpam-5478	7	16	formulation	formulation	NOUN
ejpam-5478	7	17	to	to	AUX
ejpam-5478	7	18	obtained	obtain	VERB
ejpam-5478	7	19	equations	equation	NOUN
ejpam-5478	7	20	of	of	ADP
ejpam-5478	7	21	motion	motion	NOUN
ejpam-5478	7	22	for	for	ADP
ejpam-5478	7	23	a	a	DET
ejpam-5478	7	24	one	one	NUM
ejpam-5478	7	25	dimensional	dimensional	ADJ
ejpam-5478	7	26	point	point	NOUN
ejpam-5478	7	27	particle	particle	NOUN
ejpam-5478	7	28	.	.	PUNCT
ejpam-5478	8	1	2020	2020	NUM
ejpam-5478	8	2	mathematics	mathematics	PROPN
ejpam-5478	8	3	subject	subject	NOUN
ejpam-5478	8	4	classifications	classification	NOUN
ejpam-5478	8	5	:	:	PUNCT
ejpam-5478	8	6	37j05	37j05	NUM
ejpam-5478	8	7	,	,	PUNCT
ejpam-5478	8	8	70h20	70h20	NUM
ejpam-5478	8	9	,	,	PUNCT
ejpam-5478	8	10	49s05	49s05	NUM
ejpam-5478	8	11	,	,	PUNCT
ejpam-5478	8	12	26a33	26a33	NUM
ejpam-5478	8	13	,	,	PUNCT
ejpam-5478	8	14	70g45	70g45	NUM
ejpam-5478	8	15	key	key	ADJ
ejpam-5478	8	16	words	word	NOUN
ejpam-5478	8	17	and	and	CCONJ
ejpam-5478	8	18	phrases	phrase	NOUN
ejpam-5478	8	19	:	:	PUNCT
ejpam-5478	8	20	left	left	ADJ
ejpam-5478	8	21	and	and	CCONJ
ejpam-5478	8	22	right	right	ADJ
ejpam-5478	8	23	conformable	conformable	ADJ
ejpam-5478	8	24	fractional	fractional	ADJ
ejpam-5478	8	25	,	,	PUNCT
ejpam-5478	8	26	ostrogradsky	ostrogradsky	ADJ
ejpam-5478	8	27	’s	’s	PART
ejpam-5478	8	28	hamiltonian	hamiltonian	ADJ
ejpam-5478	8	29	,	,	PUNCT
ejpam-5478	8	30	energy	energy	NOUN
ejpam-5478	8	31	and	and	CCONJ
ejpam-5478	8	32	momentum	momentum	NOUN
ejpam-5478	8	33	conservation	conservation	NOUN
ejpam-5478	8	34	,	,	PUNCT
ejpam-5478	8	35	euler	euler	NOUN
ejpam-5478	8	36	-	-	PUNCT
ejpam-5478	8	37	lagrange	lagrange	NOUN
ejpam-5478	8	38	,	,	PUNCT
ejpam-5478	8	39	conformable	conformable	ADJ
ejpam-5478	8	40	higher	high	ADJ
ejpam-5478	8	41	-	-	PUNCT
ejpam-5478	8	42	order	order	NOUN
ejpam-5478	8	43	derivatives	derivative	NOUN
ejpam-5478	8	44	,	,	PUNCT
ejpam-5478	8	45	lagrange	lagrange	NOUN
ejpam-5478	8	46	equation	equation	NOUN
ejpam-5478	8	47	1	1	NUM
ejpam-5478	8	48	.	.	PUNCT
ejpam-5478	9	1	introduction	introduction	NOUN
ejpam-5478	9	2	higher	high	ADJ
ejpam-5478	9	3	-	-	PUNCT
ejpam-5478	9	4	order	order	NOUN
ejpam-5478	9	5	derivatives	derivative	NOUN
ejpam-5478	9	6	is	be	AUX
ejpam-5478	9	7	proving	prove	VERB
ejpam-5478	9	8	to	to	PART
ejpam-5478	9	9	be	be	AUX
ejpam-5478	9	10	invaluable	invaluable	ADJ
ejpam-5478	9	11	across	across	ADP
ejpam-5478	9	12	a	a	DET
ejpam-5478	9	13	spectrum	spectrum	NOUN
ejpam-5478	9	14	of	of	ADP
ejpam-5478	9	15	disciplines	discipline	NOUN
ejpam-5478	9	16	including	include	VERB
ejpam-5478	9	17	chemistry	chemistry	NOUN
ejpam-5478	9	18	,	,	PUNCT
ejpam-5478	9	19	biology	biology	NOUN
ejpam-5478	9	20	,	,	PUNCT
ejpam-5478	9	21	and	and	CCONJ
ejpam-5478	9	22	electronics	electronic	NOUN
ejpam-5478	10	1	[	[	X
ejpam-5478	10	2	6	6	NUM
ejpam-5478	10	3	,	,	PUNCT
ejpam-5478	10	4	20	20	NUM
ejpam-5478	10	5	]	]	PUNCT
ejpam-5478	10	6	.	.	PUNCT
ejpam-5478	11	1	recent	recent	ADJ
ejpam-5478	11	2	research	research	NOUN
ejpam-5478	11	3	has	have	AUX
ejpam-5478	11	4	showcased	showcase	VERB
ejpam-5478	11	5	its	its	PRON
ejpam-5478	11	6	utility	utility	NOUN
ejpam-5478	11	7	in	in	ADP
ejpam-5478	11	8	scaling	scale	VERB
ejpam-5478	11	9	phenomena	phenomenon	NOUN
ejpam-5478	11	10	[	[	X
ejpam-5478	11	11	19	19	NUM
ejpam-5478	11	12	,	,	PUNCT
ejpam-5478	11	13	23	23	NUM
ejpam-5478	11	14	]	]	PUNCT
ejpam-5478	11	15	,	,	PUNCT
ejpam-5478	11	16	classical	classical	ADJ
ejpam-5478	11	17	mechanics	mechanic	NOUN
ejpam-5478	11	18	,	,	PUNCT
ejpam-5478	11	19	and	and	CCONJ
ejpam-5478	11	20	mathematical	mathematical	ADJ
ejpam-5478	11	21	modeling	modeling	NOUN
ejpam-5478	11	22	[	[	X
ejpam-5478	11	23	25	25	NUM
ejpam-5478	11	24	,	,	PUNCT
ejpam-5478	11	25	31	31	NUM
ejpam-5478	11	26	]	]	PUNCT
ejpam-5478	11	27	.	.	PUNCT
ejpam-5478	12	1	scholars	scholar	NOUN
ejpam-5478	12	2	have	have	AUX
ejpam-5478	12	3	ventured	venture	VERB
ejpam-5478	12	4	into	into	ADP
ejpam-5478	12	5	higher	high	ADJ
ejpam-5478	12	6	-	-	PUNCT
ejpam-5478	12	7	order	order	NOUN
ejpam-5478	12	8	dynamical	dynamical	ADJ
ejpam-5478	12	9	systems	system	NOUN
ejpam-5478	12	10	using	use	VERB
ejpam-5478	12	11	dirac	dirac	NOUN
ejpam-5478	12	12	’s	’s	PART
ejpam-5478	12	13	restricted	restrict	VERB
ejpam-5478	12	14	dynamics	dynamic	NOUN
ejpam-5478	12	15	[	[	X
ejpam-5478	12	16	1	1	NUM
ejpam-5478	12	17	,	,	PUNCT
ejpam-5478	12	18	2	2	NUM
ejpam-5478	12	19	]	]	PUNCT
ejpam-5478	12	20	,	,	PUNCT
ejpam-5478	12	21	examining	examine	VERB
ejpam-5478	12	22	the	the	DET
ejpam-5478	12	23	harmony	harmony	NOUN
ejpam-5478	12	24	between	between	ADP
ejpam-5478	12	25	constraints	constraint	NOUN
ejpam-5478	12	26	and	and	CCONJ
ejpam-5478	12	27	equations	equation	NOUN
ejpam-5478	12	28	of	of	ADP
ejpam-5478	12	29	motion	motion	NOUN
ejpam-5478	12	30	[	[	X
ejpam-5478	12	31	8	8	NUM
ejpam-5478	12	32	]	]	PUNCT
ejpam-5478	12	33	,	,	PUNCT
ejpam-5478	12	34	and	and	CCONJ
ejpam-5478	12	35	advancing	advance	VERB
ejpam-5478	12	36	our	our	PRON
ejpam-5478	12	37	understanding	understanding	NOUN
ejpam-5478	12	38	of	of	ADP
ejpam-5478	12	39	systems	system	NOUN
ejpam-5478	12	40	with	with	ADP
ejpam-5478	12	41	higher	high	ADJ
ejpam-5478	12	42	-	-	PUNCT
ejpam-5478	12	43	order	order	NOUN
ejpam-5478	12	44	derivatives	derivative	NOUN
ejpam-5478	12	45	[	[	X
ejpam-5478	12	46	9	9	NUM
ejpam-5478	12	47	,	,	PUNCT
ejpam-5478	12	48	17	17	NUM
ejpam-5478	12	49	]	]	PUNCT
ejpam-5478	12	50	.	.	PUNCT
ejpam-5478	13	1	simplified	simplified	ADJ
ejpam-5478	13	2	∗corresponding	∗corresponde	VERB
ejpam-5478	13	3	author	author	NOUN
ejpam-5478	13	4	.	.	PUNCT
ejpam-5478	14	1	doi	doi	NOUN
ejpam-5478	14	2	:	:	PUNCT
ejpam-5478	14	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5478	https://doi.org/10.29020/nybg.ejpam.v18i1.5478	ADJ
ejpam-5478	14	4	email	email	NOUN
ejpam-5478	14	5	addresses	address	NOUN
ejpam-5478	14	6	:	:	PUNCT
ejpam-5478	14	7	yazen.awaida@yahoo.com	yazen.awaida@yahoo.com	X
ejpam-5478	14	8	(	(	PUNCT
ejpam-5478	14	9	y.	y.	PROPN
ejpam-5478	14	10	m.	m.	PROPN
ejpam-5478	14	11	alawaideh	alawaideh	PROPN
ejpam-5478	14	12	)	)	PUNCT
ejpam-5478	14	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5478	15	1	1	1	NUM
ejpam-5478	15	2	copyright	copyright	NOUN
ejpam-5478	15	3	:	:	PUNCT
ejpam-5478	15	4	©	©	PROPN
ejpam-5478	15	5	2025	2025	NUM
ejpam-5478	15	6	the	the	DET
ejpam-5478	15	7	author(s	author(s	NOUN
ejpam-5478	15	8	)	)	PUNCT
ejpam-5478	15	9	.	.	PUNCT
ejpam-5478	16	1	(	(	PUNCT
ejpam-5478	16	2	cc	cc	NOUN
ejpam-5478	16	3	by	by	ADP
ejpam-5478	16	4	-	-	PUNCT
ejpam-5478	16	5	nc	nc	PROPN
ejpam-5478	16	6	4.0	4.0	NUM
ejpam-5478	16	7	)	)	PUNCT
ejpam-5478	16	8	y.	y.	NOUN
ejpam-5478	16	9	m.	m.	NOUN
ejpam-5478	16	10	alawaideh	alawaideh	PROPN
ejpam-5478	16	11	et	et	PROPN
ejpam-5478	16	12	al	al	PROPN
ejpam-5478	16	13	.	.	PUNCT
ejpam-5478	16	14	/	/	SYM
ejpam-5478	16	15	eur	eur	PROPN
ejpam-5478	16	16	.	.	PUNCT
ejpam-5478	17	1	j.	j.	PROPN
ejpam-5478	17	2	pure	pure	PROPN
ejpam-5478	17	3	appl	appl	PROPN
ejpam-5478	17	4	.	.	PROPN
ejpam-5478	17	5	math	math	PROPN
ejpam-5478	17	6	,	,	PUNCT
ejpam-5478	17	7	18	18	NUM
ejpam-5478	17	8	(	(	PUNCT
ejpam-5478	17	9	1	1	NUM
ejpam-5478	17	10	)	)	PUNCT
ejpam-5478	17	11	(	(	PUNCT
ejpam-5478	17	12	2025	2025	NUM
ejpam-5478	17	13	)	)	PUNCT
ejpam-5478	17	14	,	,	PUNCT
ejpam-5478	17	15	5478	5478	NUM
ejpam-5478	17	16	2	2	NUM
ejpam-5478	17	17	of	of	ADP
ejpam-5478	17	18	14	14	NUM
ejpam-5478	17	19	quantization	quantization	NOUN
ejpam-5478	17	20	techniques	technique	NOUN
ejpam-5478	17	21	have	have	AUX
ejpam-5478	17	22	been	be	AUX
ejpam-5478	17	23	devised	devise	VERB
ejpam-5478	17	24	for	for	ADP
ejpam-5478	17	25	both	both	CCONJ
ejpam-5478	17	26	conservative	conservative	ADJ
ejpam-5478	17	27	and	and	CCONJ
ejpam-5478	17	28	non	non	ADJ
ejpam-5478	17	29	-	-	ADJ
ejpam-5478	17	30	conservative	conservative	ADJ
ejpam-5478	17	31	systems	system	NOUN
ejpam-5478	17	32	[	[	X
ejpam-5478	17	33	16	16	NUM
ejpam-5478	17	34	]	]	PUNCT
ejpam-5478	17	35	,	,	PUNCT
ejpam-5478	17	36	with	with	ADP
ejpam-5478	17	37	discrete	discrete	ADJ
ejpam-5478	17	38	systems	system	NOUN
ejpam-5478	17	39	receiving	receive	VERB
ejpam-5478	17	40	particular	particular	ADJ
ejpam-5478	17	41	attention	attention	NOUN
ejpam-5478	17	42	[	[	X
ejpam-5478	17	43	4	4	NUM
ejpam-5478	17	44	]	]	PUNCT
ejpam-5478	17	45	.	.	PUNCT
ejpam-5478	18	1	recent	recent	ADJ
ejpam-5478	18	2	inquiries	inquiry	NOUN
ejpam-5478	18	3	have	have	AUX
ejpam-5478	18	4	extended	extend	VERB
ejpam-5478	18	5	fractional	fractional	ADJ
ejpam-5478	18	6	equations	equation	NOUN
ejpam-5478	18	7	to	to	PART
ejpam-5478	18	8	encompass	encompass	VERB
ejpam-5478	18	9	fields	field	NOUN
ejpam-5478	18	10	like	like	ADP
ejpam-5478	18	11	the	the	DET
ejpam-5478	18	12	lee	lee	PROPN
ejpam-5478	18	13	-	-	PUNCT
ejpam-5478	18	14	wick	wick	NOUN
ejpam-5478	18	15	field	field	NOUN
ejpam-5478	18	16	[	[	X
ejpam-5478	18	17	22	22	NUM
ejpam-5478	18	18	]	]	PUNCT
ejpam-5478	18	19	,	,	PUNCT
ejpam-5478	18	20	complex	complex	ADJ
ejpam-5478	18	21	scalar	scalar	ADJ
ejpam-5478	18	22	fields	field	NOUN
ejpam-5478	18	23	[	[	X
ejpam-5478	18	24	5	5	NUM
ejpam-5478	18	25	]	]	PUNCT
ejpam-5478	18	26	,	,	PUNCT
ejpam-5478	18	27	and	and	CCONJ
ejpam-5478	18	28	the	the	DET
ejpam-5478	18	29	dirac	dirac	NOUN
ejpam-5478	18	30	field	field	NOUN
ejpam-5478	18	31	[	[	X
ejpam-5478	18	32	7	7	NUM
ejpam-5478	18	33	]	]	PUNCT
ejpam-5478	18	34	.	.	PUNCT
ejpam-5478	19	1	moreover	moreover	ADV
ejpam-5478	19	2	,	,	PUNCT
ejpam-5478	19	3	noether	noether	PROPN
ejpam-5478	19	4	’s	’s	PART
ejpam-5478	19	5	theorem	theorem	NOUN
ejpam-5478	19	6	has	have	AUX
ejpam-5478	19	7	been	be	AUX
ejpam-5478	19	8	invoked	invoke	VERB
ejpam-5478	19	9	to	to	PART
ejpam-5478	19	10	determine	determine	VERB
ejpam-5478	19	11	conserved	conserve	VERB
ejpam-5478	19	12	quantities	quantity	NOUN
ejpam-5478	19	13	[	[	X
ejpam-5478	19	14	3	3	NUM
ejpam-5478	19	15	]	]	PUNCT
ejpam-5478	19	16	,	,	PUNCT
ejpam-5478	19	17	while	while	SCONJ
ejpam-5478	19	18	the	the	DET
ejpam-5478	19	19	application	application	NOUN
ejpam-5478	19	20	of	of	ADP
ejpam-5478	19	21	hamilton	hamilton	PROPN
ejpam-5478	19	22	formalism	formalism	NOUN
ejpam-5478	19	23	with	with	ADP
ejpam-5478	19	24	higher	high	ADJ
ejpam-5478	19	25	-	-	PUNCT
ejpam-5478	19	26	order	order	NOUN
ejpam-5478	19	27	derivatives	derivative	NOUN
ejpam-5478	19	28	has	have	AUX
ejpam-5478	19	29	facilitated	facilitate	VERB
ejpam-5478	19	30	the	the	DET
ejpam-5478	19	31	derivation	derivation	NOUN
ejpam-5478	19	32	of	of	ADP
ejpam-5478	19	33	equations	equation	NOUN
ejpam-5478	19	34	of	of	ADP
ejpam-5478	19	35	motion	motion	NOUN
ejpam-5478	19	36	,	,	PUNCT
ejpam-5478	19	37	maintaining	maintain	VERB
ejpam-5478	19	38	consistency	consistency	NOUN
ejpam-5478	19	39	with	with	ADP
ejpam-5478	19	40	conventional	conventional	ADJ
ejpam-5478	19	41	mechanics	mechanic	NOUN
ejpam-5478	19	42	[	[	X
ejpam-5478	19	43	10	10	NUM
ejpam-5478	19	44	]	]	PUNCT
ejpam-5478	19	45	.	.	PUNCT
ejpam-5478	20	1	the	the	DET
ejpam-5478	20	2	riemann	riemann	PROPN
ejpam-5478	20	3	-	-	PUNCT
ejpam-5478	20	4	liouville	liouville	VERB
ejpam-5478	20	5	derivative	derivative	NOUN
ejpam-5478	20	6	has	have	AUX
ejpam-5478	20	7	emerged	emerge	VERB
ejpam-5478	20	8	as	as	ADP
ejpam-5478	20	9	a	a	DET
ejpam-5478	20	10	powerful	powerful	ADJ
ejpam-5478	20	11	tool	tool	NOUN
ejpam-5478	20	12	for	for	ADP
ejpam-5478	20	13	problem	problem	NOUN
ejpam-5478	20	14	-	-	PUNCT
ejpam-5478	20	15	solving	solve	VERB
ejpam-5478	20	16	[	[	X
ejpam-5478	20	17	12	12	NUM
ejpam-5478	20	18	]	]	PUNCT
ejpam-5478	20	19	,	,	PUNCT
ejpam-5478	20	20	exhibiting	exhibit	VERB
ejpam-5478	20	21	convergence	convergence	NOUN
ejpam-5478	20	22	in	in	ADP
ejpam-5478	20	23	the	the	DET
ejpam-5478	20	24	time	time	NOUN
ejpam-5478	20	25	domain	domain	NOUN
ejpam-5478	20	26	as	as	ADP
ejpam-5478	20	27	segment	segment	NOUN
ejpam-5478	20	28	size	size	NOUN
ejpam-5478	20	29	increases	increase	NOUN
ejpam-5478	20	30	.	.	PUNCT
ejpam-5478	21	1	many	many	ADJ
ejpam-5478	21	2	studies	study	NOUN
ejpam-5478	21	3	have	have	VERB
ejpam-5478	21	4	advanced	advance	VERB
ejpam-5478	21	5	hamilton	hamilton	PROPN
ejpam-5478	21	6	-	-	PUNCT
ejpam-5478	21	7	ostrogradskii	ostrogradskii	VERB
ejpam-5478	21	8	principle	principle	NOUN
ejpam-5478	21	9	formulations	formulation	NOUN
ejpam-5478	21	10	for	for	ADP
ejpam-5478	21	11	higher	high	ADJ
ejpam-5478	21	12	-	-	PUNCT
ejpam-5478	21	13	order	order	NOUN
ejpam-5478	21	14	dynamical	dynamical	ADJ
ejpam-5478	21	15	systems	system	NOUN
ejpam-5478	21	16	,	,	PUNCT
ejpam-5478	21	17	including	include	VERB
ejpam-5478	21	18	developments	development	NOUN
ejpam-5478	21	19	in	in	ADP
ejpam-5478	21	20	systems	system	NOUN
ejpam-5478	21	21	with	with	ADP
ejpam-5478	21	22	higher	high	ADJ
ejpam-5478	21	23	-	-	PUNCT
ejpam-5478	21	24	order	order	NOUN
ejpam-5478	21	25	derivatives	derivative	NOUN
ejpam-5478	21	26	and	and	CCONJ
ejpam-5478	21	27	fractional	fractional	ADJ
ejpam-5478	21	28	derivatives	derivative	NOUN
ejpam-5478	21	29	,	,	PUNCT
ejpam-5478	21	30	as	as	ADV
ejpam-5478	21	31	well	well	ADV
ejpam-5478	21	32	as	as	ADP
ejpam-5478	21	33	innovations	innovation	NOUN
ejpam-5478	21	34	in	in	ADP
ejpam-5478	21	35	path	path	NOUN
ejpam-5478	21	36	integral	integral	ADJ
ejpam-5478	21	37	quantization	quantization	NOUN
ejpam-5478	21	38	[	[	X
ejpam-5478	21	39	13	13	NUM
ejpam-5478	21	40	,	,	PUNCT
ejpam-5478	21	41	15	15	NUM
ejpam-5478	21	42	,	,	PUNCT
ejpam-5478	21	43	24	24	NUM
ejpam-5478	21	44	,	,	PUNCT
ejpam-5478	21	45	29	29	NUM
ejpam-5478	21	46	]	]	PUNCT
ejpam-5478	21	47	.	.	PUNCT
ejpam-5478	22	1	on	on	ADP
ejpam-5478	22	2	the	the	DET
ejpam-5478	22	3	other	other	ADJ
ejpam-5478	22	4	hand	hand	NOUN
ejpam-5478	22	5	,	,	PUNCT
ejpam-5478	22	6	the	the	DET
ejpam-5478	22	7	riemann	riemann	PROPN
ejpam-5478	22	8	-	-	PUNCT
ejpam-5478	22	9	liouville	liouville	VERB
ejpam-5478	22	10	derivative	derivative	NOUN
ejpam-5478	22	11	and	and	CCONJ
ejpam-5478	22	12	caputo	caputo	PROPN
ejpam-5478	22	13	derivative	derivative	PROPN
ejpam-5478	22	14	do	do	AUX
ejpam-5478	22	15	not	not	PART
ejpam-5478	22	16	obey	obey	VERB
ejpam-5478	22	17	the	the	DET
ejpam-5478	22	18	leibniz	leibniz	NOUN
ejpam-5478	22	19	rule	rule	NOUN
ejpam-5478	22	20	and	and	CCONJ
ejpam-5478	22	21	chain	chain	NOUN
ejpam-5478	22	22	rule	rule	NOUN
ejpam-5478	22	23	,	,	PUNCT
ejpam-5478	22	24	which	which	PRON
ejpam-5478	22	25	prevent	prevent	VERB
ejpam-5478	22	26	us	we	PRON
ejpam-5478	22	27	from	from	ADP
ejpam-5478	22	28	applying	apply	VERB
ejpam-5478	22	29	these	these	DET
ejpam-5478	22	30	derivatives	derivative	NOUN
ejpam-5478	22	31	to	to	ADP
ejpam-5478	22	32	the	the	DET
ejpam-5478	22	33	ordinary	ordinary	ADJ
ejpam-5478	22	34	physical	physical	ADJ
ejpam-5478	22	35	system	system	NOUN
ejpam-5478	22	36	with	with	ADP
ejpam-5478	22	37	high	high	ADJ
ejpam-5478	22	38	-	-	PUNCT
ejpam-5478	22	39	order	order	NOUN
ejpam-5478	22	40	derivatives	derivative	NOUN
ejpam-5478	22	41	.	.	PUNCT
ejpam-5478	23	1	the	the	DET
ejpam-5478	23	2	conformable	conformable	ADJ
ejpam-5478	23	3	derivative	derivative	NOUN
ejpam-5478	23	4	was	be	AUX
ejpam-5478	23	5	introduced	introduce	VERB
ejpam-5478	23	6	in	in	ADP
ejpam-5478	23	7	[	[	X
ejpam-5478	23	8	18	18	NUM
ejpam-5478	23	9	,	,	PUNCT
ejpam-5478	23	10	21	21	NUM
ejpam-5478	23	11	]	]	PUNCT
ejpam-5478	23	12	.	.	PUNCT
ejpam-5478	24	1	this	this	DET
ejpam-5478	24	2	derivative	derivative	ADJ
ejpam-5478	24	3	obeys	obey	NOUN
ejpam-5478	24	4	the	the	DET
ejpam-5478	24	5	leibniz	leibniz	NOUN
ejpam-5478	24	6	rule	rule	NOUN
ejpam-5478	24	7	and	and	CCONJ
ejpam-5478	24	8	the	the	DET
ejpam-5478	24	9	chain	chain	NOUN
ejpam-5478	24	10	rule	rule	NOUN
ejpam-5478	24	11	.	.	PUNCT
ejpam-5478	25	1	the	the	DET
ejpam-5478	25	2	innovative	innovative	ADJ
ejpam-5478	25	3	approach	approach	NOUN
ejpam-5478	25	4	,	,	PUNCT
ejpam-5478	25	5	based	base	VERB
ejpam-5478	25	6	on	on	ADP
ejpam-5478	25	7	leibniz	leibniz	PROPN
ejpam-5478	25	8	and	and	CCONJ
ejpam-5478	25	9	chain	chain	NOUN
ejpam-5478	25	10	principles	principle	NOUN
ejpam-5478	25	11	,	,	PUNCT
ejpam-5478	25	12	gives	give	VERB
ejpam-5478	25	13	identical	identical	ADJ
ejpam-5478	25	14	derivatives	derivative	NOUN
ejpam-5478	25	15	of	of	ADP
ejpam-5478	25	16	all	all	DET
ejpam-5478	25	17	orders	order	NOUN
ejpam-5478	25	18	under	under	ADP
ejpam-5478	25	19	one	one	NUM
ejpam-5478	25	20	,	,	PUNCT
ejpam-5478	25	21	creating	create	VERB
ejpam-5478	25	22	a	a	DET
ejpam-5478	25	23	flexible	flexible	ADJ
ejpam-5478	25	24	framework	framework	NOUN
ejpam-5478	25	25	for	for	ADP
ejpam-5478	25	26	studying	study	VERB
ejpam-5478	25	27	higher	high	ADJ
ejpam-5478	25	28	-	-	PUNCT
ejpam-5478	25	29	order	order	NOUN
ejpam-5478	25	30	derivatives	derivative	NOUN
ejpam-5478	25	31	.	.	PUNCT
ejpam-5478	26	1	with	with	ADP
ejpam-5478	26	2	increasing	increase	VERB
ejpam-5478	26	3	adoption	adoption	NOUN
ejpam-5478	26	4	by	by	ADP
ejpam-5478	26	5	researchers	researcher	NOUN
ejpam-5478	26	6	,	,	PUNCT
ejpam-5478	26	7	this	this	DET
ejpam-5478	26	8	definition	definition	NOUN
ejpam-5478	26	9	broadens	broaden	VERB
ejpam-5478	26	10	its	its	PRON
ejpam-5478	26	11	applicability	applicability	NOUN
ejpam-5478	26	12	to	to	PART
ejpam-5478	26	13	include	include	VERB
ejpam-5478	26	14	hamiltonian	hamiltonian	ADJ
ejpam-5478	26	15	formalism	formalism	NOUN
ejpam-5478	26	16	with	with	ADP
ejpam-5478	26	17	high	high	ADJ
ejpam-5478	26	18	-	-	PUNCT
ejpam-5478	26	19	order	order	NOUN
ejpam-5478	26	20	identical	identical	ADJ
ejpam-5478	26	21	derivatives	derivative	NOUN
ejpam-5478	26	22	,	,	PUNCT
ejpam-5478	26	23	ensuring	ensure	VERB
ejpam-5478	26	24	independence	independence	NOUN
ejpam-5478	26	25	from	from	ADP
ejpam-5478	26	26	higher	high	ADJ
ejpam-5478	26	27	-	-	PUNCT
ejpam-5478	26	28	order	order	NOUN
ejpam-5478	26	29	coordinate	coordinate	NOUN
ejpam-5478	26	30	derivatives	derivative	NOUN
ejpam-5478	26	31	.	.	PUNCT
ejpam-5478	27	1	this	this	DET
ejpam-5478	27	2	novel	novel	ADJ
ejpam-5478	27	3	mathematical	mathematical	ADJ
ejpam-5478	27	4	framework	framework	NOUN
ejpam-5478	27	5	enables	enable	VERB
ejpam-5478	27	6	a	a	DET
ejpam-5478	27	7	more	more	ADV
ejpam-5478	27	8	detailed	detailed	ADJ
ejpam-5478	27	9	depiction	depiction	NOUN
ejpam-5478	27	10	of	of	ADP
ejpam-5478	27	11	dynamical	dynamical	ADJ
ejpam-5478	27	12	systems	system	NOUN
ejpam-5478	27	13	characterized	characterize	VERB
ejpam-5478	27	14	by	by	ADP
ejpam-5478	27	15	complex	complex	ADJ
ejpam-5478	27	16	behaviors	behavior	NOUN
ejpam-5478	27	17	such	such	ADJ
ejpam-5478	27	18	as	as	ADP
ejpam-5478	27	19	memory	memory	NOUN
ejpam-5478	27	20	effects	effect	NOUN
ejpam-5478	27	21	,	,	PUNCT
ejpam-5478	27	22	non	non	ADJ
ejpam-5478	27	23	-	-	ADJ
ejpam-5478	27	24	local	local	ADJ
ejpam-5478	27	25	interactions	interaction	NOUN
ejpam-5478	27	26	,	,	PUNCT
ejpam-5478	27	27	and	and	CCONJ
ejpam-5478	27	28	anomalous	anomalous	ADJ
ejpam-5478	27	29	diffusion	diffusion	NOUN
ejpam-5478	27	30	.	.	PUNCT
ejpam-5478	28	1	efforts	effort	NOUN
ejpam-5478	28	2	focusing	focus	VERB
ejpam-5478	28	3	on	on	ADP
ejpam-5478	28	4	fractional	fractional	ADJ
ejpam-5478	28	5	calculus	calculus	NOUN
ejpam-5478	28	6	within	within	ADP
ejpam-5478	28	7	classical	classical	ADJ
ejpam-5478	28	8	domains	domain	NOUN
ejpam-5478	28	9	,	,	PUNCT
ejpam-5478	28	10	mechanical	mechanical	ADJ
ejpam-5478	28	11	systems	system	NOUN
ejpam-5478	28	12	,	,	PUNCT
ejpam-5478	28	13	and	and	CCONJ
ejpam-5478	28	14	variation	variation	NOUN
ejpam-5478	28	15	problems	problem	NOUN
ejpam-5478	28	16	aim	aim	VERB
ejpam-5478	28	17	to	to	PART
ejpam-5478	28	18	deepen	deepen	VERB
ejpam-5478	28	19	our	our	PRON
ejpam-5478	28	20	understanding	understanding	NOUN
ejpam-5478	28	21	of	of	ADP
ejpam-5478	28	22	anomalous	anomalous	ADJ
ejpam-5478	28	23	dynamics	dynamic	NOUN
ejpam-5478	28	24	and	and	CCONJ
ejpam-5478	28	25	non	non	ADJ
ejpam-5478	28	26	-	-	ADJ
ejpam-5478	28	27	local	local	ADJ
ejpam-5478	28	28	influences	influence	NOUN
ejpam-5478	28	29	in	in	ADP
ejpam-5478	28	30	physics	physics	NOUN
ejpam-5478	28	31	and	and	CCONJ
ejpam-5478	28	32	engineering	engineering	NOUN
ejpam-5478	28	33	.	.	PUNCT
ejpam-5478	29	1	this	this	DET
ejpam-5478	29	2	paper	paper	NOUN
ejpam-5478	29	3	aims	aim	VERB
ejpam-5478	29	4	to	to	PART
ejpam-5478	29	5	address	address	VERB
ejpam-5478	29	6	the	the	DET
ejpam-5478	29	7	identified	identify	VERB
ejpam-5478	29	8	limitations	limitation	NOUN
ejpam-5478	29	9	by	by	ADP
ejpam-5478	29	10	introducing	introduce	VERB
ejpam-5478	29	11	a	a	DET
ejpam-5478	29	12	novel	novel	ADJ
ejpam-5478	29	13	hamiltonian	hamiltonian	ADJ
ejpam-5478	29	14	formulation	formulation	NOUN
ejpam-5478	29	15	for	for	ADP
ejpam-5478	29	16	systems	system	NOUN
ejpam-5478	29	17	involving	involve	VERB
ejpam-5478	29	18	higher	high	ADJ
ejpam-5478	29	19	-	-	PUNCT
ejpam-5478	29	20	order	order	NOUN
ejpam-5478	29	21	derivatives	derivative	NOUN
ejpam-5478	29	22	.	.	PUNCT
ejpam-5478	30	1	our	our	PRON
ejpam-5478	30	2	approach	approach	NOUN
ejpam-5478	30	3	leverages	leverage	VERB
ejpam-5478	30	4	a	a	DET
ejpam-5478	30	5	new	new	ADJ
ejpam-5478	30	6	definition	definition	NOUN
ejpam-5478	30	7	of	of	ADP
ejpam-5478	30	8	the	the	DET
ejpam-5478	30	9	conformable	conformable	ADJ
ejpam-5478	30	10	derivative	derivative	NOUN
ejpam-5478	30	11	that	that	PRON
ejpam-5478	30	12	complies	comply	VERB
ejpam-5478	30	13	with	with	ADP
ejpam-5478	30	14	both	both	CCONJ
ejpam-5478	30	15	the	the	DET
ejpam-5478	30	16	leibniz	leibniz	NOUN
ejpam-5478	30	17	and	and	CCONJ
ejpam-5478	30	18	chain	chain	NOUN
ejpam-5478	30	19	rules	rule	NOUN
ejpam-5478	30	20	,	,	PUNCT
ejpam-5478	30	21	thereby	thereby	ADV
ejpam-5478	30	22	enhancing	enhance	VERB
ejpam-5478	30	23	its	its	PRON
ejpam-5478	30	24	applicability	applicability	NOUN
ejpam-5478	30	25	.	.	PUNCT
ejpam-5478	31	1	we	we	PRON
ejpam-5478	31	2	anticipate	anticipate	VERB
ejpam-5478	31	3	that	that	SCONJ
ejpam-5478	31	4	this	this	DET
ejpam-5478	31	5	proposed	propose	VERB
ejpam-5478	31	6	method	method	NOUN
ejpam-5478	31	7	will	will	AUX
ejpam-5478	31	8	provide	provide	VERB
ejpam-5478	31	9	a	a	DET
ejpam-5478	31	10	wide	wide	ADJ
ejpam-5478	31	11	range	range	NOUN
ejpam-5478	31	12	of	of	ADP
ejpam-5478	31	13	accurate	accurate	ADJ
ejpam-5478	31	14	solutions	solution	NOUN
ejpam-5478	31	15	to	to	ADP
ejpam-5478	31	16	generalized	generalized	ADJ
ejpam-5478	31	17	differential	differential	ADJ
ejpam-5478	31	18	equations	equation	NOUN
ejpam-5478	31	19	with	with	ADP
ejpam-5478	31	20	higher	high	ADJ
ejpam-5478	31	21	derivatives	derivative	NOUN
ejpam-5478	31	22	,	,	PUNCT
ejpam-5478	31	23	effectively	effectively	ADV
ejpam-5478	31	24	overcoming	overcome	VERB
ejpam-5478	31	25	existing	exist	VERB
ejpam-5478	31	26	limitations	limitation	NOUN
ejpam-5478	31	27	.	.	PUNCT
ejpam-5478	32	1	by	by	ADP
ejpam-5478	32	2	integrating	integrate	VERB
ejpam-5478	32	3	higher	high	ADJ
ejpam-5478	32	4	-	-	PUNCT
ejpam-5478	32	5	order	order	NOUN
ejpam-5478	32	6	derivatives	derivative	NOUN
ejpam-5478	32	7	and	and	CCONJ
ejpam-5478	32	8	fractional	fractional	ADJ
ejpam-5478	32	9	operators	operator	NOUN
ejpam-5478	32	10	into	into	ADP
ejpam-5478	32	11	our	our	PRON
ejpam-5478	32	12	framework	framework	NOUN
ejpam-5478	32	13	,	,	PUNCT
ejpam-5478	32	14	we	we	PRON
ejpam-5478	32	15	expect	expect	VERB
ejpam-5478	32	16	to	to	PART
ejpam-5478	32	17	create	create	VERB
ejpam-5478	32	18	more	more	ADV
ejpam-5478	32	19	adaptable	adaptable	ADJ
ejpam-5478	32	20	models	model	NOUN
ejpam-5478	32	21	compared	compare	VERB
ejpam-5478	32	22	to	to	ADP
ejpam-5478	32	23	those	those	PRON
ejpam-5478	32	24	derived	derive	VERB
ejpam-5478	32	25	from	from	ADP
ejpam-5478	32	26	traditional	traditional	ADJ
ejpam-5478	32	27	calculus	calculus	NOUN
ejpam-5478	32	28	.	.	PUNCT
ejpam-5478	33	1	furthermore	furthermore	ADV
ejpam-5478	33	2	,	,	PUNCT
ejpam-5478	33	3	we	we	PRON
ejpam-5478	33	4	intend	intend	VERB
ejpam-5478	33	5	to	to	PART
ejpam-5478	33	6	demonstrate	demonstrate	VERB
ejpam-5478	33	7	that	that	SCONJ
ejpam-5478	33	8	our	our	PRON
ejpam-5478	33	9	hamiltonian	hamiltonian	ADJ
ejpam-5478	33	10	formulation	formulation	NOUN
ejpam-5478	33	11	can	can	AUX
ejpam-5478	33	12	be	be	AUX
ejpam-5478	33	13	developed	develop	VERB
ejpam-5478	33	14	independently	independently	ADV
ejpam-5478	33	15	of	of	ADP
ejpam-5478	33	16	higher	high	ADJ
ejpam-5478	33	17	-	-	PUNCT
ejpam-5478	33	18	order	order	NOUN
ejpam-5478	33	19	derivatives	derivative	NOUN
ejpam-5478	33	20	of	of	ADP
ejpam-5478	33	21	the	the	DET
ejpam-5478	33	22	coordinates	coordinate	NOUN
ejpam-5478	33	23	,	,	PUNCT
ejpam-5478	33	24	which	which	PRON
ejpam-5478	33	25	will	will	AUX
ejpam-5478	33	26	simplify	simplify	VERB
ejpam-5478	33	27	the	the	DET
ejpam-5478	33	28	analysis	analysis	NOUN
ejpam-5478	33	29	of	of	ADP
ejpam-5478	33	30	complex	complex	ADJ
ejpam-5478	33	31	dynamical	dynamical	ADJ
ejpam-5478	33	32	systems	system	NOUN
ejpam-5478	33	33	and	and	CCONJ
ejpam-5478	33	34	improve	improve	VERB
ejpam-5478	33	35	our	our	PRON
ejpam-5478	33	36	understanding	understanding	NOUN
ejpam-5478	33	37	of	of	ADP
ejpam-5478	33	38	their	their	PRON
ejpam-5478	33	39	dynamics	dynamic	NOUN
ejpam-5478	33	40	.	.	PUNCT
ejpam-5478	34	1	the	the	DET
ejpam-5478	34	2	structure	structure	NOUN
ejpam-5478	34	3	of	of	ADP
ejpam-5478	34	4	this	this	DET
ejpam-5478	34	5	paper	paper	NOUN
ejpam-5478	34	6	is	be	AUX
ejpam-5478	34	7	as	as	SCONJ
ejpam-5478	34	8	follows	follow	VERB
ejpam-5478	34	9	:	:	PUNCT
ejpam-5478	34	10	section	section	NOUN
ejpam-5478	34	11	2	2	NUM
ejpam-5478	34	12	briefly	briefly	NOUN
ejpam-5478	34	13	discusses	discuss	VERB
ejpam-5478	34	14	the	the	DET
ejpam-5478	34	15	definitions	definition	NOUN
ejpam-5478	34	16	of	of	ADP
ejpam-5478	34	17	conformable	conformable	ADJ
ejpam-5478	34	18	derivatives	derivative	NOUN
ejpam-5478	34	19	.	.	PUNCT
ejpam-5478	35	1	section	section	NOUN
ejpam-5478	35	2	3	3	NUM
ejpam-5478	35	3	presents	present	VERB
ejpam-5478	35	4	the	the	DET
ejpam-5478	35	5	generalized	generalized	ADJ
ejpam-5478	35	6	ostrogradsky	ostrogradsky	ADJ
ejpam-5478	35	7	’s	’s	PART
ejpam-5478	35	8	construction	construction	NOUN
ejpam-5478	35	9	form	form	NOUN
ejpam-5478	35	10	.	.	PUNCT
ejpam-5478	36	1	section	section	NOUN
ejpam-5478	36	2	4	4	NUM
ejpam-5478	36	3	provides	provide	VERB
ejpam-5478	36	4	illustrative	illustrative	ADJ
ejpam-5478	36	5	examples	example	NOUN
ejpam-5478	36	6	,	,	PUNCT
ejpam-5478	36	7	and	and	CCONJ
ejpam-5478	36	8	section	section	NOUN
ejpam-5478	36	9	5	5	NUM
ejpam-5478	36	10	introduces	introduce	NOUN
ejpam-5478	36	11	applications	application	NOUN
ejpam-5478	36	12	of	of	ADP
ejpam-5478	36	13	conformable	conformable	ADJ
ejpam-5478	36	14	calculus	calculus	NOUN
ejpam-5478	36	15	along	along	ADP
ejpam-5478	36	16	with	with	ADP
ejpam-5478	36	17	suggestions	suggestion	NOUN
ejpam-5478	36	18	for	for	ADP
ejpam-5478	36	19	further	further	ADJ
ejpam-5478	36	20	research	research	NOUN
ejpam-5478	36	21	.	.	PUNCT
ejpam-5478	37	1	finally	finally	ADV
ejpam-5478	37	2	,	,	PUNCT
ejpam-5478	37	3	the	the	DET
ejpam-5478	37	4	paper	paper	NOUN
ejpam-5478	37	5	concludes	conclude	VERB
ejpam-5478	37	6	with	with	ADP
ejpam-5478	37	7	closing	closing	NOUN
ejpam-5478	37	8	remarks	remark	NOUN
ejpam-5478	37	9	.	.	PUNCT
ejpam-5478	38	1	y.	y.	PROPN
ejpam-5478	38	2	m.	m.	PROPN
ejpam-5478	38	3	alawaideh	alawaideh	PROPN
ejpam-5478	38	4	et	et	PROPN
ejpam-5478	38	5	al	al	PROPN
ejpam-5478	38	6	.	.	PUNCT
ejpam-5478	38	7	/	/	SYM
ejpam-5478	38	8	eur	eur	PROPN
ejpam-5478	38	9	.	.	PUNCT
ejpam-5478	39	1	j.	j.	PROPN
ejpam-5478	39	2	pure	pure	PROPN
ejpam-5478	39	3	appl	appl	PROPN
ejpam-5478	39	4	.	.	PROPN
ejpam-5478	39	5	math	math	PROPN
ejpam-5478	39	6	,	,	PUNCT
ejpam-5478	39	7	18	18	NUM
ejpam-5478	39	8	(	(	PUNCT
ejpam-5478	39	9	1	1	NUM
ejpam-5478	39	10	)	)	PUNCT
ejpam-5478	39	11	(	(	PUNCT
ejpam-5478	39	12	2025	2025	NUM
ejpam-5478	39	13	)	)	PUNCT
ejpam-5478	39	14	,	,	PUNCT
ejpam-5478	39	15	5478	5478	NUM
ejpam-5478	39	16	3	3	NUM
ejpam-5478	39	17	of	of	ADP
ejpam-5478	39	18	14	14	NUM
ejpam-5478	39	19	2	2	NUM
ejpam-5478	39	20	.	.	PUNCT
ejpam-5478	39	21	calculus	calculus	NOUN
ejpam-5478	39	22	of	of	ADP
ejpam-5478	39	23	variations	variation	NOUN
ejpam-5478	39	24	this	this	DET
ejpam-5478	39	25	section	section	NOUN
ejpam-5478	39	26	presents	present	VERB
ejpam-5478	39	27	two	two	NUM
ejpam-5478	39	28	distinct	distinct	ADJ
ejpam-5478	39	29	definitions	definition	NOUN
ejpam-5478	39	30	of	of	ADP
ejpam-5478	39	31	derivatives	derivative	NOUN
ejpam-5478	39	32	:	:	PUNCT
ejpam-5478	39	33	leftand	leftand	VERB
ejpam-5478	39	34	right	right	ADJ
ejpam-5478	39	35	-	-	PUNCT
ejpam-5478	39	36	conformable	conformable	ADJ
ejpam-5478	39	37	derivatives	derivative	NOUN
ejpam-5478	39	38	(	(	PUNCT
ejpam-5478	39	39	denoted	denote	VERB
ejpam-5478	39	40	cfds	cfds	NOUN
ejpam-5478	39	41	)	)	PUNCT
ejpam-5478	39	42	.	.	PUNCT
ejpam-5478	40	1	these	these	DET
ejpam-5478	40	2	definitions	definition	NOUN
ejpam-5478	40	3	are	be	AUX
ejpam-5478	40	4	integral	integral	ADJ
ejpam-5478	40	5	to	to	ADP
ejpam-5478	40	6	the	the	DET
ejpam-5478	40	7	hamiltonian	hamiltonian	ADJ
ejpam-5478	40	8	formulation	formulation	NOUN
ejpam-5478	40	9	and	and	CCONJ
ejpam-5478	40	10	are	be	AUX
ejpam-5478	40	11	employed	employ	VERB
ejpam-5478	40	12	in	in	ADP
ejpam-5478	40	13	solving	solve	VERB
ejpam-5478	40	14	cases	case	NOUN
ejpam-5478	40	15	that	that	PRON
ejpam-5478	40	16	result	result	VERB
ejpam-5478	40	17	in	in	ADP
ejpam-5478	40	18	equations	equation	NOUN
ejpam-5478	40	19	of	of	ADP
ejpam-5478	40	20	motion	motion	NOUN
ejpam-5478	40	21	of	of	ADP
ejpam-5478	40	22	various	various	ADJ
ejpam-5478	40	23	orders	order	NOUN
ejpam-5478	40	24	,	,	PUNCT
ejpam-5478	40	25	such	such	ADJ
ejpam-5478	40	26	as	as	ADP
ejpam-5478	40	27	(	(	PUNCT
ejpam-5478	40	28	1/2	1/2	NUM
ejpam-5478	40	29	,	,	PUNCT
ejpam-5478	40	30	1	1	NUM
ejpam-5478	40	31	,	,	PUNCT
ejpam-5478	40	32	3/2	3/2	NUM
ejpam-5478	40	33	,	,	PUNCT
ejpam-5478	40	34	2	2	NUM
ejpam-5478	40	35	...	...	PUNCT
ejpam-5478	40	36	)	)	PUNCT
ejpam-5478	40	37	.	.	PUNCT
ejpam-5478	41	1	the	the	DET
ejpam-5478	41	2	left	left	ADJ
ejpam-5478	41	3	conformable	conformable	ADJ
ejpam-5478	41	4	derivative	derivative	NOUN
ejpam-5478	41	5	and	and	CCONJ
ejpam-5478	41	6	the	the	DET
ejpam-5478	41	7	right	right	ADJ
ejpam-5478	41	8	-	-	PUNCT
ejpam-5478	41	9	conformable	conformable	ADJ
ejpam-5478	41	10	derivative	derivative	NOUN
ejpam-5478	41	11	are	be	AUX
ejpam-5478	41	12	defined	define	VERB
ejpam-5478	41	13	and	and	CCONJ
ejpam-5478	41	14	explored	explore	VERB
ejpam-5478	41	15	,	,	PUNCT
ejpam-5478	41	16	along	along	ADP
ejpam-5478	41	17	with	with	ADP
ejpam-5478	41	18	their	their	PRON
ejpam-5478	41	19	corresponding	correspond	VERB
ejpam-5478	41	20	integrals	integral	NOUN
ejpam-5478	41	21	,	,	PUNCT
ejpam-5478	41	22	the	the	DET
ejpam-5478	41	23	left	left	ADJ
ejpam-5478	41	24	conformable	conformable	ADJ
ejpam-5478	41	25	integral	integral	ADJ
ejpam-5478	41	26	(	(	PUNCT
ejpam-5478	41	27	cfi	cfi	NOUN
ejpam-5478	41	28	)	)	PUNCT
ejpam-5478	41	29	and	and	CCONJ
ejpam-5478	41	30	the	the	DET
ejpam-5478	41	31	right	right	ADJ
ejpam-5478	41	32	conformable	conformable	ADJ
ejpam-5478	41	33	integral	integral	ADJ
ejpam-5478	41	34	(	(	PUNCT
ejpam-5478	41	35	cfi	cfi	NOUN
ejpam-5478	41	36	)	)	PUNCT
ejpam-5478	42	1	[	[	X
ejpam-5478	42	2	11	11	NUM
ejpam-5478	42	3	,	,	PUNCT
ejpam-5478	42	4	18	18	NUM
ejpam-5478	42	5	]	]	PUNCT
ejpam-5478	42	6	.	.	PUNCT
ejpam-5478	43	1	these	these	DET
ejpam-5478	43	2	concepts	concept	NOUN
ejpam-5478	43	3	are	be	AUX
ejpam-5478	43	4	fundamental	fundamental	ADJ
ejpam-5478	43	5	to	to	ADP
ejpam-5478	43	6	understanding	understanding	NOUN
ejpam-5478	43	7	and	and	CCONJ
ejpam-5478	43	8	applying	apply	VERB
ejpam-5478	43	9	higher	high	ADJ
ejpam-5478	43	10	-	-	PUNCT
ejpam-5478	43	11	order	order	NOUN
ejpam-5478	43	12	calculus	calculus	NOUN
ejpam-5478	43	13	in	in	ADP
ejpam-5478	43	14	various	various	ADJ
ejpam-5478	43	15	physical	physical	ADJ
ejpam-5478	43	16	contexts	contexts	NOUN
ejpam-5478	43	17	.	.	PUNCT
ejpam-5478	44	1	the	the	DET
ejpam-5478	44	2	right	right	ADJ
ejpam-5478	44	3	conformable	conformable	ADJ
ejpam-5478	44	4	derivative	derivative	NOUN
ejpam-5478	44	5	is	be	AUX
ejpam-5478	44	6	defined	define	VERB
ejpam-5478	44	7	as	as	SCONJ
ejpam-5478	44	8	follows	follow	VERB
ejpam-5478	44	9	[	[	X
ejpam-5478	44	10	11	11	NUM
ejpam-5478	44	11	,	,	PUNCT
ejpam-5478	44	12	18	18	NUM
ejpam-5478	44	13	]	]	PUNCT
ejpam-5478	44	14	:	:	PUNCT
ejpam-5478	44	15	dα	dα	ADJ
ejpam-5478	44	16	s|xf(t	s|xf(t	NOUN
ejpam-5478	44	17	)	)	PUNCT
ejpam-5478	45	1	=	=	SYM
ejpam-5478	45	2	lim	lim	PROPN
ejpam-5478	45	3	ϵ→∞	ϵ→∞	NUM
ejpam-5478	45	4	(	(	PUNCT
ejpam-5478	45	5	t+	t+	NOUN
ejpam-5478	45	6	ϵ(t−	ϵ(t−	NOUN
ejpam-5478	45	7	s)1−α)−	s)1−α)−	PUNCT
ejpam-5478	45	8	f(t	f(t	NOUN
ejpam-5478	45	9	)	)	PUNCT
ejpam-5478	45	10	ϵ	ϵ	X
ejpam-5478	45	11	with	with	ADP
ejpam-5478	45	12	the	the	DET
ejpam-5478	45	13	condition	condition	NOUN
ejpam-5478	45	14	that	that	PRON
ejpam-5478	45	15	s	s	VERB
ejpam-5478	45	16	<	<	X
ejpam-5478	45	17	t	t	NOUN
ejpam-5478	45	18	for	for	SCONJ
ejpam-5478	45	19	the	the	DET
ejpam-5478	45	20	derivative	derivative	NOUN
ejpam-5478	45	21	to	to	PART
ejpam-5478	45	22	be	be	AUX
ejpam-5478	45	23	valid	valid	ADJ
ejpam-5478	45	24	for	for	ADP
ejpam-5478	45	25	all	all	DET
ejpam-5478	45	26	t	t	PROPN
ejpam-5478	45	27	≥	≥	PRON
ejpam-5478	45	28	s.	s.	PROPN
ejpam-5478	46	1	the	the	DET
ejpam-5478	46	2	leftconformable	leftconformable	ADJ
ejpam-5478	46	3	derivative	derivative	NOUN
ejpam-5478	46	4	is	be	AUX
ejpam-5478	46	5	defined	define	VERB
ejpam-5478	46	6	as	as	SCONJ
ejpam-5478	46	7	follows	follow	VERB
ejpam-5478	46	8	[	[	X
ejpam-5478	46	9	11	11	NUM
ejpam-5478	46	10	,	,	PUNCT
ejpam-5478	46	11	18	18	NUM
ejpam-5478	46	12	]	]	PUNCT
ejpam-5478	46	13	:	:	PUNCT
ejpam-5478	46	14	dα	dα	ADJ
ejpam-5478	46	15	t|s′f(t	t|s′f(t	NOUN
ejpam-5478	46	16	)	)	PUNCT
ejpam-5478	47	1	=	=	SYM
ejpam-5478	48	1	−	−	PROPN
ejpam-5478	48	2	lim	lim	NOUN
ejpam-5478	48	3	ϵ→∞	ϵ→∞	NUM
ejpam-5478	48	4	(	(	PUNCT
ejpam-5478	48	5	t+	t+	PUNCT
ejpam-5478	48	6	ϵ(s	ϵ(s	PROPN
ejpam-5478	48	7	′	′	NUM
ejpam-5478	48	8	−	−	NOUN
ejpam-5478	48	9	t)1−α)−	t)1−α)−	PUNCT
ejpam-5478	48	10	f(t	f(t	PROPN
ejpam-5478	48	11	)	)	PUNCT
ejpam-5478	48	12	ϵ	ϵ	ADP
ejpam-5478	48	13	noting	note	VERB
ejpam-5478	48	14	that	that	SCONJ
ejpam-5478	48	15	t	t	PROPN
ejpam-5478	48	16	≥	≥	NOUN
ejpam-5478	48	17	s	s	VERB
ejpam-5478	48	18	to	to	PART
ejpam-5478	48	19	avoid	avoid	VERB
ejpam-5478	48	20	undefined	undefined	ADJ
ejpam-5478	48	21	expressions	expression	NOUN
ejpam-5478	48	22	,	,	PUNCT
ejpam-5478	48	23	as	as	ADP
ejpam-5478	48	24	(	(	PUNCT
ejpam-5478	48	25	t	t	PROPN
ejpam-5478	48	26	−	−	PROPN
ejpam-5478	48	27	s)α	s)α	NOUN
ejpam-5478	48	28	becomes	become	VERB
ejpam-5478	48	29	negative	negative	ADJ
ejpam-5478	48	30	in	in	ADP
ejpam-5478	48	31	such	such	ADJ
ejpam-5478	48	32	cases	case	NOUN
ejpam-5478	48	33	.	.	PUNCT
ejpam-5478	49	1	in	in	ADP
ejpam-5478	49	2	the	the	DET
ejpam-5478	49	3	case	case	NOUN
ejpam-5478	49	4	where	where	SCONJ
ejpam-5478	49	5	0	0	X
ejpam-5478	49	6	<	<	X
ejpam-5478	49	7	α	α	X
ejpam-5478	49	8	≤	≤	NUM
ejpam-5478	49	9	1	1	NUM
ejpam-5478	49	10	,	,	PUNCT
ejpam-5478	49	11	the	the	DET
ejpam-5478	49	12	left	left	ADJ
ejpam-5478	49	13	conformable	conformable	ADJ
ejpam-5478	49	14	integral	integral	ADJ
ejpam-5478	49	15	(	(	PUNCT
ejpam-5478	49	16	cfi	cfi	NOUN
ejpam-5478	49	17	)	)	PUNCT
ejpam-5478	49	18	is	be	AUX
ejpam-5478	49	19	defined	define	VERB
ejpam-5478	49	20	as	as	SCONJ
ejpam-5478	49	21	follows	follow	VERB
ejpam-5478	49	22	:	:	PUNCT
ejpam-5478	49	23	iαs|tf(t	iαs|tf(t	NUM
ejpam-5478	49	24	)	)	PUNCT
ejpam-5478	49	25	=	=	SYM
ejpam-5478	50	1	∫	∫	PROPN
ejpam-5478	50	2	t	t	PROPN
ejpam-5478	50	3	s	s	X
ejpam-5478	50	4	(	(	PUNCT
ejpam-5478	50	5	ξ	ξ	PROPN
ejpam-5478	50	6	−	−	X
ejpam-5478	50	7	s)1−αf(ξ)dξ	s)1−αf(ξ)dξ	ADV
ejpam-5478	50	8	ensuring	ensure	VERB
ejpam-5478	50	9	the	the	DET
ejpam-5478	50	10	integral	integral	ADJ
ejpam-5478	50	11	limits	limit	NOUN
ejpam-5478	50	12	are	be	AUX
ejpam-5478	50	13	correctly	correctly	ADV
ejpam-5478	50	14	defined	define	VERB
ejpam-5478	50	15	from	from	ADP
ejpam-5478	50	16	s	s	PRON
ejpam-5478	50	17	to	to	ADP
ejpam-5478	50	18	t.	t.	PROPN
ejpam-5478	50	19	the	the	DET
ejpam-5478	50	20	right	right	ADJ
ejpam-5478	50	21	conformable	conformable	ADJ
ejpam-5478	50	22	integral	integral	ADJ
ejpam-5478	50	23	(	(	PUNCT
ejpam-5478	50	24	cfi	cfi	NOUN
ejpam-5478	50	25	)	)	PUNCT
ejpam-5478	50	26	is	be	AUX
ejpam-5478	50	27	defined	define	VERB
ejpam-5478	50	28	as	as	SCONJ
ejpam-5478	50	29	follows	follow	VERB
ejpam-5478	50	30	:	:	PUNCT
ejpam-5478	50	31	iα	iα	INTJ
ejpam-5478	50	32	t|s′f(t	t|s′f(t	PUNCT
ejpam-5478	50	33	)	)	PUNCT
ejpam-5478	51	1	=	=	SYM
ejpam-5478	51	2	∫	∫	PROPN
ejpam-5478	51	3	s	s	PART
ejpam-5478	51	4	′	′	PROPN
ejpam-5478	51	5	t	t	PROPN
ejpam-5478	51	6	(	(	PUNCT
ejpam-5478	51	7	s	s	NOUN
ejpam-5478	51	8	′	′	NUM
ejpam-5478	51	9	−	−	NUM
ejpam-5478	51	10	ξ)1−αf(ξ)dξ	ξ)1−αf(ξ)dξ	NUM
ejpam-5478	51	11	the	the	DET
ejpam-5478	51	12	relationships	relationship	NOUN
ejpam-5478	51	13	between	between	ADP
ejpam-5478	51	14	the	the	DET
ejpam-5478	51	15	conformable	conformable	ADJ
ejpam-5478	51	16	derivatives	derivative	NOUN
ejpam-5478	51	17	(	(	PUNCT
ejpam-5478	51	18	cfd	cfd	NOUN
ejpam-5478	51	19	)	)	PUNCT
ejpam-5478	51	20	and	and	CCONJ
ejpam-5478	51	21	integrals	integral	NOUN
ejpam-5478	51	22	(	(	PUNCT
ejpam-5478	51	23	cfi	cfi	NOUN
ejpam-5478	51	24	)	)	PUNCT
ejpam-5478	51	25	are	be	AUX
ejpam-5478	51	26	expressed	express	VERB
ejpam-5478	51	27	as	as	SCONJ
ejpam-5478	51	28	follows	follow	VERB
ejpam-5478	51	29	:	:	PUNCT
ejpam-5478	51	30	dα	dα	NUM
ejpam-5478	51	31	s|ti	s|ti	PROPN
ejpam-5478	51	32	α	α	NOUN
ejpam-5478	51	33	s|tf(t	s|tf(t	NOUN
ejpam-5478	51	34	)	)	PUNCT
ejpam-5478	51	35	=	=	SYM
ejpam-5478	51	36	f(t	f(t	NOUN
ejpam-5478	51	37	)	)	PUNCT
ejpam-5478	51	38	,	,	PUNCT
ejpam-5478	51	39	dα	dα	ADP
ejpam-5478	51	40	t|s′i	t|s′i	VERB
ejpam-5478	51	41	α	α	NOUN
ejpam-5478	51	42	t|s′f(t	t|s′f(t	PUNCT
ejpam-5478	51	43	)	)	PUNCT
ejpam-5478	52	1	=	=	SYM
ejpam-5478	52	2	f(t)−	f(t)−	PROPN
ejpam-5478	52	3	f(a	f(a	PROPN
ejpam-5478	52	4	)	)	PUNCT
ejpam-5478	52	5	,	,	PUNCT
ejpam-5478	52	6	next	next	ADV
ejpam-5478	52	7	,	,	PUNCT
ejpam-5478	52	8	we	we	PRON
ejpam-5478	52	9	generalize	generalize	VERB
ejpam-5478	52	10	to	to	ADP
ejpam-5478	52	11	the	the	DET
ejpam-5478	52	12	case	case	NOUN
ejpam-5478	52	13	when	when	SCONJ
ejpam-5478	52	14	s	s	VERB
ejpam-5478	52	15	=	=	NOUN
ejpam-5478	52	16	0	0	NUM
ejpam-5478	52	17	,	,	PUNCT
ejpam-5478	52	18	and	and	CCONJ
ejpam-5478	52	19	use	use	VERB
ejpam-5478	52	20	the	the	DET
ejpam-5478	52	21	notationdα	notationdα	PROPN
ejpam-5478	52	22	s|t	s|t	PROPN
ejpam-5478	52	23	to	to	PART
ejpam-5478	52	24	denote	denote	VERB
ejpam-5478	52	25	(	(	PUNCT
ejpam-5478	52	26	d	d	X
ejpam-5478	52	27	α	α	X
ejpam-5478	52	28	s|t	s|t	PUNCT
ejpam-5478	53	1	=	=	PRON
ejpam-5478	53	2	dα	dα	PROPN
ejpam-5478	53	3	t	t	PROPN
ejpam-5478	53	4	)	)	PUNCT
ejpam-5478	53	5	as	as	SCONJ
ejpam-5478	53	6	follows	follow	VERB
ejpam-5478	53	7	:	:	PUNCT
ejpam-5478	53	8	dα	dα	ADJ
ejpam-5478	53	9	s|xf(t	s|xf(t	NOUN
ejpam-5478	53	10	)	)	PUNCT
ejpam-5478	54	1	=	=	SYM
ejpam-5478	54	2	lim	lim	PROPN
ejpam-5478	54	3	ϵ→∞	ϵ→∞	NUM
ejpam-5478	54	4	(	(	PUNCT
ejpam-5478	54	5	t+	t+	NOUN
ejpam-5478	54	6	ϵt1−α)−	ϵt1−α)−	NOUN
ejpam-5478	54	7	f(t	f(t	NOUN
ejpam-5478	54	8	)	)	PUNCT
ejpam-5478	54	9	ϵ	ϵ	X
ejpam-5478	54	10	where	where	SCONJ
ejpam-5478	54	11	0	0	X
ejpam-5478	54	12	<	<	X
ejpam-5478	54	13	α	α	PROPN
ejpam-5478	54	14	≤	≤	NUM
ejpam-5478	54	15	1	1	NUM
ejpam-5478	54	16	and	and	CCONJ
ejpam-5478	54	17	dα	dα	ADJ
ejpam-5478	54	18	x	x	PUNCT
ejpam-5478	54	19	represents	represent	VERB
ejpam-5478	54	20	a	a	DET
ejpam-5478	54	21	right	right	ADJ
ejpam-5478	54	22	cfd	cfd	NOUN
ejpam-5478	54	23	.	.	PUNCT
ejpam-5478	55	1	the	the	DET
ejpam-5478	55	2	definition	definition	NOUN
ejpam-5478	55	3	of	of	ADP
ejpam-5478	55	4	cfd	cfd	NOUN
ejpam-5478	55	5	can	can	AUX
ejpam-5478	55	6	be	be	AUX
ejpam-5478	55	7	reformulated	reformulate	VERB
ejpam-5478	55	8	using	use	VERB
ejpam-5478	55	9	l’hôpital	l’hôpital	PROPN
ejpam-5478	55	10	’s	’s	PART
ejpam-5478	55	11	rule	rule	NOUN
ejpam-5478	55	12	as	as	SCONJ
ejpam-5478	55	13	follows	follow	VERB
ejpam-5478	55	14	[	[	X
ejpam-5478	55	15	30	30	NUM
ejpam-5478	55	16	]	]	X
ejpam-5478	55	17	:	:	PUNCT
ejpam-5478	55	18	y.	y.	PROPN
ejpam-5478	55	19	m.	m.	PROPN
ejpam-5478	55	20	alawaideh	alawaideh	PROPN
ejpam-5478	55	21	et	et	PROPN
ejpam-5478	55	22	al	al	PROPN
ejpam-5478	55	23	.	.	PUNCT
ejpam-5478	55	24	/	/	SYM
ejpam-5478	55	25	eur	eur	PROPN
ejpam-5478	55	26	.	.	PUNCT
ejpam-5478	56	1	j.	j.	PROPN
ejpam-5478	56	2	pure	pure	PROPN
ejpam-5478	56	3	appl	appl	PROPN
ejpam-5478	56	4	.	.	PROPN
ejpam-5478	56	5	math	math	PROPN
ejpam-5478	56	6	,	,	PUNCT
ejpam-5478	56	7	18	18	NUM
ejpam-5478	56	8	(	(	PUNCT
ejpam-5478	56	9	1	1	NUM
ejpam-5478	56	10	)	)	PUNCT
ejpam-5478	56	11	(	(	PUNCT
ejpam-5478	56	12	2025	2025	NUM
ejpam-5478	56	13	)	)	PUNCT
ejpam-5478	56	14	,	,	PUNCT
ejpam-5478	56	15	5478	5478	NUM
ejpam-5478	56	16	4	4	NUM
ejpam-5478	56	17	of	of	ADP
ejpam-5478	56	18	14	14	NUM
ejpam-5478	56	19	dα	dα	ADJ
ejpam-5478	56	20	s|tf(t	s|tf(t	NOUN
ejpam-5478	56	21	)	)	PUNCT
ejpam-5478	57	1	=	=	SYM
ejpam-5478	58	1	f	f	X
ejpam-5478	58	2	′	′	NUM
ejpam-5478	59	1	(	(	PUNCT
ejpam-5478	59	2	t)t1−t	t)t1−t	PROPN
ejpam-5478	59	3	,	,	PUNCT
ejpam-5478	59	4	assuming	assume	VERB
ejpam-5478	59	5	f	f	PROPN
ejpam-5478	59	6	is	be	AUX
ejpam-5478	59	7	differentiable	differentiable	ADJ
ejpam-5478	59	8	,	,	PUNCT
ejpam-5478	59	9	which	which	PRON
ejpam-5478	59	10	is	be	AUX
ejpam-5478	59	11	necessary	necessary	ADJ
ejpam-5478	59	12	for	for	ADP
ejpam-5478	59	13	equation	equation	NOUN
ejpam-5478	59	14	2	2	NUM
ejpam-5478	59	15	to	to	PART
ejpam-5478	59	16	hold	hold	VERB
ejpam-5478	59	17	true	true	ADJ
ejpam-5478	59	18	.	.	PUNCT
ejpam-5478	60	1	3	3	X
ejpam-5478	60	2	.	.	X
ejpam-5478	60	3	generalized	generalize	VERB
ejpam-5478	60	4	ostrogradsky	ostrogradsky	ADJ
ejpam-5478	60	5	’s	’s	PART
ejpam-5478	60	6	construction	construction	NOUN
ejpam-5478	60	7	form	form	NOUN
ejpam-5478	60	8	this	this	DET
ejpam-5478	60	9	section	section	NOUN
ejpam-5478	60	10	explores	explore	VERB
ejpam-5478	60	11	the	the	DET
ejpam-5478	60	12	lagrangian	lagrangian	ADJ
ejpam-5478	60	13	and	and	CCONJ
ejpam-5478	60	14	hamiltonian	hamiltonian	ADJ
ejpam-5478	60	15	formulations	formulation	NOUN
ejpam-5478	60	16	of	of	ADP
ejpam-5478	60	17	mechanical	mechanical	ADJ
ejpam-5478	60	18	systems	system	NOUN
ejpam-5478	60	19	characterized	characterize	VERB
ejpam-5478	60	20	by	by	ADP
ejpam-5478	60	21	higher	high	ADJ
ejpam-5478	60	22	-	-	PUNCT
ejpam-5478	60	23	order	order	NOUN
ejpam-5478	60	24	partial	partial	ADJ
ejpam-5478	60	25	derivatives	derivative	NOUN
ejpam-5478	60	26	.	.	PUNCT
ejpam-5478	61	1	it	it	PRON
ejpam-5478	61	2	defines	define	VERB
ejpam-5478	61	3	the	the	DET
ejpam-5478	61	4	configuration	configuration	NOUN
ejpam-5478	61	5	space	space	NOUN
ejpam-5478	61	6	using	use	VERB
ejpam-5478	61	7	generalized	generalized	ADJ
ejpam-5478	61	8	coordinates	coordinate	NOUN
ejpam-5478	61	9	and	and	CCONJ
ejpam-5478	61	10	derives	derive	VERB
ejpam-5478	61	11	equations	equation	NOUN
ejpam-5478	61	12	of	of	ADP
ejpam-5478	61	13	motion	motion	NOUN
ejpam-5478	61	14	through	through	ADP
ejpam-5478	61	15	the	the	DET
ejpam-5478	61	16	euler	euler	NOUN
ejpam-5478	61	17	-	-	PUNCT
ejpam-5478	61	18	lagrange	lagrange	NOUN
ejpam-5478	61	19	equations	equation	NOUN
ejpam-5478	61	20	[	[	X
ejpam-5478	61	21	14	14	NUM
ejpam-5478	61	22	,	,	PUNCT
ejpam-5478	61	23	28	28	NUM
ejpam-5478	61	24	]	]	PUNCT
ejpam-5478	61	25	.	.	PUNCT
ejpam-5478	62	1	lagrangian	lagrangian	ADJ
ejpam-5478	62	2	formulation	formulation	NOUN
ejpam-5478	62	3	we	we	PRON
ejpam-5478	62	4	begin	begin	VERB
ejpam-5478	62	5	with	with	ADP
ejpam-5478	62	6	a	a	DET
ejpam-5478	62	7	configuration	configuration	NOUN
ejpam-5478	62	8	space	space	NOUN
ejpam-5478	62	9	defined	define	VERB
ejpam-5478	62	10	by	by	ADP
ejpam-5478	62	11	n	n	CCONJ
ejpam-5478	62	12	generalized	generalized	ADJ
ejpam-5478	62	13	coordinates	coordinate	NOUN
ejpam-5478	62	14	q(t	q(t	PROPN
ejpam-5478	62	15	)	)	PUNCT
ejpam-5478	62	16	,	,	PUNCT
ejpam-5478	62	17	dα	dα	DET
ejpam-5478	62	18	s|tq(t	s|tq(t	NOUN
ejpam-5478	62	19	)	)	PUNCT
ejpam-5478	62	20	and	and	CCONJ
ejpam-5478	62	21	d2α	d2α	NOUN
ejpam-5478	62	22	s|tq(t	s|tq(t	ADJ
ejpam-5478	62	23	)	)	PUNCT
ejpam-5478	62	24	,	,	PUNCT
ejpam-5478	62	25	and	and	CCONJ
ejpam-5478	62	26	d2α	d2α	NOUN
ejpam-5478	62	27	s|tαq(t	s|tαq(t	NUM
ejpam-5478	62	28	)	)	PUNCT
ejpam-5478	62	29	.	.	PUNCT
ejpam-5478	63	1	the	the	DET
ejpam-5478	63	2	equations	equation	NOUN
ejpam-5478	63	3	of	of	ADP
ejpam-5478	63	4	motion	motion	NOUN
ejpam-5478	63	5	arise	arise	VERB
ejpam-5478	63	6	from	from	ADP
ejpam-5478	63	7	the	the	DET
ejpam-5478	63	8	euler	euler	PROPN
ejpam-5478	63	9	-	-	PUNCT
ejpam-5478	63	10	lagrange	lagrange	NOUN
ejpam-5478	63	11	equations	equation	NOUN
ejpam-5478	63	12	,	,	PUNCT
ejpam-5478	63	13	represented	represent	VERB
ejpam-5478	63	14	as	as	ADP
ejpam-5478	63	15	:	:	PUNCT
ejpam-5478	63	16	jα	jα	PROPN
ejpam-5478	63	17	[	[	X
ejpam-5478	63	18	t	t	X
ejpam-5478	63	19	]	]	X
ejpam-5478	63	20	=	=	SYM
ejpam-5478	63	21	iα0|t0l(qi(t	iα0|t0l(qi(t	PROPN
ejpam-5478	63	22	,	,	PUNCT
ejpam-5478	63	23	ϵ	ϵ	PROPN
ejpam-5478	63	24	α	α	NOUN
ejpam-5478	63	25	)	)	PUNCT
ejpam-5478	63	26	,	,	PUNCT
ejpam-5478	63	27	dα	dα	PRON
ejpam-5478	63	28	s|tqi(t	s|tqi(t	NOUN
ejpam-5478	63	29	,	,	PUNCT
ejpam-5478	63	30	ϵ	ϵ	PROPN
ejpam-5478	63	31	α	α	NOUN
ejpam-5478	63	32	)	)	PUNCT
ejpam-5478	63	33	,	,	PUNCT
ejpam-5478	63	34	d2α	d2α	NOUN
ejpam-5478	63	35	s|tqi(t	s|tqi(t	NOUN
ejpam-5478	63	36	,	,	PUNCT
ejpam-5478	63	37	ϵ	ϵ	PROPN
ejpam-5478	63	38	α	α	NOUN
ejpam-5478	63	39	)	)	PUNCT
ejpam-5478	63	40	)	)	PUNCT
ejpam-5478	64	1	where	where	SCONJ
ejpam-5478	64	2	qi(t	qi(t	NOUN
ejpam-5478	64	3	,	,	PUNCT
ejpam-5478	64	4	ϵ	ϵ	PROPN
ejpam-5478	64	5	α	α	NOUN
ejpam-5478	64	6	)	)	PUNCT
ejpam-5478	64	7	=	=	SYM
ejpam-5478	64	8	q(t	q(t	ADJ
ejpam-5478	64	9	)	)	PUNCT
ejpam-5478	65	1	+	+	NUM
ejpam-5478	65	2	ϵη(t	ϵη(t	X
ejpam-5478	65	3	)	)	PUNCT
ejpam-5478	65	4	dα	dα	ADP
ejpam-5478	65	5	t	t	PROPN
ejpam-5478	65	6	qi(t	qi(t	PROPN
ejpam-5478	65	7	,	,	PUNCT
ejpam-5478	65	8	ϵ	ϵ	PROPN
ejpam-5478	65	9	α	α	NOUN
ejpam-5478	65	10	)	)	PUNCT
ejpam-5478	65	11	=	=	PRON
ejpam-5478	66	1	dα	dα	PROPN
ejpam-5478	66	2	t	t	PROPN
ejpam-5478	66	3	q(t	q(t	PROPN
ejpam-5478	66	4	)	)	PUNCT
ejpam-5478	67	1	+	+	NUM
ejpam-5478	67	2	ϵdα	ϵdα	NUM
ejpam-5478	67	3	t	t	PROPN
ejpam-5478	67	4	η(t	η(t	NOUN
ejpam-5478	67	5	)	)	PUNCT
ejpam-5478	67	6	and	and	CCONJ
ejpam-5478	67	7	η(0	η(0	PROPN
ejpam-5478	67	8	)	)	PUNCT
ejpam-5478	68	1	=	=	SYM
ejpam-5478	68	2	η(t0	η(t0	NOUN
ejpam-5478	68	3	)	)	PUNCT
ejpam-5478	69	1	=	=	SYM
ejpam-5478	69	2	0	0	PUNCT
ejpam-5478	70	1	subsequently	subsequently	ADV
ejpam-5478	70	2	,	,	PUNCT
ejpam-5478	70	3	the	the	DET
ejpam-5478	70	4	need	need	NOUN
ejpam-5478	70	5	for	for	ADP
ejpam-5478	70	6	an	an	DET
ejpam-5478	70	7	external	external	ADJ
ejpam-5478	70	8	value	value	NOUN
ejpam-5478	70	9	can	can	AUX
ejpam-5478	70	10	be	be	AUX
ejpam-5478	70	11	expressed	express	VERB
ejpam-5478	70	12	as	as	SCONJ
ejpam-5478	70	13	follows	follow	VERB
ejpam-5478	70	14	:	:	PUNCT
ejpam-5478	71	1	[	[	X
ejpam-5478	71	2	∂ϵs]ϵ=0	∂ϵs]ϵ=0	PROPN
ejpam-5478	71	3	=	=	PUNCT
ejpam-5478	71	4	iα0|t0	iα0|t0	PROPN
ejpam-5478	72	1	[	[	X
ejpam-5478	72	2	∂ϵl(qi(t	∂ϵl(qi(t	X
ejpam-5478	72	3	,	,	PUNCT
ejpam-5478	72	4	ϵ	ϵ	NOUN
ejpam-5478	72	5	)	)	PUNCT
ejpam-5478	72	6	,	,	PUNCT
ejpam-5478	72	7	d	d	PROPN
ejpam-5478	72	8	α	α	PROPN
ejpam-5478	72	9	t	t	NOUN
ejpam-5478	72	10	qi(t	qi(t	PROPN
ejpam-5478	72	11	,	,	PUNCT
ejpam-5478	72	12	ϵ	ϵ	X
ejpam-5478	72	13	)	)	PUNCT
ejpam-5478	72	14	,	,	PUNCT
ejpam-5478	73	1	d	d	PROPN
ejpam-5478	73	2	α	α	NOUN
ejpam-5478	73	3	t	t	X
ejpam-5478	73	4	d	d	X
ejpam-5478	73	5	α	α	PROPN
ejpam-5478	73	6	t	t	PROPN
ejpam-5478	73	7	qi(t	qi(t	PROPN
ejpam-5478	73	8	,	,	PUNCT
ejpam-5478	73	9	ϵ	ϵ	NOUN
ejpam-5478	73	10	)	)	PUNCT
ejpam-5478	73	11	)	)	PUNCT
ejpam-5478	73	12	]	]	PUNCT
ejpam-5478	74	1	=	=	PUNCT
ejpam-5478	74	2	∫	∫	PROPN
ejpam-5478	74	3	t	t	NOUN
ejpam-5478	74	4	0	0	NUM
ejpam-5478	75	1	tα−1	tα−1	NOUN
ejpam-5478	75	2	[	[	PUNCT
ejpam-5478	75	3	∂l	∂l	PROPN
ejpam-5478	75	4	∂qi	∂qi	PROPN
ejpam-5478	75	5	∂qi	∂qi	PROPN
ejpam-5478	75	6	∂ϵ	∂ϵ	PROPN
ejpam-5478	76	1	+	+	CCONJ
ejpam-5478	76	2	∂l	∂l	PROPN
ejpam-5478	76	3	∂dα	∂dα	PROPN
ejpam-5478	76	4	t	t	PROPN
ejpam-5478	76	5	qi	qi	PROPN
ejpam-5478	76	6	∂dα	∂dα	PROPN
ejpam-5478	76	7	t	t	PROPN
ejpam-5478	76	8	qi	qi	PROPN
ejpam-5478	76	9	∂ϵ	∂ϵ	PROPN
ejpam-5478	76	10	∂l	∂l	PROPN
ejpam-5478	77	1	∂dα	∂dα	PROPN
ejpam-5478	77	2	t	t	PROPN
ejpam-5478	78	1	d	d	X
ejpam-5478	78	2	α	α	PROPN
ejpam-5478	78	3	t	t	X
ejpam-5478	78	4	qi	qi	PROPN
ejpam-5478	78	5	+	+	CCONJ
ejpam-5478	78	6	∂dα	∂dα	PROPN
ejpam-5478	78	7	t	t	PROPN
ejpam-5478	79	1	d	d	NOUN
ejpam-5478	79	2	α	α	PROPN
ejpam-5478	79	3	t	t	PROPN
ejpam-5478	79	4	qi	qi	PROPN
ejpam-5478	79	5	∂ϵ	∂ϵ	PROPN
ejpam-5478	79	6	]	]	PUNCT
ejpam-5478	80	1	dt	dt	X
ejpam-5478	81	1	=	=	SYM
ejpam-5478	81	2	∫	∫	PROPN
ejpam-5478	81	3	t	t	NOUN
ejpam-5478	81	4	0	0	NUM
ejpam-5478	82	1	tα−1	tα−1	NOUN
ejpam-5478	82	2	[	[	PUNCT
ejpam-5478	82	3	∂l	∂l	PROPN
ejpam-5478	82	4	∂qi	∂qi	PROPN
ejpam-5478	82	5	η	η	PROPN
ejpam-5478	82	6	+	+	PROPN
ejpam-5478	82	7	∂l	∂l	PROPN
ejpam-5478	82	8	∂dα	∂dα	PROPN
ejpam-5478	82	9	t	t	PROPN
ejpam-5478	82	10	qi	qi	PROPN
ejpam-5478	82	11	dα	dα	PROPN
ejpam-5478	82	12	t	t	PROPN
ejpam-5478	82	13	η	η	PROPN
ejpam-5478	82	14	+	+	PROPN
ejpam-5478	82	15	∂l	∂l	PROPN
ejpam-5478	82	16	∂dα	∂dα	PROPN
ejpam-5478	82	17	t	t	PROPN
ejpam-5478	83	1	d	d	NOUN
ejpam-5478	83	2	α	α	PROPN
ejpam-5478	83	3	t	t	PROPN
ejpam-5478	83	4	qi	qi	PROPN
ejpam-5478	83	5	dα	dα	PROPN
ejpam-5478	83	6	t	t	PROPN
ejpam-5478	83	7	d	d	PROPN
ejpam-5478	83	8	α	α	PROPN
ejpam-5478	83	9	t	t	PROPN
ejpam-5478	83	10	η	η	X
ejpam-5478	83	11	]	]	X
ejpam-5478	83	12	dt	dt	X
ejpam-5478	83	13	by	by	ADP
ejpam-5478	83	14	employing	employ	VERB
ejpam-5478	83	15	integration	integration	NOUN
ejpam-5478	83	16	by	by	ADP
ejpam-5478	83	17	parts	part	NOUN
ejpam-5478	83	18	,	,	PUNCT
ejpam-5478	83	19	we	we	PRON
ejpam-5478	83	20	obtain	obtain	VERB
ejpam-5478	83	21	the	the	DET
ejpam-5478	83	22	following	follow	VERB
ejpam-5478	83	23	expression	expression	NOUN
ejpam-5478	83	24	:	:	PUNCT
ejpam-5478	83	25	0	0	PUNCT
ejpam-5478	84	1	=	=	SYM
ejpam-5478	84	2	∫	∫	PROPN
ejpam-5478	84	3	t	t	NOUN
ejpam-5478	84	4	0	0	NUM
ejpam-5478	85	1	tα−1	tα−1	NOUN
ejpam-5478	85	2	[	[	PUNCT
ejpam-5478	85	3	∂l	∂l	PROPN
ejpam-5478	85	4	∂qi	∂qi	PROPN
ejpam-5478	85	5	−dα	−dα	PROPN
ejpam-5478	85	6	t	t	PROPN
ejpam-5478	85	7	(	(	PUNCT
ejpam-5478	85	8	∂l	∂l	PROPN
ejpam-5478	85	9	∂dα	∂dα	PROPN
ejpam-5478	85	10	t	t	PROPN
ejpam-5478	85	11	qi	qi	PROPN
ejpam-5478	85	12	)	)	PUNCT
ejpam-5478	86	1	+	+	CCONJ
ejpam-5478	87	1	(	(	PUNCT
ejpam-5478	87	2	∂l	∂l	PROPN
ejpam-5478	87	3	∂dα	∂dα	PROPN
ejpam-5478	87	4	t	t	PROPN
ejpam-5478	87	5	d	d	X
ejpam-5478	87	6	α	α	PROPN
ejpam-5478	87	7	t	t	PROPN
ejpam-5478	87	8	qi	qi	PROPN
ejpam-5478	87	9	)	)	PUNCT
ejpam-5478	87	10	]	]	PUNCT
ejpam-5478	87	11	η(t)dt	η(t)dt	PROPN
ejpam-5478	87	12	this	this	DET
ejpam-5478	87	13	results	result	VERB
ejpam-5478	87	14	in	in	ADP
ejpam-5478	87	15	the	the	DET
ejpam-5478	87	16	fractional	fractional	ADJ
ejpam-5478	87	17	euler	euler	PROPN
ejpam-5478	87	18	-	-	PUNCT
ejpam-5478	87	19	lagrange	lagrange	NOUN
ejpam-5478	87	20	equation	equation	NOUN
ejpam-5478	87	21	.	.	PUNCT
ejpam-5478	88	1	∂l	∂l	PROPN
ejpam-5478	88	2	∂qi	∂qi	PROPN
ejpam-5478	88	3	−dα	−dα	PROPN
ejpam-5478	88	4	t	t	PROPN
ejpam-5478	88	5	(	(	PUNCT
ejpam-5478	88	6	∂l	∂l	PROPN
ejpam-5478	88	7	∂dα	∂dα	PROPN
ejpam-5478	88	8	t	t	PROPN
ejpam-5478	88	9	qi	qi	PROPN
ejpam-5478	88	10	)	)	PUNCT
ejpam-5478	89	1	+	+	CCONJ
ejpam-5478	89	2	(	(	PUNCT
ejpam-5478	89	3	∂l	∂l	PROPN
ejpam-5478	89	4	∂dα	∂dα	PROPN
ejpam-5478	89	5	t	t	PROPN
ejpam-5478	89	6	d	d	X
ejpam-5478	89	7	α	α	PROPN
ejpam-5478	89	8	t	t	PROPN
ejpam-5478	89	9	qi	qi	PROPN
ejpam-5478	89	10	)	)	PUNCT
ejpam-5478	90	1	=	=	PUNCT
ejpam-5478	90	2	0	0	PUNCT
ejpam-5478	90	3	(	(	PUNCT
ejpam-5478	90	4	1	1	NUM
ejpam-5478	90	5	)	)	PUNCT
ejpam-5478	90	6	by	by	ADP
ejpam-5478	90	7	comparing	compare	VERB
ejpam-5478	90	8	equations	equation	NOUN
ejpam-5478	90	9	(	(	PUNCT
ejpam-5478	90	10	a.3	a.3	NOUN
ejpam-5478	90	11	)	)	PUNCT
ejpam-5478	90	12	and	and	CCONJ
ejpam-5478	90	13	(	(	PUNCT
ejpam-5478	90	14	a.4	a.4	X
ejpam-5478	90	15	)	)	PUNCT
ejpam-5478	90	16	,	,	PUNCT
ejpam-5478	90	17	we	we	PRON
ejpam-5478	90	18	observe	observe	VERB
ejpam-5478	90	19	that	that	SCONJ
ejpam-5478	90	20	the	the	DET
ejpam-5478	90	21	differential	differential	ADJ
ejpam-5478	90	22	representation	representation	NOUN
ejpam-5478	90	23	of	of	ADP
ejpam-5478	90	24	the	the	DET
ejpam-5478	90	25	hamiltonian	hamiltonian	NOUN
ejpam-5478	90	26	requires	require	VERB
ejpam-5478	90	27	identifying	identify	VERB
ejpam-5478	90	28	the	the	DET
ejpam-5478	90	29	partial	partial	ADJ
ejpam-5478	90	30	derivatives	derivative	NOUN
ejpam-5478	90	31	of	of	ADP
ejpam-5478	90	32	h	h	NOUN
ejpam-5478	90	33	with	with	ADP
ejpam-5478	90	34	respect	respect	NOUN
ejpam-5478	90	35	to	to	ADP
ejpam-5478	90	36	qi	qi	PROPN
ejpam-5478	90	37	,	,	PUNCT
ejpam-5478	90	38	p1	p1	PROPN
ejpam-5478	90	39	,	,	PUNCT
ejpam-5478	90	40	p2	p2	PROPN
ejpam-5478	90	41	,	,	PUNCT
ejpam-5478	90	42	and	and	CCONJ
ejpam-5478	90	43	t.	t.	NOUN
ejpam-5478	90	44	using	use	VERB
ejpam-5478	90	45	this	this	DET
ejpam-5478	90	46	comparison	comparison	NOUN
ejpam-5478	90	47	,	,	PUNCT
ejpam-5478	90	48	we	we	PRON
ejpam-5478	90	49	derive	derive	VERB
ejpam-5478	90	50	the	the	DET
ejpam-5478	90	51	hamiltonian	hamiltonian	ADJ
ejpam-5478	90	52	equations	equation	NOUN
ejpam-5478	90	53	of	of	ADP
ejpam-5478	90	54	motion	motion	NOUN
ejpam-5478	90	55	as	as	SCONJ
ejpam-5478	90	56	follows	follow	VERB
ejpam-5478	90	57	(	(	PUNCT
ejpam-5478	90	58	see	see	VERB
ejpam-5478	90	59	appendix	appendix	NOUN
ejpam-5478	90	60	a	a	PRON
ejpam-5478	90	61	):	):	PUNCT
ejpam-5478	90	62	y.	y.	PROPN
ejpam-5478	90	63	m.	m.	NOUN
ejpam-5478	90	64	alawaideh	alawaideh	PROPN
ejpam-5478	90	65	et	et	PROPN
ejpam-5478	90	66	al	al	PROPN
ejpam-5478	90	67	.	.	PUNCT
ejpam-5478	90	68	/	/	SYM
ejpam-5478	90	69	eur	eur	PROPN
ejpam-5478	90	70	.	.	PUNCT
ejpam-5478	91	1	j.	j.	PROPN
ejpam-5478	91	2	pure	pure	PROPN
ejpam-5478	91	3	appl	appl	PROPN
ejpam-5478	91	4	.	.	PROPN
ejpam-5478	91	5	math	math	PROPN
ejpam-5478	91	6	,	,	PUNCT
ejpam-5478	91	7	18	18	NUM
ejpam-5478	91	8	(	(	PUNCT
ejpam-5478	91	9	1	1	NUM
ejpam-5478	91	10	)	)	PUNCT
ejpam-5478	91	11	(	(	PUNCT
ejpam-5478	91	12	2025	2025	NUM
ejpam-5478	91	13	)	)	PUNCT
ejpam-5478	91	14	,	,	PUNCT
ejpam-5478	91	15	5478	5478	NUM
ejpam-5478	91	16	5	5	NUM
ejpam-5478	91	17	of	of	ADP
ejpam-5478	91	18	14	14	NUM
ejpam-5478	91	19	•	•	NOUN
ejpam-5478	91	20	first	first	ADJ
ejpam-5478	91	21	equation	equation	NOUN
ejpam-5478	91	22	of	of	ADP
ejpam-5478	91	23	motion	motion	NOUN
ejpam-5478	91	24	:	:	PUNCT
ejpam-5478	91	25	since	since	SCONJ
ejpam-5478	91	26	the	the	DET
ejpam-5478	91	27	term	term	NOUN
ejpam-5478	91	28	dα	dα	ADP
ejpam-5478	91	29	s|tqid(p1	s|tqid(p1	NOUN
ejpam-5478	91	30	)	)	PUNCT
ejpam-5478	91	31	in	in	ADP
ejpam-5478	91	32	equation	equation	NOUN
ejpam-5478	91	33	(	(	PUNCT
ejpam-5478	91	34	a.3	a.3	X
ejpam-5478	91	35	)	)	PUNCT
ejpam-5478	91	36	should	should	AUX
ejpam-5478	91	37	correspond	correspond	VERB
ejpam-5478	91	38	to	to	ADP
ejpam-5478	91	39	the	the	DET
ejpam-5478	91	40	term	term	NOUN
ejpam-5478	91	41	∂h	∂h	PROPN
ejpam-5478	91	42	∂p1	∂p1	PROPN
ejpam-5478	91	43	dp1	dp1	PROPN
ejpam-5478	91	44	in	in	ADP
ejpam-5478	91	45	equation	equation	NOUN
ejpam-5478	91	46	(	(	PUNCT
ejpam-5478	91	47	a.4	a.4	PROPN
ejpam-5478	91	48	)	)	PUNCT
ejpam-5478	91	49	,	,	PUNCT
ejpam-5478	91	50	we	we	PRON
ejpam-5478	91	51	obtain	obtain	VERB
ejpam-5478	91	52	:	:	PUNCT
ejpam-5478	91	53	dα	dα	DET
ejpam-5478	91	54	s|tqi	s|tqi	PROPN
ejpam-5478	91	55	=	=	SYM
ejpam-5478	91	56	∂h	∂h	PROPN
ejpam-5478	91	57	∂p1	∂p1	NOUN
ejpam-5478	91	58	,	,	PUNCT
ejpam-5478	91	59	•	•	NUM
ejpam-5478	91	60	second	second	ADJ
ejpam-5478	91	61	equation	equation	NOUN
ejpam-5478	91	62	of	of	ADP
ejpam-5478	91	63	motion	motion	NOUN
ejpam-5478	91	64	:	:	PUNCT
ejpam-5478	91	65	similarly	similarly	ADV
ejpam-5478	91	66	,	,	PUNCT
ejpam-5478	91	67	the	the	DET
ejpam-5478	91	68	term	term	NOUN
ejpam-5478	91	69	d2α	d2α	NOUN
ejpam-5478	91	70	s|tqid(p2	s|tqid(p2	PUNCT
ejpam-5478	91	71	)	)	PUNCT
ejpam-5478	91	72	should	should	AUX
ejpam-5478	91	73	match	match	VERB
ejpam-5478	91	74	the	the	DET
ejpam-5478	91	75	term	term	NOUN
ejpam-5478	91	76	∂h	∂h	PROPN
ejpam-5478	91	77	∂p2	∂p2	PROPN
ejpam-5478	91	78	dp2	dp2	NOUN
ejpam-5478	91	79	in	in	ADP
ejpam-5478	91	80	equation	equation	NOUN
ejpam-5478	91	81	(	(	PUNCT
ejpam-5478	91	82	a.4	a.4	PROPN
ejpam-5478	91	83	)	)	PUNCT
ejpam-5478	91	84	,	,	PUNCT
ejpam-5478	91	85	leading	lead	VERB
ejpam-5478	91	86	to	to	ADP
ejpam-5478	91	87	:	:	PUNCT
ejpam-5478	91	88	d2α	d2α	NOUN
ejpam-5478	91	89	s|tqi	s|tqi	NOUN
ejpam-5478	91	90	=	=	SYM
ejpam-5478	91	91	∂h	∂h	PROPN
ejpam-5478	91	92	∂p2	∂p2	PROPN
ejpam-5478	91	93	,	,	PUNCT
ejpam-5478	91	94	•	•	NUM
ejpam-5478	91	95	third	third	ADJ
ejpam-5478	91	96	equation	equation	NOUN
ejpam-5478	91	97	of	of	ADP
ejpam-5478	91	98	motion	motion	NOUN
ejpam-5478	91	99	:	:	PUNCT
ejpam-5478	91	100	moving	move	VERB
ejpam-5478	91	101	to	to	ADP
ejpam-5478	91	102	the	the	DET
ejpam-5478	91	103	term	term	NOUN
ejpam-5478	91	104	involving	involve	VERB
ejpam-5478	91	105	dqi	dqi	ADV
ejpam-5478	91	106	in	in	ADP
ejpam-5478	91	107	equation	equation	NOUN
ejpam-5478	91	108	(	(	PUNCT
ejpam-5478	91	109	a.3	a.3	NOUN
ejpam-5478	91	110	)	)	PUNCT
ejpam-5478	91	111	,	,	PUNCT
ejpam-5478	91	112	we	we	PRON
ejpam-5478	91	113	observe	observe	VERB
ejpam-5478	91	114	that	that	SCONJ
ejpam-5478	91	115	it	it	PRON
ejpam-5478	91	116	should	should	AUX
ejpam-5478	91	117	be	be	AUX
ejpam-5478	91	118	equivalent	equivalent	ADJ
ejpam-5478	91	119	to	to	ADP
ejpam-5478	91	120	the	the	DET
ejpam-5478	91	121	term	term	NOUN
ejpam-5478	91	122	(	(	PUNCT
ejpam-5478	91	123	dα	dα	DET
ejpam-5478	91	124	s|tp1+d2α	s|tp1+d2α	PROPN
ejpam-5478	91	125	s|tp2)dqi	s|tp2)dqi	NOUN
ejpam-5478	91	126	in	in	ADP
ejpam-5478	91	127	equation	equation	NOUN
ejpam-5478	91	128	(	(	PUNCT
ejpam-5478	91	129	4	4	NUM
ejpam-5478	91	130	)	)	PUNCT
ejpam-5478	91	131	.	.	PUNCT
ejpam-5478	92	1	thus	thus	ADV
ejpam-5478	92	2	,	,	PUNCT
ejpam-5478	92	3	we	we	PRON
ejpam-5478	92	4	find	find	VERB
ejpam-5478	92	5	:	:	PUNCT
ejpam-5478	92	6	∂h	∂h	PROPN
ejpam-5478	92	7	∂qi	∂qi	PROPN
ejpam-5478	92	8	=	=	PUNCT
ejpam-5478	92	9	−dα	−dα	VERB
ejpam-5478	92	10	s|tp1	s|tp1	NOUN
ejpam-5478	93	1	+	+	ADJ
ejpam-5478	93	2	d2α	d2α	NOUN
ejpam-5478	93	3	s|tp2	s|tp2	ADV
ejpam-5478	93	4	,	,	PUNCT
ejpam-5478	93	5	•	•	NUM
ejpam-5478	93	6	fourth	fourth	ADJ
ejpam-5478	93	7	equation	equation	NOUN
ejpam-5478	93	8	of	of	ADP
ejpam-5478	93	9	motion	motion	NOUN
ejpam-5478	93	10	:	:	PUNCT
ejpam-5478	93	11	the	the	DET
ejpam-5478	93	12	term	term	NOUN
ejpam-5478	93	13	∂h	∂h	PROPN
ejpam-5478	93	14	∂(t	∂(t	PROPN
ejpam-5478	93	15	)	)	PUNCT
ejpam-5478	93	16	represents	represent	VERB
ejpam-5478	93	17	the	the	DET
ejpam-5478	93	18	temporal	temporal	ADJ
ejpam-5478	93	19	change	change	NOUN
ejpam-5478	93	20	of	of	ADP
ejpam-5478	93	21	the	the	DET
ejpam-5478	93	22	hamiltonian	hamiltonian	NOUN
ejpam-5478	93	23	,	,	PUNCT
ejpam-5478	93	24	which	which	PRON
ejpam-5478	93	25	is	be	AUX
ejpam-5478	93	26	related	relate	VERB
ejpam-5478	93	27	to	to	ADP
ejpam-5478	93	28	the	the	DET
ejpam-5478	93	29	temporal	temporal	ADJ
ejpam-5478	93	30	change	change	NOUN
ejpam-5478	93	31	of	of	ADP
ejpam-5478	93	32	the	the	DET
ejpam-5478	93	33	term	term	NOUN
ejpam-5478	93	34	as	as	SCONJ
ejpam-5478	93	35	:	:	PUNCT
ejpam-5478	93	36	∂h	∂h	PROPN
ejpam-5478	93	37	∂t	∂t	PROPN
ejpam-5478	93	38	=	=	SYM
ejpam-5478	93	39	−	−	PROPN
ejpam-5478	93	40	∂l	∂l	PROPN
ejpam-5478	93	41	∂t′	∂t′	ADV
ejpam-5478	93	42	it	it	PRON
ejpam-5478	93	43	should	should	AUX
ejpam-5478	93	44	be	be	AUX
ejpam-5478	93	45	highlighted	highlight	VERB
ejpam-5478	93	46	that	that	SCONJ
ejpam-5478	93	47	the	the	DET
ejpam-5478	93	48	results	result	NOUN
ejpam-5478	93	49	deduced	deduce	VERB
ejpam-5478	93	50	from	from	ADP
ejpam-5478	93	51	the	the	DET
ejpam-5478	93	52	above	above	ADJ
ejpam-5478	93	53	equations	equation	NOUN
ejpam-5478	93	54	are	be	AUX
ejpam-5478	93	55	closely	closely	ADV
ejpam-5478	93	56	aligned	align	VERB
ejpam-5478	93	57	with	with	ADP
ejpam-5478	93	58	what	what	PRON
ejpam-5478	93	59	is	be	AUX
ejpam-5478	93	60	observed	observe	VERB
ejpam-5478	93	61	in	in	ADP
ejpam-5478	93	62	classical	classical	ADJ
ejpam-5478	93	63	field	field	NOUN
ejpam-5478	93	64	theory	theory	NOUN
ejpam-5478	93	65	,	,	PUNCT
ejpam-5478	93	66	especially	especially	ADV
ejpam-5478	93	67	when	when	SCONJ
ejpam-5478	93	68	dealing	deal	VERB
ejpam-5478	93	69	with	with	ADP
ejpam-5478	93	70	integer	integer	NOUN
ejpam-5478	93	71	orders	order	NOUN
ejpam-5478	93	72	within	within	ADP
ejpam-5478	93	73	equations	equation	NOUN
ejpam-5478	93	74	of	of	ADP
ejpam-5478	93	75	motion	motion	NOUN
ejpam-5478	93	76	.	.	PUNCT
ejpam-5478	94	1	l	l	X
ejpam-5478	94	2	=	=	PUNCT
ejpam-5478	94	3	l(qi	l(qi	PROPN
ejpam-5478	94	4	,	,	PUNCT
ejpam-5478	94	5	d	d	PROPN
ejpam-5478	94	6	α	α	PROPN
ejpam-5478	94	7	t	t	PROPN
ejpam-5478	94	8	qi	qi	PROPN
ejpam-5478	94	9	,	,	PUNCT
ejpam-5478	94	10	d	d	PROPN
ejpam-5478	94	11	2α	2α	PROPN
ejpam-5478	94	12	t	t	PROPN
ejpam-5478	94	13	qi	qi	PROPN
ejpam-5478	94	14	,	,	PUNCT
ejpam-5478	94	15	d	d	PROPN
ejpam-5478	94	16	3α	3α	NUM
ejpam-5478	94	17	t	t	PROPN
ejpam-5478	94	18	qi	qi	PROPN
ejpam-5478	94	19	,	,	PUNCT
ejpam-5478	94	20	·	·	PUNCT
ejpam-5478	94	21	·	·	PUNCT
ejpam-5478	94	22	·	·	PUNCT
ejpam-5478	94	23	,	,	PUNCT
ejpam-5478	94	24	dnα	dnα	AUX
ejpam-5478	94	25	t	t	PROPN
ejpam-5478	94	26	qi	qi	PROPN
ejpam-5478	94	27	,	,	PUNCT
ejpam-5478	94	28	t	t	PROPN
ejpam-5478	94	29	)	)	PUNCT
ejpam-5478	94	30	integrating	integrate	VERB
ejpam-5478	94	31	the	the	DET
ejpam-5478	94	32	lagrangian	lagrangian	ADJ
ejpam-5478	94	33	values	value	NOUN
ejpam-5478	94	34	with	with	ADP
ejpam-5478	94	35	respect	respect	NOUN
ejpam-5478	94	36	to	to	ADP
ejpam-5478	94	37	time	time	NOUN
ejpam-5478	94	38	yields	yield	NOUN
ejpam-5478	94	39	the	the	DET
ejpam-5478	94	40	action	action	NOUN
ejpam-5478	94	41	,	,	PUNCT
ejpam-5478	94	42	which	which	PRON
ejpam-5478	94	43	is	be	AUX
ejpam-5478	94	44	a	a	DET
ejpam-5478	94	45	functional	functional	ADJ
ejpam-5478	94	46	that	that	PRON
ejpam-5478	94	47	describes	describe	VERB
ejpam-5478	94	48	the	the	DET
ejpam-5478	94	49	path	path	NOUN
ejpam-5478	94	50	followed	follow	VERB
ejpam-5478	94	51	in	in	ADP
ejpam-5478	94	52	configuration	configuration	NOUN
ejpam-5478	94	53	space	space	NOUN
ejpam-5478	94	54	,	,	PUNCT
ejpam-5478	94	55	represented	represent	VERB
ejpam-5478	94	56	as	as	ADP
ejpam-5478	94	57	:	:	PUNCT
ejpam-5478	94	58	s	s	PART
ejpam-5478	94	59	=	=	X
ejpam-5478	94	60	∫	∫	PROPN
ejpam-5478	94	61	l(qi	l(qi	PROPN
ejpam-5478	94	62	,	,	PUNCT
ejpam-5478	94	63	d	d	PROPN
ejpam-5478	94	64	α	α	PROPN
ejpam-5478	94	65	t	t	PROPN
ejpam-5478	94	66	qi	qi	PROPN
ejpam-5478	94	67	,	,	PUNCT
ejpam-5478	94	68	d	d	PROPN
ejpam-5478	94	69	2α	2α	PROPN
ejpam-5478	94	70	t	t	PROPN
ejpam-5478	94	71	qi	qi	PROPN
ejpam-5478	94	72	,	,	PUNCT
ejpam-5478	94	73	d	d	PROPN
ejpam-5478	94	74	3α	3α	NUM
ejpam-5478	94	75	t	t	PROPN
ejpam-5478	94	76	qi	qi	PROPN
ejpam-5478	94	77	,	,	PUNCT
ejpam-5478	94	78	·	·	PUNCT
ejpam-5478	94	79	·	·	PUNCT
ejpam-5478	94	80	·	·	PUNCT
ejpam-5478	94	81	,	,	PUNCT
ejpam-5478	94	82	dnα	dnα	PROPN
ejpam-5478	94	83	t	t	PROPN
ejpam-5478	94	84	qi	qi	PROPN
ejpam-5478	94	85	,	,	PUNCT
ejpam-5478	94	86	t)dt	t)dt	PROPN
ejpam-5478	94	87	,	,	PUNCT
ejpam-5478	94	88	the	the	DET
ejpam-5478	94	89	evolution	evolution	NOUN
ejpam-5478	94	90	of	of	ADP
ejpam-5478	94	91	the	the	DET
ejpam-5478	94	92	classical	classical	ADJ
ejpam-5478	94	93	system	system	NOUN
ejpam-5478	94	94	is	be	AUX
ejpam-5478	94	95	determined	determine	VERB
ejpam-5478	94	96	by	by	ADP
ejpam-5478	94	97	solving	solve	VERB
ejpam-5478	94	98	the	the	DET
ejpam-5478	94	99	euler	euler	PROPN
ejpam-5478	94	100	–	–	PUNCT
ejpam-5478	94	101	lagrange	lagrange	NOUN
ejpam-5478	94	102	equations	equation	NOUN
ejpam-5478	94	103	of	of	ADP
ejpam-5478	94	104	motion	motion	NOUN
ejpam-5478	94	105	,	,	PUNCT
ejpam-5478	94	106	which	which	PRON
ejpam-5478	94	107	are	be	AUX
ejpam-5478	94	108	derived	derive	VERB
ejpam-5478	94	109	as	as	SCONJ
ejpam-5478	94	110	follows	follow	VERB
ejpam-5478	94	111	:	:	PUNCT
ejpam-5478	94	112	n∑	n∑	PROPN
ejpam-5478	94	113	i=0	i=0	PROPN
ejpam-5478	94	114	(	(	PUNCT
ejpam-5478	94	115	−1)idiα	−1)idiα	PROPN
ejpam-5478	94	116	t	t	PROPN
ejpam-5478	94	117	(	(	PUNCT
ejpam-5478	94	118	dl	dl	INTJ
ejpam-5478	94	119	dqi	dqi	ADV
ejpam-5478	94	120	)	)	PUNCT
ejpam-5478	94	121	=	=	SYM
ejpam-5478	94	122	0	0	NUM
ejpam-5478	95	1	qi	qi	NOUN
ejpam-5478	95	2	=	=	NOUN
ejpam-5478	95	3	diα	diα	NOUN
ejpam-5478	95	4	t	t	X
ejpam-5478	95	5	q	q	PROPN
ejpam-5478	96	1	i	i	NOUN
ejpam-5478	96	2	=	=	NOUN
ejpam-5478	96	3	1	1	NUM
ejpam-5478	96	4	,	,	PUNCT
ejpam-5478	96	5	2	2	NUM
ejpam-5478	96	6	,	,	PUNCT
ejpam-5478	96	7	3	3	NUM
ejpam-5478	96	8	,	,	PUNCT
ejpam-5478	96	9	·	·	PUNCT
ejpam-5478	96	10	·	·	PUNCT
ejpam-5478	96	11	·	·	PUNCT
ejpam-5478	97	1	the	the	DET
ejpam-5478	97	2	hamiltonian	hamiltonian	ADJ
ejpam-5478	97	3	formulation	formulation	NOUN
ejpam-5478	97	4	is	be	AUX
ejpam-5478	97	5	defined	define	VERB
ejpam-5478	97	6	as	as	SCONJ
ejpam-5478	97	7	follows	follow	VERB
ejpam-5478	97	8	:	:	PUNCT
ejpam-5478	97	9	n∑	n∑	PROPN
ejpam-5478	97	10	i=1	i=1	PROPN
ejpam-5478	97	11	piqi	piqi	NOUN
ejpam-5478	97	12	−	−	PROPN
ejpam-5478	97	13	l	l	NOUN
ejpam-5478	97	14	,	,	PUNCT
ejpam-5478	97	15	qi	qi	PROPN
ejpam-5478	97	16	=	=	SYM
ejpam-5478	97	17	diα	diα	NOUN
ejpam-5478	97	18	t	t	PROPN
ejpam-5478	98	1	q	q	NOUN
ejpam-5478	98	2	,	,	PUNCT
ejpam-5478	98	3	i	i	PRON
ejpam-5478	98	4	=	=	NOUN
ejpam-5478	98	5	1	1	NUM
ejpam-5478	98	6	,	,	PUNCT
ejpam-5478	98	7	2	2	NUM
ejpam-5478	98	8	,	,	PUNCT
ejpam-5478	98	9	3	3	NUM
ejpam-5478	98	10	,	,	PUNCT
ejpam-5478	98	11	·	·	PUNCT
ejpam-5478	98	12	·	·	PUNCT
ejpam-5478	98	13	·	·	PUNCT
ejpam-5478	98	14	when	when	SCONJ
ejpam-5478	98	15	calculating	calculate	VERB
ejpam-5478	98	16	the	the	DET
ejpam-5478	98	17	total	total	ADJ
ejpam-5478	98	18	differential	differential	NOUN
ejpam-5478	98	19	of	of	ADP
ejpam-5478	98	20	the	the	DET
ejpam-5478	98	21	hamiltonian	hamiltonian	NOUN
ejpam-5478	98	22	,	,	PUNCT
ejpam-5478	98	23	we	we	PRON
ejpam-5478	98	24	obtain	obtain	VERB
ejpam-5478	98	25	the	the	DET
ejpam-5478	98	26	following	follow	VERB
ejpam-5478	98	27	result	result	NOUN
ejpam-5478	98	28	.	.	PUNCT
ejpam-5478	99	1	dh	dh	NOUN
ejpam-5478	100	1	=	=	PUNCT
ejpam-5478	100	2	n∑	n∑	PROPN
ejpam-5478	100	3	i=1	i=1	PROPN
ejpam-5478	101	1	pid(d	pid(d	PROPN
ejpam-5478	102	1	iα	iα	INTJ
ejpam-5478	102	2	t	t	PROPN
ejpam-5478	102	3	qi)+(diα	qi)+(diα	PROPN
ejpam-5478	102	4	t	t	NOUN
ejpam-5478	102	5	qi)dpi−	qi)dpi−	VERB
ejpam-5478	102	6	∂l	∂l	PROPN
ejpam-5478	102	7	∂(diα	∂(diα	AUX
ejpam-5478	102	8	t	t	PROPN
ejpam-5478	102	9	qi	qi	PROPN
ejpam-5478	102	10	)	)	PUNCT
ejpam-5478	102	11	d(diα	d(diα	NOUN
ejpam-5478	102	12	t	t	PROPN
ejpam-5478	102	13	qi)−	qi)−	NOUN
ejpam-5478	102	14	∂l	∂l	PROPN
ejpam-5478	102	15	∂qi	∂qi	PROPN
ejpam-5478	102	16	,	,	PUNCT
ejpam-5478	102	17	qi	qi	PROPN
ejpam-5478	102	18	=	=	NOUN
ejpam-5478	102	19	diα	diα	NOUN
ejpam-5478	102	20	t	t	PROPN
ejpam-5478	102	21	q	q	NOUN
ejpam-5478	102	22	,	,	PUNCT
ejpam-5478	102	23	i	i	PRON
ejpam-5478	102	24	=	=	NOUN
ejpam-5478	102	25	1	1	NUM
ejpam-5478	102	26	,	,	PUNCT
ejpam-5478	102	27	2	2	NUM
ejpam-5478	102	28	,	,	PUNCT
ejpam-5478	102	29	3	3	NUM
ejpam-5478	102	30	,	,	PUNCT
ejpam-5478	102	31	·	·	PUNCT
ejpam-5478	102	32	·	·	PUNCT
ejpam-5478	102	33	·	·	PUNCT
ejpam-5478	102	34	(	(	PUNCT
ejpam-5478	102	35	2	2	X
ejpam-5478	102	36	)	)	PUNCT
ejpam-5478	102	37	y.	y.	NOUN
ejpam-5478	102	38	m.	m.	NOUN
ejpam-5478	102	39	alawaideh	alawaideh	PROPN
ejpam-5478	102	40	et	et	PROPN
ejpam-5478	102	41	al	al	PROPN
ejpam-5478	102	42	.	.	PUNCT
ejpam-5478	102	43	/	/	SYM
ejpam-5478	102	44	eur	eur	PROPN
ejpam-5478	102	45	.	.	PUNCT
ejpam-5478	103	1	j.	j.	PROPN
ejpam-5478	103	2	pure	pure	PROPN
ejpam-5478	103	3	appl	appl	PROPN
ejpam-5478	103	4	.	.	PROPN
ejpam-5478	103	5	math	math	PROPN
ejpam-5478	103	6	,	,	PUNCT
ejpam-5478	103	7	18	18	NUM
ejpam-5478	103	8	(	(	PUNCT
ejpam-5478	103	9	1	1	NUM
ejpam-5478	103	10	)	)	PUNCT
ejpam-5478	103	11	(	(	PUNCT
ejpam-5478	103	12	2025	2025	NUM
ejpam-5478	103	13	)	)	PUNCT
ejpam-5478	103	14	,	,	PUNCT
ejpam-5478	103	15	5478	5478	NUM
ejpam-5478	103	16	6	6	NUM
ejpam-5478	103	17	of	of	ADP
ejpam-5478	103	18	14	14	NUM
ejpam-5478	103	19	to	to	PART
ejpam-5478	103	20	provide	provide	VERB
ejpam-5478	103	21	an	an	DET
ejpam-5478	103	22	alternative	alternative	ADJ
ejpam-5478	103	23	perspective	perspective	NOUN
ejpam-5478	103	24	on	on	ADP
ejpam-5478	103	25	the	the	DET
ejpam-5478	103	26	generalized	generalize	VERB
ejpam-5478	103	27	momenta	momenta	NOUN
ejpam-5478	103	28	pi	pi	NOUN
ejpam-5478	103	29	,	,	PUNCT
ejpam-5478	103	30	which	which	PRON
ejpam-5478	103	31	is	be	AUX
ejpam-5478	103	32	linked	link	VERB
ejpam-5478	103	33	to	to	ADP
ejpam-5478	103	34	the	the	DET
ejpam-5478	103	35	expression	expression	NOUN
ejpam-5478	103	36	qi	qi	PROPN
ejpam-5478	103	37	=	=	PUNCT
ejpam-5478	103	38	diα	diα	PROPN
ejpam-5478	103	39	t	t	PROPN
ejpam-5478	104	1	q	q	PROPN
ejpam-5478	104	2	,	,	PUNCT
ejpam-5478	104	3	let	let	VERB
ejpam-5478	104	4	’s	’s	PRON
ejpam-5478	104	5	examine	examine	VERB
ejpam-5478	104	6	the	the	DET
ejpam-5478	104	7	following	follow	VERB
ejpam-5478	104	8	formulation	formulation	NOUN
ejpam-5478	104	9	.	.	PUNCT
ejpam-5478	105	1	we	we	PRON
ejpam-5478	105	2	can	can	AUX
ejpam-5478	105	3	uniquely	uniquely	ADV
ejpam-5478	105	4	present	present	VERB
ejpam-5478	105	5	the	the	DET
ejpam-5478	105	6	generalized	generalized	ADJ
ejpam-5478	105	7	momenta	momenta	NOUN
ejpam-5478	105	8	by	by	ADP
ejpam-5478	105	9	utilizing	utilize	VERB
ejpam-5478	105	10	the	the	DET
ejpam-5478	105	11	equation	equation	NOUN
ejpam-5478	105	12	qi	qi	NOUN
ejpam-5478	105	13	=	=	NOUN
ejpam-5478	105	14	diα	diα	NOUN
ejpam-5478	105	15	t	t	NOUN
ejpam-5478	105	16	q	q	NOUN
ejpam-5478	105	17	:	:	PUNCT
ejpam-5478	105	18	pi	pi	NOUN
ejpam-5478	105	19	=	=	SYM
ejpam-5478	105	20	∂l	∂l	PROPN
ejpam-5478	105	21	∂qi	∂qi	NOUN
ejpam-5478	105	22	=	=	SYM
ejpam-5478	105	23	∂l	∂l	PROPN
ejpam-5478	105	24	∂diα	∂diα	NOUN
ejpam-5478	105	25	t	t	NOUN
ejpam-5478	105	26	q	q	X
ejpam-5478	105	27	(	(	PUNCT
ejpam-5478	105	28	3	3	NUM
ejpam-5478	105	29	)	)	PUNCT
ejpam-5478	105	30	after	after	ADP
ejpam-5478	105	31	substituting	substitute	VERB
ejpam-5478	105	32	the	the	DET
ejpam-5478	105	33	momentum	momentum	NOUN
ejpam-5478	105	34	values	value	NOUN
ejpam-5478	105	35	into	into	ADP
ejpam-5478	105	36	(	(	PUNCT
ejpam-5478	105	37	3	3	NUM
ejpam-5478	105	38	)	)	PUNCT
ejpam-5478	105	39	,	,	PUNCT
ejpam-5478	105	40	we	we	PRON
ejpam-5478	105	41	obtain	obtain	VERB
ejpam-5478	105	42	at	at	ADP
ejpam-5478	105	43	the	the	DET
ejpam-5478	105	44	following	follow	VERB
ejpam-5478	105	45	outcome	outcome	NOUN
ejpam-5478	105	46	:	:	PUNCT
ejpam-5478	106	1	dh	dh	NOUN
ejpam-5478	106	2	=	=	PUNCT
ejpam-5478	106	3	n∑	n∑	PROPN
ejpam-5478	106	4	i=1	i=1	PROPN
ejpam-5478	107	1	diα	diα	NOUN
ejpam-5478	107	2	s|tqd(pi)−	s|tqd(pi)−	NOUN
ejpam-5478	107	3	∂l	∂l	NOUN
ejpam-5478	107	4	∂q	∂q	PROPN
ejpam-5478	107	5	dq	dq	NOUN
ejpam-5478	107	6	−	−	PROPN
ejpam-5478	108	1	∂l	∂l	PROPN
ejpam-5478	109	1	∂t	∂t	PROPN
ejpam-5478	109	2	dt	dt	PROPN
ejpam-5478	109	3	,	,	PUNCT
ejpam-5478	109	4	(	(	PUNCT
ejpam-5478	109	5	4	4	NUM
ejpam-5478	109	6	)	)	PUNCT
ejpam-5478	109	7	by	by	ADP
ejpam-5478	109	8	employing	employ	VERB
ejpam-5478	109	9	the	the	DET
ejpam-5478	109	10	euler	euler	NOUN
ejpam-5478	109	11	-	-	PUNCT
ejpam-5478	109	12	lagrange	lagrange	NOUN
ejpam-5478	109	13	(	(	PUNCT
ejpam-5478	109	14	1	1	NUM
ejpam-5478	109	15	)	)	PUNCT
ejpam-5478	109	16	,	,	PUNCT
ejpam-5478	109	17	we	we	PRON
ejpam-5478	109	18	obtain	obtain	VERB
ejpam-5478	109	19	at	at	ADP
ejpam-5478	109	20	the	the	DET
ejpam-5478	109	21	following	following	ADJ
ejpam-5478	109	22	result	result	NOUN
ejpam-5478	109	23	:	:	PUNCT
ejpam-5478	110	1	−∂l	−∂l	NOUN
ejpam-5478	110	2	∂q	∂q	NOUN
ejpam-5478	110	3	=	=	PUNCT
ejpam-5478	110	4	n∑	n∑	PROPN
ejpam-5478	110	5	i=1	i=1	PROPN
ejpam-5478	111	1	(	(	PUNCT
ejpam-5478	111	2	−1)idiα	−1)idiα	PROPN
ejpam-5478	111	3	s|t	s|t	PROPN
ejpam-5478	111	4	(	(	PUNCT
ejpam-5478	111	5	∂l	∂l	PROPN
ejpam-5478	111	6	∂qi	∂qi	PROPN
ejpam-5478	111	7	)	)	PUNCT
ejpam-5478	112	1	=	=	PUNCT
ejpam-5478	113	1	n∑	n∑	NOUN
ejpam-5478	113	2	i=1	i=1	PROPN
ejpam-5478	113	3	(	(	PUNCT
ejpam-5478	113	4	−1)i	−1)i	X
ejpam-5478	113	5	(	(	PUNCT
ejpam-5478	113	6	∂ipi	∂ipi	ADP
ejpam-5478	113	7	∂ti	∂ti	PROPN
ejpam-5478	113	8	)	)	PUNCT
ejpam-5478	114	1	i	i	PRON
ejpam-5478	114	2	=	=	NOUN
ejpam-5478	114	3	1	1	NUM
ejpam-5478	114	4	,	,	PUNCT
ejpam-5478	114	5	2	2	NUM
ejpam-5478	114	6	,	,	PUNCT
ejpam-5478	114	7	3	3	NUM
ejpam-5478	114	8	,	,	PUNCT
ejpam-5478	114	9	·	·	PUNCT
ejpam-5478	114	10	·	·	PUNCT
ejpam-5478	114	11	·	·	PUNCT
ejpam-5478	114	12	,	,	PUNCT
ejpam-5478	114	13	n.	n.	NOUN
ejpam-5478	114	14	(	(	PUNCT
ejpam-5478	114	15	5	5	NUM
ejpam-5478	114	16	)	)	PUNCT
ejpam-5478	114	17	when	when	SCONJ
ejpam-5478	114	18	we	we	PRON
ejpam-5478	114	19	substitute	substitute	VERB
ejpam-5478	114	20	(	(	PUNCT
ejpam-5478	114	21	5	5	NUM
ejpam-5478	114	22	)	)	PUNCT
ejpam-5478	114	23	with	with	ADP
ejpam-5478	114	24	(	(	PUNCT
ejpam-5478	114	25	4	4	NUM
ejpam-5478	114	26	)	)	PUNCT
ejpam-5478	114	27	,	,	PUNCT
ejpam-5478	114	28	the	the	DET
ejpam-5478	114	29	outcome	outcome	NOUN
ejpam-5478	114	30	is	be	AUX
ejpam-5478	114	31	as	as	SCONJ
ejpam-5478	114	32	follows	follow	VERB
ejpam-5478	114	33	:	:	PUNCT
ejpam-5478	115	1	dh	dh	NOUN
ejpam-5478	115	2	=	=	PUNCT
ejpam-5478	115	3	n∑	n∑	PROPN
ejpam-5478	115	4	i=1	i=1	PROPN
ejpam-5478	116	1	pid(d	pid(d	PROPN
ejpam-5478	116	2	iα	iα	NOUN
ejpam-5478	116	3	s|tqd(pi	s|tqd(pi	NOUN
ejpam-5478	116	4	)	)	PUNCT
ejpam-5478	116	5	)	)	PUNCT
ejpam-5478	117	1	+	+	CCONJ
ejpam-5478	117	2	(	(	PUNCT
ejpam-5478	117	3	−1)i	−1)i	X
ejpam-5478	117	4	(	(	PUNCT
ejpam-5478	117	5	∂ipi	∂ipi	ADP
ejpam-5478	117	6	∂ti	∂ti	PROPN
ejpam-5478	117	7	)	)	PUNCT
ejpam-5478	117	8	dq	dq	PROPN
ejpam-5478	117	9	−diα	−diα	NOUN
ejpam-5478	117	10	s|tldt	s|tldt	NOUN
ejpam-5478	117	11	.	.	PUNCT
ejpam-5478	118	1	(	(	PUNCT
ejpam-5478	118	2	6	6	X
ejpam-5478	118	3	)	)	PUNCT
ejpam-5478	118	4	this	this	PRON
ejpam-5478	118	5	indicates	indicate	VERB
ejpam-5478	118	6	that	that	SCONJ
ejpam-5478	118	7	the	the	DET
ejpam-5478	118	8	hamiltonian	hamiltonian	NOUN
ejpam-5478	118	9	can	can	AUX
ejpam-5478	118	10	be	be	AUX
ejpam-5478	118	11	expressed	express	VERB
ejpam-5478	118	12	in	in	ADP
ejpam-5478	118	13	the	the	DET
ejpam-5478	118	14	following	follow	VERB
ejpam-5478	118	15	manner	manner	NOUN
ejpam-5478	118	16	:	:	PUNCT
ejpam-5478	118	17	h	h	NOUN
ejpam-5478	118	18	=	=	PUNCT
ejpam-5478	118	19	h(q	h(q	ADJ
ejpam-5478	118	20	,	,	PUNCT
ejpam-5478	118	21	pi	pi	PROPN
ejpam-5478	118	22	,	,	PUNCT
ejpam-5478	118	23	t	t	PROPN
ejpam-5478	118	24	)	)	PUNCT
ejpam-5478	118	25	i	i	NOUN
ejpam-5478	119	1	=	=	NOUN
ejpam-5478	119	2	1	1	NUM
ejpam-5478	119	3	,	,	PUNCT
ejpam-5478	119	4	2	2	NUM
ejpam-5478	119	5	,	,	PUNCT
ejpam-5478	119	6	3	3	NUM
ejpam-5478	119	7	,	,	PUNCT
ejpam-5478	119	8	·	·	PUNCT
ejpam-5478	119	9	·	·	PUNCT
ejpam-5478	119	10	·	·	PUNCT
ejpam-5478	119	11	,	,	PUNCT
ejpam-5478	119	12	n.	n.	VERB
ejpam-5478	119	13	the	the	DET
ejpam-5478	119	14	total	total	ADJ
ejpam-5478	119	15	differential	differential	NOUN
ejpam-5478	119	16	of	of	ADP
ejpam-5478	119	17	this	this	DET
ejpam-5478	119	18	function	function	NOUN
ejpam-5478	119	19	is	be	AUX
ejpam-5478	119	20	represented	represent	VERB
ejpam-5478	119	21	as	as	SCONJ
ejpam-5478	119	22	follows	follow	VERB
ejpam-5478	119	23	:	:	PUNCT
ejpam-5478	120	1	dh	dh	NOUN
ejpam-5478	120	2	=	=	SYM
ejpam-5478	120	3	∂h	∂h	PROPN
ejpam-5478	121	1	∂q	∂q	PROPN
ejpam-5478	121	2	∂q	∂q	PROPN
ejpam-5478	122	1	+	+	CCONJ
ejpam-5478	122	2	n∑	n∑	ADJ
ejpam-5478	122	3	i=1	i=1	PROPN
ejpam-5478	123	1	∂h	∂h	PROPN
ejpam-5478	123	2	∂qi	∂qi	PROPN
ejpam-5478	123	3	d(pi	d(pi	NOUN
ejpam-5478	123	4	)	)	PUNCT
ejpam-5478	124	1	+	+	CCONJ
ejpam-5478	125	1	∂h	∂h	PROPN
ejpam-5478	125	2	∂t	∂t	PROPN
ejpam-5478	125	3	dt	dt	PROPN
ejpam-5478	125	4	,	,	PUNCT
ejpam-5478	125	5	(	(	PUNCT
ejpam-5478	125	6	7	7	X
ejpam-5478	125	7	)	)	PUNCT
ejpam-5478	125	8	when	when	SCONJ
ejpam-5478	125	9	we	we	PRON
ejpam-5478	125	10	compare	compare	VERB
ejpam-5478	125	11	(	(	PUNCT
ejpam-5478	125	12	6	6	NUM
ejpam-5478	125	13	)	)	PUNCT
ejpam-5478	125	14	and	and	CCONJ
ejpam-5478	125	15	(	(	PUNCT
ejpam-5478	125	16	7	7	NUM
ejpam-5478	125	17	)	)	PUNCT
ejpam-5478	125	18	,	,	PUNCT
ejpam-5478	125	19	we	we	PRON
ejpam-5478	125	20	can	can	AUX
ejpam-5478	125	21	derive	derive	VERB
ejpam-5478	125	22	the	the	DET
ejpam-5478	125	23	following	follow	VERB
ejpam-5478	125	24	set	set	NOUN
ejpam-5478	125	25	of	of	ADP
ejpam-5478	125	26	hamilton	hamilton	PROPN
ejpam-5478	125	27	’s	’s	PART
ejpam-5478	125	28	equations	equation	NOUN
ejpam-5478	125	29	of	of	ADP
ejpam-5478	125	30	motion	motion	NOUN
ejpam-5478	125	31	.	.	PUNCT
ejpam-5478	126	1	∂h	∂h	PROPN
ejpam-5478	126	2	∂q	∂q	PROPN
ejpam-5478	126	3	=	=	PUNCT
ejpam-5478	126	4	n∑	n∑	PROPN
ejpam-5478	127	1	i=1	i=1	PROPN
ejpam-5478	127	2	(	(	PUNCT
ejpam-5478	127	3	−1)ipi	−1)ipi	PROPN
ejpam-5478	127	4	,	,	PUNCT
ejpam-5478	127	5	diα	diα	NOUN
ejpam-5478	127	6	s|t	s|t	PUNCT
ejpam-5478	128	1	=	=	PUNCT
ejpam-5478	129	1	∂h	∂h	PROPN
ejpam-5478	129	2	∂pi	∂pi	NOUN
ejpam-5478	129	3	,	,	PUNCT
ejpam-5478	129	4	to	to	PART
ejpam-5478	129	5	further	far	ADV
ejpam-5478	129	6	establish	establish	VERB
ejpam-5478	129	7	the	the	DET
ejpam-5478	129	8	validity	validity	NOUN
ejpam-5478	129	9	of	of	ADP
ejpam-5478	129	10	our	our	PRON
ejpam-5478	129	11	method	method	NOUN
ejpam-5478	129	12	for	for	ADP
ejpam-5478	129	13	handling	handle	VERB
ejpam-5478	129	14	high	high	ADJ
ejpam-5478	129	15	-	-	PUNCT
ejpam-5478	129	16	order	order	NOUN
ejpam-5478	129	17	derivatives	derivative	NOUN
ejpam-5478	129	18	,	,	PUNCT
ejpam-5478	129	19	we	we	PRON
ejpam-5478	129	20	will	will	AUX
ejpam-5478	129	21	provide	provide	VERB
ejpam-5478	129	22	two	two	NUM
ejpam-5478	129	23	examples	example	NOUN
ejpam-5478	129	24	of	of	ADP
ejpam-5478	129	25	generalized	generalized	ADJ
ejpam-5478	129	26	conformable	conformable	ADJ
ejpam-5478	129	27	derivative	derivative	ADJ
ejpam-5478	129	28	concepts	concept	NOUN
ejpam-5478	129	29	.	.	PUNCT
ejpam-5478	130	1	these	these	DET
ejpam-5478	130	2	examples	example	NOUN
ejpam-5478	130	3	will	will	AUX
ejpam-5478	130	4	serve	serve	VERB
ejpam-5478	130	5	to	to	PART
ejpam-5478	130	6	introduce	introduce	VERB
ejpam-5478	130	7	and	and	CCONJ
ejpam-5478	130	8	clarify	clarify	VERB
ejpam-5478	130	9	the	the	DET
ejpam-5478	130	10	application	application	NOUN
ejpam-5478	130	11	of	of	ADP
ejpam-5478	130	12	these	these	DET
ejpam-5478	130	13	concepts	concept	NOUN
ejpam-5478	130	14	in	in	ADP
ejpam-5478	130	15	supporting	support	VERB
ejpam-5478	130	16	our	our	PRON
ejpam-5478	130	17	approach	approach	NOUN
ejpam-5478	130	18	.	.	PUNCT
ejpam-5478	131	1	in	in	ADP
ejpam-5478	131	2	this	this	DET
ejpam-5478	131	3	context	context	NOUN
ejpam-5478	131	4	,	,	PUNCT
ejpam-5478	131	5	the	the	DET
ejpam-5478	131	6	path	path	NOUN
ejpam-5478	131	7	integral	integral	ADJ
ejpam-5478	131	8	quantization	quantization	NOUN
ejpam-5478	131	9	is	be	AUX
ejpam-5478	131	10	given	give	VERB
ejpam-5478	131	11	as	as	SCONJ
ejpam-5478	131	12	follows	follow	VERB
ejpam-5478	131	13	:	:	PUNCT
ejpam-5478	131	14	k	k	PROPN
ejpam-5478	131	15	=	=	SYM
ejpam-5478	131	16	∫	∫	PROPN
ejpam-5478	131	17	dpdqei	dpdqei	VERB
ejpam-5478	131	18	∑n	∑n	PROPN
ejpam-5478	131	19	k=1(pkq	k=1(pkq	PROPN
ejpam-5478	131	20	k−h(q	k−h(q	PROPN
ejpam-5478	131	21	,	,	PUNCT
ejpam-5478	131	22	qk	qk	INTJ
ejpam-5478	131	23	,	,	PUNCT
ejpam-5478	131	24	t)dt	t)dt	PROPN
ejpam-5478	131	25	for	for	ADP
ejpam-5478	131	26	quadratic	quadratic	ADJ
ejpam-5478	131	27	h(q	h(q	ADV
ejpam-5478	131	28	,	,	PUNCT
ejpam-5478	131	29	qk	qk	INTJ
ejpam-5478	131	30	,	,	PUNCT
ejpam-5478	131	31	t	t	PROPN
ejpam-5478	131	32	)	)	PUNCT
ejpam-5478	131	33	in	in	ADP
ejpam-5478	131	34	terms	term	NOUN
ejpam-5478	131	35	of	of	ADP
ejpam-5478	131	36	pk	pk	NOUN
ejpam-5478	131	37	,	,	PUNCT
ejpam-5478	131	38	and	and	CCONJ
ejpam-5478	131	39	after	after	ADP
ejpam-5478	131	40	integration	integration	NOUN
ejpam-5478	131	41	over	over	ADP
ejpam-5478	131	42	the	the	DET
ejpam-5478	131	43	momenta	momenta	ADJ
ejpam-5478	131	44	pk	pk	NOUN
ejpam-5478	131	45	we	we	PRON
ejpam-5478	131	46	obtain	obtain	VERB
ejpam-5478	131	47	:	:	PUNCT
ejpam-5478	131	48	y.	y.	PROPN
ejpam-5478	131	49	m.	m.	PROPN
ejpam-5478	131	50	alawaideh	alawaideh	PROPN
ejpam-5478	131	51	et	et	PROPN
ejpam-5478	131	52	al	al	PROPN
ejpam-5478	131	53	.	.	PUNCT
ejpam-5478	131	54	/	/	SYM
ejpam-5478	131	55	eur	eur	PROPN
ejpam-5478	131	56	.	.	PUNCT
ejpam-5478	132	1	j.	j.	PROPN
ejpam-5478	132	2	pure	pure	PROPN
ejpam-5478	132	3	appl	appl	PROPN
ejpam-5478	132	4	.	.	PROPN
ejpam-5478	132	5	math	math	PROPN
ejpam-5478	132	6	,	,	PUNCT
ejpam-5478	132	7	18	18	NUM
ejpam-5478	132	8	(	(	PUNCT
ejpam-5478	132	9	1	1	NUM
ejpam-5478	132	10	)	)	PUNCT
ejpam-5478	132	11	(	(	PUNCT
ejpam-5478	132	12	2025	2025	NUM
ejpam-5478	132	13	)	)	PUNCT
ejpam-5478	132	14	,	,	PUNCT
ejpam-5478	132	15	5478	5478	NUM
ejpam-5478	132	16	7	7	NUM
ejpam-5478	132	17	of	of	ADP
ejpam-5478	132	18	14	14	NUM
ejpam-5478	132	19	k	k	NOUN
ejpam-5478	132	20	=	=	SYM
ejpam-5478	132	21	∫	∫	PROPN
ejpam-5478	133	1	dqei	dqei	PROPN
ejpam-5478	133	2	∫	∫	PROPN
ejpam-5478	133	3	ldt	ldt	PROPN
ejpam-5478	133	4	one	one	PRON
ejpam-5478	133	5	should	should	AUX
ejpam-5478	133	6	notice	notice	VERB
ejpam-5478	133	7	that	that	SCONJ
ejpam-5478	133	8	the	the	DET
ejpam-5478	133	9	path	path	NOUN
ejpam-5478	133	10	integral	integral	ADJ
ejpam-5478	133	11	quantization	quantization	NOUN
ejpam-5478	133	12	is	be	AUX
ejpam-5478	133	13	obtained	obtain	VERB
ejpam-5478	133	14	as	as	ADP
ejpam-5478	133	15	an	an	DET
ejpam-5478	133	16	integration	integration	NOUN
ejpam-5478	133	17	over	over	ADP
ejpam-5478	133	18	the	the	DET
ejpam-5478	133	19	canonical	canonical	ADJ
ejpam-5478	133	20	coordinates	coordinate	NOUN
ejpam-5478	133	21	qi	qi	PROPN
ejpam-5478	133	22	without	without	ADP
ejpam-5478	133	23	any	any	DET
ejpam-5478	133	24	need	need	NOUN
ejpam-5478	133	25	to	to	PART
ejpam-5478	133	26	integrate	integrate	VERB
ejpam-5478	133	27	over	over	ADP
ejpam-5478	133	28	higher	high	ADJ
ejpam-5478	133	29	order	order	NOUN
ejpam-5478	133	30	derivatives	derivative	NOUN
ejpam-5478	133	31	(	(	PUNCT
ejpam-5478	133	32	qi	qi	NOUN
ejpam-5478	133	33	,	,	PUNCT
ejpam-5478	133	34	ql	ql	PROPN
ejpam-5478	133	35	)	)	PUNCT
ejpam-5478	133	36	as	as	SCONJ
ejpam-5478	133	37	given	give	VERB
ejpam-5478	133	38	by	by	ADP
ejpam-5478	133	39	ostrogradskii	ostrogradskii	ADJ
ejpam-5478	133	40	formulation	formulation	NOUN
ejpam-5478	133	41	.	.	PUNCT
ejpam-5478	134	1	4	4	X
ejpam-5478	134	2	.	.	X
ejpam-5478	134	3	generalized	generalize	VERB
ejpam-5478	134	4	conformable	conformable	ADJ
ejpam-5478	134	5	fractional	fractional	ADJ
ejpam-5478	134	6	higher	high	ADJ
ejpam-5478	134	7	-	-	PUNCT
ejpam-5478	134	8	order	order	NOUN
ejpam-5478	134	9	derivatives	derivative	NOUN
ejpam-5478	134	10	classical	classical	ADJ
ejpam-5478	134	11	mechanics	mechanic	NOUN
ejpam-5478	134	12	describes	describe	VERB
ejpam-5478	134	13	the	the	DET
ejpam-5478	134	14	motion	motion	NOUN
ejpam-5478	134	15	of	of	ADP
ejpam-5478	134	16	particles	particle	NOUN
ejpam-5478	134	17	and	and	CCONJ
ejpam-5478	134	18	systems	system	NOUN
ejpam-5478	134	19	under	under	ADP
ejpam-5478	134	20	forces	force	NOUN
ejpam-5478	134	21	,	,	PUNCT
ejpam-5478	134	22	often	often	ADV
ejpam-5478	134	23	described	describe	VERB
ejpam-5478	134	24	by	by	ADP
ejpam-5478	134	25	a	a	DET
ejpam-5478	134	26	lagrangian	lagrangian	ADJ
ejpam-5478	134	27	function	function	NOUN
ejpam-5478	134	28	.	.	PUNCT
ejpam-5478	135	1	recent	recent	ADJ
ejpam-5478	135	2	interest	interest	NOUN
ejpam-5478	135	3	in	in	ADP
ejpam-5478	135	4	incorporating	incorporate	VERB
ejpam-5478	135	5	fractional	fractional	ADJ
ejpam-5478	135	6	derivatives	derivative	NOUN
ejpam-5478	135	7	has	have	AUX
ejpam-5478	135	8	led	lead	VERB
ejpam-5478	135	9	to	to	ADP
ejpam-5478	135	10	the	the	DET
ejpam-5478	135	11	development	development	NOUN
ejpam-5478	135	12	of	of	ADP
ejpam-5478	135	13	fractional	fractional	ADJ
ejpam-5478	135	14	mechanics	mechanic	NOUN
ejpam-5478	135	15	,	,	PUNCT
ejpam-5478	135	16	using	use	VERB
ejpam-5478	135	17	conformable	conformable	ADJ
ejpam-5478	135	18	derivatives	derivative	NOUN
ejpam-5478	135	19	.	.	PUNCT
ejpam-5478	136	1	this	this	DET
ejpam-5478	136	2	work	work	NOUN
ejpam-5478	136	3	builds	build	VERB
ejpam-5478	136	4	upon	upon	SCONJ
ejpam-5478	136	5	fractional	fractional	ADJ
ejpam-5478	136	6	mechanics	mechanic	NOUN
ejpam-5478	136	7	and	and	CCONJ
ejpam-5478	136	8	conformable	conformable	ADJ
ejpam-5478	136	9	derivatives	derivative	NOUN
ejpam-5478	136	10	to	to	PART
ejpam-5478	136	11	derive	derive	VERB
ejpam-5478	136	12	a	a	DET
ejpam-5478	136	13	generalized	generalized	ADJ
ejpam-5478	136	14	form	form	NOUN
ejpam-5478	136	15	of	of	ADP
ejpam-5478	136	16	euler	euler	NOUN
ejpam-5478	136	17	-	-	PUNCT
ejpam-5478	136	18	lagrange	lagrange	NOUN
ejpam-5478	136	19	equations	equation	NOUN
ejpam-5478	136	20	for	for	ADP
ejpam-5478	136	21	higher	high	ADJ
ejpam-5478	136	22	order	order	NOUN
ejpam-5478	136	23	conformable	conformable	ADJ
ejpam-5478	136	24	derivatives	derivative	NOUN
ejpam-5478	136	25	,	,	PUNCT
ejpam-5478	136	26	establishing	establish	VERB
ejpam-5478	136	27	energy	energy	NOUN
ejpam-5478	136	28	and	and	CCONJ
ejpam-5478	136	29	momentum	momentum	NOUN
ejpam-5478	136	30	conservation	conservation	NOUN
ejpam-5478	136	31	in	in	ADP
ejpam-5478	136	32	the	the	DET
ejpam-5478	136	33	presence	presence	NOUN
ejpam-5478	136	34	of	of	ADP
ejpam-5478	136	35	time	time	NOUN
ejpam-5478	136	36	independence	independence	NOUN
ejpam-5478	136	37	and	and	CCONJ
ejpam-5478	136	38	translational	translational	ADJ
ejpam-5478	136	39	invariance	invariance	NOUN
ejpam-5478	136	40	of	of	ADP
ejpam-5478	136	41	the	the	DET
ejpam-5478	136	42	lagrangian	lagrangian	ADJ
ejpam-5478	136	43	[	[	X
ejpam-5478	136	44	26	26	NUM
ejpam-5478	136	45	]	]	PUNCT
ejpam-5478	136	46	.	.	PUNCT
ejpam-5478	137	1	let	let	VERB
ejpam-5478	137	2	’s	’s	NOUN
ejpam-5478	137	3	begin	begin	VERB
ejpam-5478	137	4	by	by	ADP
ejpam-5478	137	5	revisiting	revisit	VERB
ejpam-5478	137	6	some	some	DET
ejpam-5478	137	7	fundamental	fundamental	ADJ
ejpam-5478	137	8	concepts	concept	NOUN
ejpam-5478	137	9	regarding	regard	VERB
ejpam-5478	137	10	theories	theory	NOUN
ejpam-5478	137	11	involving	involve	VERB
ejpam-5478	137	12	particles	particle	NOUN
ejpam-5478	137	13	in	in	ADP
ejpam-5478	137	14	one	one	NUM
ejpam-5478	137	15	dimensional	dimensional	ADJ
ejpam-5478	137	16	motion	motion	NOUN
ejpam-5478	137	17	.	.	PUNCT
ejpam-5478	138	1	these	these	DET
ejpam-5478	138	2	theories	theory	NOUN
ejpam-5478	138	3	are	be	AUX
ejpam-5478	138	4	described	describe	VERB
ejpam-5478	138	5	by	by	ADP
ejpam-5478	138	6	a	a	DET
ejpam-5478	138	7	lagrangian	lagrangian	ADJ
ejpam-5478	138	8	function	function	NOUN
ejpam-5478	138	9	denoted	denote	VERB
ejpam-5478	138	10	as	as	ADP
ejpam-5478	138	11	”	"	PUNCT
ejpam-5478	138	12	l	l	NOUN
ejpam-5478	138	13	”	"	PUNCT
ejpam-5478	138	14	which	which	PRON
ejpam-5478	138	15	depends	depend	VERB
ejpam-5478	138	16	on	on	ADP
ejpam-5478	138	17	variables	variable	NOUN
ejpam-5478	138	18	like	like	ADP
ejpam-5478	138	19	position	position	NOUN
ejpam-5478	138	20	(	(	PUNCT
ejpam-5478	138	21	x	x	NOUN
ejpam-5478	138	22	)	)	PUNCT
ejpam-5478	138	23	,	,	PUNCT
ejpam-5478	138	24	velocity	velocity	NOUN
ejpam-5478	138	25	(	(	PUNCT
ejpam-5478	138	26	dα	dα	DET
ejpam-5478	138	27	s|tx	s|tx	NOUN
ejpam-5478	138	28	)	)	PUNCT
ejpam-5478	138	29	,	,	PUNCT
ejpam-5478	138	30	and	and	CCONJ
ejpam-5478	138	31	acceleration	acceleration	NOUN
ejpam-5478	138	32	(	(	PUNCT
ejpam-5478	138	33	d2α	d2α	NOUN
ejpam-5478	138	34	s|tx	s|tx	NOUN
ejpam-5478	138	35	)	)	PUNCT
ejpam-5478	138	36	)	)	PUNCT
ejpam-5478	138	37	at	at	ADP
ejpam-5478	138	38	a	a	DET
ejpam-5478	138	39	given	give	VERB
ejpam-5478	138	40	time	time	NOUN
ejpam-5478	138	41	(	(	PUNCT
ejpam-5478	138	42	t	t	NOUN
ejpam-5478	138	43	)	)	PUNCT
ejpam-5478	138	44	.	.	PUNCT
ejpam-5478	139	1	δl−	δl−	NOUN
ejpam-5478	139	2	δt	δt	X
ejpam-5478	140	1	∂l	∂l	PROPN
ejpam-5478	140	2	∂t	∂t	PROPN
ejpam-5478	140	3	=	=	PUNCT
ejpam-5478	140	4	δqi	δqi	PROPN
ejpam-5478	141	1	∂l	∂l	PROPN
ejpam-5478	141	2	∂qi	∂qi	PROPN
ejpam-5478	141	3	+	+	NUM
ejpam-5478	141	4	δdα	δdα	PROPN
ejpam-5478	141	5	t	t	PROPN
ejpam-5478	141	6	qi	qi	PROPN
ejpam-5478	141	7	∂l	∂l	PROPN
ejpam-5478	141	8	∂dα	∂dα	PROPN
ejpam-5478	141	9	t	t	PROPN
ejpam-5478	141	10	qi	qi	PROPN
ejpam-5478	141	11	+	+	PROPN
ejpam-5478	141	12	δd2α	δd2α	PROPN
ejpam-5478	141	13	t	t	NOUN
ejpam-5478	141	14	qi	qi	PROPN
ejpam-5478	141	15	∂l	∂l	PROPN
ejpam-5478	141	16	∂d2α	∂d2α	PROPN
ejpam-5478	141	17	t	t	PROPN
ejpam-5478	141	18	qi	qi	PROPN
ejpam-5478	141	19	=	=	SYM
ejpam-5478	141	20	δqi	δqi	PROPN
ejpam-5478	141	21	(	(	PUNCT
ejpam-5478	141	22	∂l	∂l	PROPN
ejpam-5478	142	1	∂qi	∂qi	PROPN
ejpam-5478	142	2	−	−	NOUN
ejpam-5478	143	1	d	d	NOUN
ejpam-5478	143	2	dt	dt	NOUN
ejpam-5478	144	1	∂l	∂l	PROPN
ejpam-5478	144	2	∂dα	∂dα	PROPN
ejpam-5478	144	3	t	t	PROPN
ejpam-5478	144	4	qi	qi	PROPN
ejpam-5478	144	5	+	+	CCONJ
ejpam-5478	144	6	d2	d2	PROPN
ejpam-5478	144	7	dt2	dt2	PROPN
ejpam-5478	144	8	∂l	∂l	PROPN
ejpam-5478	144	9	∂d2α	∂d2α	PROPN
ejpam-5478	144	10	t	t	PROPN
ejpam-5478	144	11	qi	qi	PROPN
ejpam-5478	144	12	)	)	PUNCT
ejpam-5478	145	1	+	+	CCONJ
ejpam-5478	145	2	d	d	X
ejpam-5478	145	3	dt	dt	X
ejpam-5478	145	4	(	(	PUNCT
ejpam-5478	145	5	δqi	δqi	PROPN
ejpam-5478	145	6	∂l	∂l	PROPN
ejpam-5478	145	7	∂dα	∂dα	PROPN
ejpam-5478	145	8	t	t	PROPN
ejpam-5478	145	9	qi	qi	PROPN
ejpam-5478	145	10	+	+	CCONJ
ejpam-5478	145	11	δdα	δdα	PROPN
ejpam-5478	145	12	t	t	PROPN
ejpam-5478	145	13	qi	qi	PROPN
ejpam-5478	145	14	∂l	∂l	PROPN
ejpam-5478	145	15	∂d2α	∂d2α	PROPN
ejpam-5478	145	16	t	t	PROPN
ejpam-5478	145	17	qi	qi	PROPN
ejpam-5478	145	18	−	−	PROPN
ejpam-5478	145	19	δqi	δqi	PROPN
ejpam-5478	146	1	d	d	NOUN
ejpam-5478	146	2	dt	dt	X
ejpam-5478	147	1	∂l	∂l	PROPN
ejpam-5478	147	2	∂d2α	∂d2α	PROPN
ejpam-5478	147	3	t	t	PROPN
ejpam-5478	147	4	qi	qi	PROPN
ejpam-5478	147	5	)	)	PUNCT
ejpam-5478	147	6	.	.	PUNCT
ejpam-5478	148	1	therefore	therefore	ADV
ejpam-5478	148	2	,	,	PUNCT
ejpam-5478	148	3	the	the	DET
ejpam-5478	148	4	equation	equation	NOUN
ejpam-5478	148	5	of	of	ADP
ejpam-5478	148	6	motion	motion	NOUN
ejpam-5478	148	7	is	be	AUX
ejpam-5478	148	8	as	as	SCONJ
ejpam-5478	148	9	follows	follow	VERB
ejpam-5478	148	10	:	:	PUNCT
ejpam-5478	148	11	∂l	∂l	PROPN
ejpam-5478	148	12	∂qi	∂qi	PROPN
ejpam-5478	148	13	−dα	−dα	PROPN
ejpam-5478	148	14	t	t	PROPN
ejpam-5478	148	15	∂l	∂l	PROPN
ejpam-5478	148	16	∂dα	∂dα	PROPN
ejpam-5478	148	17	t	t	PROPN
ejpam-5478	148	18	qi	qi	PROPN
ejpam-5478	148	19	+	+	PROPN
ejpam-5478	149	1	d2α	d2α	PROPN
ejpam-5478	149	2	t	t	NOUN
ejpam-5478	149	3	∂l	∂l	PROPN
ejpam-5478	149	4	∂d2α	∂d2α	PROPN
ejpam-5478	149	5	t	t	NOUN
ejpam-5478	149	6	qi	qi	PROPN
ejpam-5478	149	7	=	=	SYM
ejpam-5478	149	8	0	0	NUM
ejpam-5478	150	1	(	(	PUNCT
ejpam-5478	150	2	8)	8)	NUM
ejpam-5478	150	3	this	this	PRON
ejpam-5478	150	4	aligns	align	VERB
ejpam-5478	150	5	with	with	ADP
ejpam-5478	150	6	the	the	DET
ejpam-5478	150	7	euler	euler	NOUN
ejpam-5478	150	8	-	-	PUNCT
ejpam-5478	150	9	lagrange	lagrange	PROPN
ejpam-5478	150	10	outcome	outcome	NOUN
ejpam-5478	150	11	(	(	PUNCT
ejpam-5478	150	12	refer	refer	VERB
ejpam-5478	150	13	to	to	ADP
ejpam-5478	150	14	(	(	PUNCT
ejpam-5478	150	15	1	1	NUM
ejpam-5478	150	16	)	)	PUNCT
ejpam-5478	150	17	)	)	PUNCT
ejpam-5478	150	18	.	.	PUNCT
ejpam-5478	151	1	through	through	ADP
ejpam-5478	151	2	the	the	DET
ejpam-5478	151	3	utilization	utilization	NOUN
ejpam-5478	151	4	of	of	ADP
ejpam-5478	151	5	fractional	fractional	ADJ
ejpam-5478	151	6	calculus	calculus	NOUN
ejpam-5478	151	7	in	in	ADP
ejpam-5478	151	8	the	the	DET
ejpam-5478	151	9	preservation	preservation	NOUN
ejpam-5478	151	10	principles	principle	NOUN
ejpam-5478	151	11	of	of	ADP
ejpam-5478	151	12	classical	classical	ADJ
ejpam-5478	151	13	mechanics	mechanic	NOUN
ejpam-5478	151	14	,	,	PUNCT
ejpam-5478	151	15	with	with	ADP
ejpam-5478	151	16	a	a	DET
ejpam-5478	151	17	particular	particular	ADJ
ejpam-5478	151	18	emphasis	emphasis	NOUN
ejpam-5478	151	19	on	on	ADP
ejpam-5478	151	20	fractional	fractional	ADJ
ejpam-5478	151	21	energy	energy	NOUN
ejpam-5478	151	22	and	and	CCONJ
ejpam-5478	151	23	momentum	momentum	NOUN
ejpam-5478	151	24	,	,	PUNCT
ejpam-5478	151	25	we	we	PRON
ejpam-5478	151	26	establish	establish	VERB
ejpam-5478	151	27	what	what	PRON
ejpam-5478	151	28	we	we	PRON
ejpam-5478	151	29	term	term	VERB
ejpam-5478	151	30	fractional	fractional	ADJ
ejpam-5478	151	31	mechanics	mechanic	NOUN
ejpam-5478	151	32	.	.	PUNCT
ejpam-5478	152	1	within	within	ADP
ejpam-5478	152	2	this	this	DET
ejpam-5478	152	3	framework	framework	NOUN
ejpam-5478	152	4	,	,	PUNCT
ejpam-5478	152	5	we	we	PRON
ejpam-5478	152	6	reassess	reassess	VERB
ejpam-5478	152	7	the	the	DET
ejpam-5478	152	8	equation	equation	NOUN
ejpam-5478	152	9	of	of	ADP
ejpam-5478	152	10	motion	motion	NOUN
ejpam-5478	152	11	.	.	PUNCT
ejpam-5478	153	1	diα	diα	NOUN
ejpam-5478	153	2	s|t	s|t	PROPN
ejpam-5478	154	1	(	(	PUNCT
ejpam-5478	154	2	l−dα	l−dα	PROPN
ejpam-5478	154	3	t	t	PROPN
ejpam-5478	154	4	qi	qi	NOUN
ejpam-5478	154	5	∂l	∂l	PROPN
ejpam-5478	154	6	∂dα	∂dα	PROPN
ejpam-5478	154	7	t	t	PROPN
ejpam-5478	154	8	qi	qi	PROPN
ejpam-5478	154	9	−d2α	−d2α	PROPN
ejpam-5478	154	10	t	t	PROPN
ejpam-5478	154	11	qi	qi	PROPN
ejpam-5478	154	12	∂l	∂l	PROPN
ejpam-5478	154	13	∂d2α	∂d2α	PROPN
ejpam-5478	154	14	t	t	PROPN
ejpam-5478	154	15	qi	qi	PROPN
ejpam-5478	155	1	+	+	PROPN
ejpam-5478	155	2	dα	dα	PROPN
ejpam-5478	155	3	t	t	NOUN
ejpam-5478	155	4	qi	qi	PROPN
ejpam-5478	156	1	d	d	NOUN
ejpam-5478	156	2	dt	dt	X
ejpam-5478	157	1	∂l	∂l	PROPN
ejpam-5478	157	2	∂dα	∂dα	PROPN
ejpam-5478	157	3	t	t	PROPN
ejpam-5478	157	4	qi	qi	PROPN
ejpam-5478	157	5	)	)	PUNCT
ejpam-5478	158	1	=	=	PUNCT
ejpam-5478	159	1	∂l	∂l	PROPN
ejpam-5478	159	2	∂t	∂t	PROPN
ejpam-5478	159	3	when	when	SCONJ
ejpam-5478	159	4	the	the	DET
ejpam-5478	159	5	lagrangian	lagrangian	ADJ
ejpam-5478	159	6	remains	remain	VERB
ejpam-5478	159	7	constant	constant	ADJ
ejpam-5478	159	8	over	over	ADP
ejpam-5478	159	9	time	time	NOUN
ejpam-5478	159	10	,	,	PUNCT
ejpam-5478	159	11	indicating	indicate	VERB
ejpam-5478	159	12	its	its	PRON
ejpam-5478	159	13	time	time	NOUN
ejpam-5478	159	14	independence	independence	NOUN
ejpam-5478	159	15	,	,	PUNCT
ejpam-5478	159	16	it	it	PRON
ejpam-5478	159	17	implies	imply	VERB
ejpam-5478	159	18	the	the	DET
ejpam-5478	159	19	existence	existence	NOUN
ejpam-5478	159	20	of	of	ADP
ejpam-5478	159	21	a	a	DET
ejpam-5478	159	22	conserved	conserve	VERB
ejpam-5478	159	23	quantity	quantity	NOUN
ejpam-5478	159	24	known	know	VERB
ejpam-5478	159	25	as	as	ADP
ejpam-5478	159	26	energy	energy	NOUN
ejpam-5478	159	27	.	.	PUNCT
ejpam-5478	160	1	consequently	consequently	ADV
ejpam-5478	160	2	,	,	PUNCT
ejpam-5478	160	3	the	the	DET
ejpam-5478	160	4	total	total	ADJ
ejpam-5478	160	5	y.	y.	PROPN
ejpam-5478	160	6	m.	m.	NOUN
ejpam-5478	160	7	alawaideh	alawaideh	PROPN
ejpam-5478	160	8	et	et	PROPN
ejpam-5478	160	9	al	al	PROPN
ejpam-5478	160	10	.	.	PUNCT
ejpam-5478	160	11	/	/	SYM
ejpam-5478	160	12	eur	eur	PROPN
ejpam-5478	160	13	.	.	PUNCT
ejpam-5478	161	1	j.	j.	PROPN
ejpam-5478	161	2	pure	pure	PROPN
ejpam-5478	161	3	appl	appl	PROPN
ejpam-5478	161	4	.	.	PROPN
ejpam-5478	161	5	math	math	PROPN
ejpam-5478	161	6	,	,	PUNCT
ejpam-5478	161	7	18	18	NUM
ejpam-5478	161	8	(	(	PUNCT
ejpam-5478	161	9	1	1	NUM
ejpam-5478	161	10	)	)	PUNCT
ejpam-5478	161	11	(	(	PUNCT
ejpam-5478	161	12	2025	2025	NUM
ejpam-5478	161	13	)	)	PUNCT
ejpam-5478	161	14	,	,	PUNCT
ejpam-5478	161	15	5478	5478	NUM
ejpam-5478	161	16	8	8	NUM
ejpam-5478	161	17	of	of	ADP
ejpam-5478	161	18	14	14	NUM
ejpam-5478	161	19	energy	energy	NOUN
ejpam-5478	161	20	remains	remain	VERB
ejpam-5478	161	21	constant	constant	ADJ
ejpam-5478	161	22	as	as	SCONJ
ejpam-5478	161	23	time	time	NOUN
ejpam-5478	161	24	progresses	progress	NOUN
ejpam-5478	161	25	.	.	PUNCT
ejpam-5478	162	1	e	e	X
ejpam-5478	162	2	=	=	NOUN
ejpam-5478	162	3	dα	dα	ADJ
ejpam-5478	162	4	s|tqi	s|tqi	NOUN
ejpam-5478	162	5	∂l	∂l	PROPN
ejpam-5478	162	6	∂dα	∂dα	PROPN
ejpam-5478	162	7	s|tqi	s|tqi	PROPN
ejpam-5478	163	1	+	+	NOUN
ejpam-5478	163	2	d2α	d2α	PROPN
ejpam-5478	163	3	s|tqi	s|tqi	ADJ
ejpam-5478	163	4	∂l	∂l	PROPN
ejpam-5478	163	5	∂d2α	∂d2α	PROPN
ejpam-5478	163	6	s|tqi	s|tqi	PROPN
ejpam-5478	163	7	−dα	−dα	VERB
ejpam-5478	163	8	s|tqi	s|tqi	PROPN
ejpam-5478	164	1	d	d	NOUN
ejpam-5478	164	2	dt	dt	NOUN
ejpam-5478	164	3	∂l	∂l	PROPN
ejpam-5478	164	4	∂dα	∂dα	PROPN
ejpam-5478	164	5	s|tqi	s|tqi	PROPN
ejpam-5478	164	6	−	−	PROPN
ejpam-5478	164	7	l	l	NOUN
ejpam-5478	164	8	in	in	ADP
ejpam-5478	164	9	the	the	DET
ejpam-5478	164	10	presence	presence	NOUN
ejpam-5478	164	11	of	of	ADP
ejpam-5478	164	12	translational	translational	ADJ
ejpam-5478	164	13	invariance	invariance	NOUN
ejpam-5478	164	14	within	within	ADP
ejpam-5478	164	15	the	the	DET
ejpam-5478	164	16	lagrangian	lagrangian	ADJ
ejpam-5478	164	17	∂l	∂l	NOUN
ejpam-5478	164	18	∂qi	∂qi	PROPN
ejpam-5478	164	19	=	=	SYM
ejpam-5478	164	20	0	0	NUM
ejpam-5478	164	21	,	,	PUNCT
ejpam-5478	164	22	we	we	PRON
ejpam-5478	164	23	anticipate	anticipate	VERB
ejpam-5478	164	24	the	the	DET
ejpam-5478	164	25	conservation	conservation	NOUN
ejpam-5478	164	26	of	of	ADP
ejpam-5478	164	27	momentum	momentum	NOUN
ejpam-5478	164	28	.	.	PUNCT
ejpam-5478	165	1	considering	consider	VERB
ejpam-5478	165	2	the	the	DET
ejpam-5478	165	3	equation	equation	NOUN
ejpam-5478	165	4	for	for	ADP
ejpam-5478	165	5	the	the	DET
ejpam-5478	165	6	equation	equation	NOUN
ejpam-5478	165	7	of	of	ADP
ejpam-5478	165	8	motion	motion	NOUN
ejpam-5478	165	9	,	,	PUNCT
ejpam-5478	165	10	we	we	PRON
ejpam-5478	165	11	introduce	introduce	VERB
ejpam-5478	165	12	the	the	DET
ejpam-5478	165	13	momentum	momentum	NOUN
ejpam-5478	165	14	px	px	NOUN
ejpam-5478	165	15	with	with	ADP
ejpam-5478	165	16	the	the	DET
ejpam-5478	165	17	following	follow	VERB
ejpam-5478	165	18	expression	expression	NOUN
ejpam-5478	165	19	:	:	PUNCT
ejpam-5478	165	20	pqi	pqi	NOUN
ejpam-5478	165	21	=	=	SYM
ejpam-5478	165	22	l	l	NOUN
ejpam-5478	165	23	∂dα	∂dα	PROPN
ejpam-5478	165	24	s|tqi	s|tqi	NOUN
ejpam-5478	166	1	−	−	PROPN
ejpam-5478	166	2	d	d	NOUN
ejpam-5478	166	3	dt	dt	X
ejpam-5478	166	4	∂l	∂l	PROPN
ejpam-5478	166	5	∂d2α	∂d2α	NOUN
ejpam-5478	166	6	s|tqi	s|tqi	NOUN
ejpam-5478	166	7	this	this	DET
ejpam-5478	166	8	results	result	NOUN
ejpam-5478	166	9	in	in	ADP
ejpam-5478	166	10	equation	equation	NOUN
ejpam-5478	166	11	(	(	PUNCT
ejpam-5478	166	12	11	11	NUM
ejpam-5478	166	13	)	)	PUNCT
ejpam-5478	166	14	being	be	AUX
ejpam-5478	166	15	expressed	express	VERB
ejpam-5478	166	16	as	as	SCONJ
ejpam-5478	166	17	follows	follow	VERB
ejpam-5478	166	18	:	:	PUNCT
ejpam-5478	166	19	d2α	d2α	NOUN
ejpam-5478	166	20	s|tpqi	s|tpqi	ADJ
ejpam-5478	167	1	=	=	SYM
ejpam-5478	167	2	∂l	∂l	PROPN
ejpam-5478	167	3	∂qi	∂qi	PROPN
ejpam-5478	167	4	therefore	therefore	ADV
ejpam-5478	167	5	,	,	PUNCT
ejpam-5478	167	6	when	when	SCONJ
ejpam-5478	167	7	the	the	DET
ejpam-5478	167	8	lagrangian	lagrangian	ADJ
ejpam-5478	167	9	exhibits	exhibit	VERB
ejpam-5478	167	10	translational	translational	ADJ
ejpam-5478	167	11	invariance	invariance	NOUN
ejpam-5478	167	12	,	,	PUNCT
ejpam-5478	167	13	the	the	DET
ejpam-5478	167	14	conservation	conservation	NOUN
ejpam-5478	167	15	of	of	ADP
ejpam-5478	167	16	momentum	momentum	NOUN
ejpam-5478	167	17	in	in	ADP
ejpam-5478	167	18	the	the	DET
ejpam-5478	167	19	x	x	NOUN
ejpam-5478	167	20	-	-	NOUN
ejpam-5478	167	21	direction	direction	NOUN
ejpam-5478	167	22	is	be	AUX
ejpam-5478	167	23	expressed	express	VERB
ejpam-5478	167	24	as	as	SCONJ
ejpam-5478	167	25	px	px	PROPN
ejpam-5478	167	26	follows	follow	VERB
ejpam-5478	167	27	.	.	PUNCT
ejpam-5478	168	1	consequently	consequently	ADV
ejpam-5478	168	2	,	,	PUNCT
ejpam-5478	168	3	the	the	DET
ejpam-5478	168	4	energy	energy	NOUN
ejpam-5478	168	5	can	can	AUX
ejpam-5478	168	6	be	be	AUX
ejpam-5478	168	7	defined	define	VERB
ejpam-5478	168	8	as	as	ADP
ejpam-5478	168	9	:	:	PUNCT
ejpam-5478	168	10	e	e	X
ejpam-5478	168	11	=	=	NOUN
ejpam-5478	168	12	dα	dα	PRON
ejpam-5478	168	13	s|tqipqi	s|tqipqi	ADV
ejpam-5478	168	14	+	+	PROPN
ejpam-5478	168	15	d2α	d2α	PROPN
ejpam-5478	168	16	s|tqi	s|tqi	ADJ
ejpam-5478	168	17	∂l	∂l	PROPN
ejpam-5478	168	18	∂d2α	∂d2α	PROPN
ejpam-5478	168	19	s|tqi	s|tqi	PROPN
ejpam-5478	168	20	−	−	PROPN
ejpam-5478	168	21	l	l	NOUN
ejpam-5478	168	22	example	example	NOUN
ejpam-5478	168	23	1	1	X
ejpam-5478	168	24	.	.	PUNCT
ejpam-5478	169	1	let	let	VERB
ejpam-5478	169	2	us	we	PRON
ejpam-5478	169	3	consider	consider	VERB
ejpam-5478	169	4	the	the	DET
ejpam-5478	169	5	lagrangian	lagrangian	ADJ
ejpam-5478	170	1	[	[	X
ejpam-5478	170	2	22	22	NUM
ejpam-5478	170	3	]	]	X
ejpam-5478	170	4	l	l	NOUN
ejpam-5478	170	5	=	=	SYM
ejpam-5478	170	6	1	1	NUM
ejpam-5478	170	7	2	2	NUM
ejpam-5478	170	8	ax(d2α	ax(d2α	PROPN
ejpam-5478	170	9	t	t	NOUN
ejpam-5478	170	10	x)2	x)2	VERB
ejpam-5478	170	11	−	−	NOUN
ejpam-5478	170	12	1	1	NUM
ejpam-5478	170	13	2	2	NUM
ejpam-5478	170	14	bx(dα	bx(dα	VERB
ejpam-5478	170	15	t	t	PROPN
ejpam-5478	170	16	x	x	SYM
ejpam-5478	170	17	)	)	PUNCT
ejpam-5478	170	18	2	2	NUM
ejpam-5478	170	19	by	by	ADP
ejpam-5478	170	20	applying	apply	VERB
ejpam-5478	170	21	the	the	DET
ejpam-5478	170	22	euler	euler	NOUN
ejpam-5478	170	23	-	-	PUNCT
ejpam-5478	170	24	lagrange	lagrange	NOUN
ejpam-5478	170	25	equation	equation	NOUN
ejpam-5478	170	26	1	1	NUM
ejpam-5478	170	27	with	with	ADP
ejpam-5478	170	28	respect	respect	NOUN
ejpam-5478	170	29	to	to	ADP
ejpam-5478	170	30	the	the	DET
ejpam-5478	170	31	independent	independent	ADJ
ejpam-5478	170	32	variable	variable	NOUN
ejpam-5478	170	33	qi	qi	NOUN
ejpam-5478	170	34	,	,	PUNCT
ejpam-5478	170	35	we	we	PRON
ejpam-5478	170	36	obtain	obtain	VERB
ejpam-5478	170	37	:	:	PUNCT
ejpam-5478	170	38	3	3	NUM
ejpam-5478	170	39	2	2	NUM
ejpam-5478	170	40	α(d2	α(d2	NOUN
ejpam-5478	170	41	s|tqi	s|tqi	NOUN
ejpam-5478	170	42	)	)	PUNCT
ejpam-5478	170	43	2	2	NUM
ejpam-5478	171	1	+	+	CCONJ
ejpam-5478	171	2	bqid	bqid	X
ejpam-5478	171	3	2	2	NUM
ejpam-5478	171	4	s|tqi	s|tqi	PROPN
ejpam-5478	171	5	+	+	CCONJ
ejpam-5478	171	6	2α(d	2α(d	NOUN
ejpam-5478	171	7	s|t	s|t	X
ejpam-5478	171	8	1	1	NUM
ejpam-5478	171	9	qi)q	qi)q	PROPN
ejpam-5478	171	10	(	(	PUNCT
ejpam-5478	171	11	3	3	NUM
ejpam-5478	171	12	)	)	PUNCT
ejpam-5478	171	13	i	i	PRON
ejpam-5478	172	1	+	+	NOUN
ejpam-5478	172	2	1	1	NUM
ejpam-5478	172	3	2	2	NUM
ejpam-5478	172	4	b(d	b(d	PROPN
ejpam-5478	172	5	s|t	s|t	X
ejpam-5478	172	6	1	1	NUM
ejpam-5478	172	7	qi	qi	NOUN
ejpam-5478	172	8	)	)	PUNCT
ejpam-5478	172	9	2	2	NUM
ejpam-5478	173	1	+	+	CCONJ
ejpam-5478	173	2	aqiq	aqiq	NOUN
ejpam-5478	173	3	(	(	PUNCT
ejpam-5478	173	4	4	4	NUM
ejpam-5478	173	5	)	)	PUNCT
ejpam-5478	173	6	i	i	NOUN
ejpam-5478	173	7	=	=	NOUN
ejpam-5478	173	8	0	0	X
ejpam-5478	173	9	.	.	PUNCT
ejpam-5478	174	1	(	(	PUNCT
ejpam-5478	174	2	9	9	X
ejpam-5478	174	3	)	)	PUNCT
ejpam-5478	174	4	the	the	DET
ejpam-5478	174	5	momenta	momenta	NOUN
ejpam-5478	174	6	p1	p1	NOUN
ejpam-5478	174	7	and	and	CCONJ
ejpam-5478	174	8	p2	p2	PROPN
ejpam-5478	174	9	are	be	AUX
ejpam-5478	174	10	given	give	VERB
ejpam-5478	174	11	as	as	ADP
ejpam-5478	174	12	:	:	PUNCT
ejpam-5478	174	13	p1	p1	NOUN
ejpam-5478	174	14	=	=	PUNCT
ejpam-5478	174	15	∂l	∂l	PROPN
ejpam-5478	174	16	∂dα	∂dα	NOUN
ejpam-5478	174	17	s|tx	s|tx	X
ejpam-5478	174	18	=	=	PUNCT
ejpam-5478	174	19	−bxdα	−bxdα	DET
ejpam-5478	174	20	t	t	NOUN
ejpam-5478	174	21	x.	x.	NOUN
ejpam-5478	174	22	p2	p2	PROPN
ejpam-5478	175	1	=	=	PUNCT
ejpam-5478	175	2	∂l	∂l	PROPN
ejpam-5478	175	3	∂d2α	∂d2α	NOUN
ejpam-5478	175	4	s|tx	s|tx	X
ejpam-5478	176	1	=	=	PUNCT
ejpam-5478	176	2	axd2α	axd2α	X
ejpam-5478	176	3	s|tx	s|tx	PROPN
ejpam-5478	176	4	.	.	PUNCT
ejpam-5478	177	1	the	the	DET
ejpam-5478	177	2	hamiltonian	hamiltonian	ADJ
ejpam-5478	177	3	density	density	NOUN
ejpam-5478	177	4	can	can	AUX
ejpam-5478	177	5	be	be	AUX
ejpam-5478	177	6	written	write	VERB
ejpam-5478	177	7	as	as	ADP
ejpam-5478	177	8	:	:	PUNCT
ejpam-5478	177	9	h	h	NOUN
ejpam-5478	177	10	=	=	PUNCT
ejpam-5478	177	11	p1d	p1d	NOUN
ejpam-5478	177	12	α	α	NOUN
ejpam-5478	177	13	s|tq	s|tq	NOUN
ejpam-5478	178	1	+	+	CCONJ
ejpam-5478	178	2	p2d	p2d	NUM
ejpam-5478	178	3	2α	2α	NOUN
ejpam-5478	178	4	s|tq	s|tq	NOUN
ejpam-5478	178	5	−	−	NOUN
ejpam-5478	178	6	l	l	NOUN
ejpam-5478	178	7	=	=	SYM
ejpam-5478	178	8	p21	p21	PROPN
ejpam-5478	178	9	2bx	2bx	NOUN
ejpam-5478	179	1	+	+	CCONJ
ejpam-5478	179	2	p22	p22	ADJ
ejpam-5478	179	3	2ax	2ax	ADJ
ejpam-5478	179	4	(	(	PUNCT
ejpam-5478	179	5	10	10	NUM
ejpam-5478	179	6	)	)	PUNCT
ejpam-5478	179	7	additionally	additionally	ADV
ejpam-5478	179	8	,	,	PUNCT
ejpam-5478	179	9	the	the	DET
ejpam-5478	179	10	equations	equation	NOUN
ejpam-5478	179	11	of	of	ADP
ejpam-5478	179	12	motion	motion	NOUN
ejpam-5478	179	13	according	accord	VERB
ejpam-5478	179	14	to	to	ADP
ejpam-5478	179	15	hamilton	hamilton	PROPN
ejpam-5478	179	16	’s	’s	PART
ejpam-5478	179	17	formalism	formalism	NOUN
ejpam-5478	179	18	are	be	AUX
ejpam-5478	179	19	:	:	PUNCT
ejpam-5478	179	20	dα	dα	X
ejpam-5478	179	21	s|tx	s|tx	NOUN
ejpam-5478	180	1	=	=	SYM
ejpam-5478	180	2	−p1	−p1	PROPN
ejpam-5478	181	1	bx	bx	VERB
ejpam-5478	181	2	.	.	PUNCT
ejpam-5478	182	1	y.	y.	PROPN
ejpam-5478	182	2	m.	m.	PROPN
ejpam-5478	182	3	alawaideh	alawaideh	PROPN
ejpam-5478	182	4	et	et	PROPN
ejpam-5478	182	5	al	al	PROPN
ejpam-5478	182	6	.	.	PUNCT
ejpam-5478	182	7	/	/	SYM
ejpam-5478	182	8	eur	eur	PROPN
ejpam-5478	182	9	.	.	PUNCT
ejpam-5478	183	1	j.	j.	PROPN
ejpam-5478	183	2	pure	pure	PROPN
ejpam-5478	183	3	appl	appl	PROPN
ejpam-5478	183	4	.	.	PROPN
ejpam-5478	183	5	math	math	PROPN
ejpam-5478	183	6	,	,	PUNCT
ejpam-5478	183	7	18	18	NUM
ejpam-5478	183	8	(	(	PUNCT
ejpam-5478	183	9	1	1	NUM
ejpam-5478	183	10	)	)	PUNCT
ejpam-5478	183	11	(	(	PUNCT
ejpam-5478	183	12	2025	2025	NUM
ejpam-5478	183	13	)	)	PUNCT
ejpam-5478	183	14	,	,	PUNCT
ejpam-5478	183	15	5478	5478	NUM
ejpam-5478	183	16	9	9	NUM
ejpam-5478	183	17	of	of	ADP
ejpam-5478	183	18	14	14	NUM
ejpam-5478	183	19	d2α	d2α	NOUN
ejpam-5478	183	20	s|tx	s|tx	X
ejpam-5478	183	21	=	=	PUNCT
ejpam-5478	183	22	p2	p2	NOUN
ejpam-5478	183	23	ax	ax	NOUN
ejpam-5478	183	24	.	.	PUNCT
ejpam-5478	184	1	h	h	NOUN
ejpam-5478	184	2	∂x	∂x	NOUN
ejpam-5478	184	3	=	=	PUNCT
ejpam-5478	184	4	−dα	−dα	VERB
ejpam-5478	184	5	s|tp1	s|tp1	NOUN
ejpam-5478	185	1	+	+	ADV
ejpam-5478	185	2	dα	dα	ADJ
ejpam-5478	185	3	s|tp2	s|tp2	ADV
ejpam-5478	185	4	.	.	PUNCT
ejpam-5478	186	1	using	use	VERB
ejpam-5478	186	2	the	the	DET
ejpam-5478	186	3	equation	equation	NOUN
ejpam-5478	186	4	above	above	ADV
ejpam-5478	186	5	,	,	PUNCT
ejpam-5478	186	6	we	we	PRON
ejpam-5478	186	7	obtain	obtain	VERB
ejpam-5478	186	8	the	the	DET
ejpam-5478	186	9	following	follow	VERB
ejpam-5478	186	10	outcome	outcome	NOUN
ejpam-5478	186	11	:	:	PUNCT
ejpam-5478	186	12	3	3	NUM
ejpam-5478	186	13	2	2	NUM
ejpam-5478	186	14	a(d2α	a(d2α	X
ejpam-5478	186	15	s|tqi	s|tqi	NOUN
ejpam-5478	186	16	)	)	PUNCT
ejpam-5478	186	17	2	2	NUM
ejpam-5478	187	1	+	+	CCONJ
ejpam-5478	187	2	bqid	bqid	PROPN
ejpam-5478	187	3	2α	2α	PROPN
ejpam-5478	187	4	s|tqi	s|tqi	PROPN
ejpam-5478	187	5	+	+	CCONJ
ejpam-5478	187	6	2a(dα	2a(dα	NUM
ejpam-5478	187	7	s|tqi)q	s|tqi)q	NOUN
ejpam-5478	187	8	(	(	PUNCT
ejpam-5478	187	9	3	3	NUM
ejpam-5478	187	10	)	)	PUNCT
ejpam-5478	187	11	i	i	PRON
ejpam-5478	187	12	+	+	NOUN
ejpam-5478	187	13	1	1	NUM
ejpam-5478	187	14	2	2	NUM
ejpam-5478	187	15	b(dα	b(dα	NOUN
ejpam-5478	187	16	s|tqi	s|tqi	NOUN
ejpam-5478	187	17	)	)	PUNCT
ejpam-5478	187	18	2	2	NUM
ejpam-5478	188	1	+	+	CCONJ
ejpam-5478	188	2	aqiq	aqiq	NOUN
ejpam-5478	188	3	(	(	PUNCT
ejpam-5478	188	4	4	4	NUM
ejpam-5478	188	5	)	)	PUNCT
ejpam-5478	188	6	i	i	NOUN
ejpam-5478	188	7	=	=	NOUN
ejpam-5478	188	8	0	0	PUNCT
ejpam-5478	188	9	(	(	PUNCT
ejpam-5478	188	10	11	11	NUM
ejpam-5478	188	11	)	)	PUNCT
ejpam-5478	188	12	the	the	DET
ejpam-5478	188	13	above	above	ADJ
ejpam-5478	188	14	equation	equation	NOUN
ejpam-5478	188	15	is	be	AUX
ejpam-5478	188	16	exactly	exactly	ADV
ejpam-5478	188	17	the	the	DET
ejpam-5478	188	18	same	same	ADJ
ejpam-5478	188	19	as	as	ADP
ejpam-5478	188	20	the	the	DET
ejpam-5478	188	21	equation	equation	NOUN
ejpam-5478	188	22	that	that	PRON
ejpam-5478	188	23	has	have	AUX
ejpam-5478	188	24	been	be	AUX
ejpam-5478	188	25	derived	derive	VERB
ejpam-5478	188	26	by	by	ADP
ejpam-5478	188	27	eulerlagrange	eulerlagrange	NOUN
ejpam-5478	188	28	9	9	NUM
ejpam-5478	188	29	in	in	ADP
ejpam-5478	188	30	fractional	fractional	ADJ
ejpam-5478	188	31	form	form	NOUN
ejpam-5478	188	32	.	.	PUNCT
ejpam-5478	189	1	for	for	ADP
ejpam-5478	189	2	α	α	NOUN
ejpam-5478	189	3	=	=	SYM
ejpam-5478	189	4	1	1	NUM
ejpam-5478	189	5	,	,	PUNCT
ejpam-5478	189	6	we	we	PRON
ejpam-5478	189	7	get	get	VERB
ejpam-5478	189	8	:	:	PUNCT
ejpam-5478	189	9	3	3	NUM
ejpam-5478	189	10	2	2	NUM
ejpam-5478	189	11	a(d2	a(d2	NOUN
ejpam-5478	189	12	s|tqi	s|tqi	NOUN
ejpam-5478	189	13	)	)	PUNCT
ejpam-5478	189	14	2	2	NUM
ejpam-5478	190	1	+	+	CCONJ
ejpam-5478	190	2	bqid	bqid	X
ejpam-5478	190	3	2	2	NUM
ejpam-5478	190	4	s|tqi	s|tqi	NOUN
ejpam-5478	190	5	+	+	CCONJ
ejpam-5478	190	6	2a(d1	2a(d1	NUM
ejpam-5478	190	7	t	t	NOUN
ejpam-5478	190	8	qi)q	qi)q	PROPN
ejpam-5478	190	9	(	(	PUNCT
ejpam-5478	190	10	3	3	NUM
ejpam-5478	190	11	)	)	PUNCT
ejpam-5478	190	12	i	i	PRON
ejpam-5478	191	1	+	+	NOUN
ejpam-5478	191	2	1	1	NUM
ejpam-5478	191	3	2	2	NUM
ejpam-5478	191	4	b(d1	b(d1	NOUN
ejpam-5478	191	5	s|tqi	s|tqi	PROPN
ejpam-5478	191	6	)	)	PUNCT
ejpam-5478	191	7	2	2	NUM
ejpam-5478	192	1	+	+	CCONJ
ejpam-5478	192	2	aqiq	aqiq	NOUN
ejpam-5478	192	3	(	(	PUNCT
ejpam-5478	192	4	4	4	NUM
ejpam-5478	192	5	)	)	PUNCT
ejpam-5478	192	6	i	i	NOUN
ejpam-5478	192	7	=	=	PUNCT
ejpam-5478	192	8	0	0	PUNCT
ejpam-5478	192	9	(	(	PUNCT
ejpam-5478	192	10	12	12	NUM
ejpam-5478	192	11	)	)	PUNCT
ejpam-5478	192	12	using	use	VERB
ejpam-5478	192	13	the	the	DET
ejpam-5478	192	14	conformable	conformable	ADJ
ejpam-5478	192	15	derivative	derivative	NOUN
ejpam-5478	192	16	[	[	X
ejpam-5478	192	17	29	29	NUM
ejpam-5478	192	18	]	]	PUNCT
ejpam-5478	192	19	and	and	CCONJ
ejpam-5478	192	20	assuming	assume	VERB
ejpam-5478	192	21	d2	d2	PROPN
ejpam-5478	192	22	s|tqi	s|tqi	PROPN
ejpam-5478	192	23	=	=	SYM
ejpam-5478	192	24	q̈l	q̈l	PROPN
ejpam-5478	192	25	,	,	PUNCT
ejpam-5478	192	26	d	d	PROPN
ejpam-5478	192	27	1	1	NUM
ejpam-5478	192	28	s|t	s|t	NOUN
ejpam-5478	192	29	=	=	PRON
ejpam-5478	193	1	q̇l	q̇l	NOUN
ejpam-5478	193	2	3	3	NUM
ejpam-5478	193	3	2	2	NUM
ejpam-5478	193	4	a(q̈l	a(q̈l	NUM
ejpam-5478	193	5	)	)	PUNCT
ejpam-5478	193	6	2	2	NUM
ejpam-5478	193	7	+	+	NUM
ejpam-5478	193	8	bqiq̈l	bqiq̈l	NOUN
ejpam-5478	193	9	+	+	CCONJ
ejpam-5478	193	10	2a(q̇l)q	2a(q̇l)q	NUM
ejpam-5478	193	11	(	(	PUNCT
ejpam-5478	193	12	3	3	NUM
ejpam-5478	193	13	)	)	PUNCT
ejpam-5478	193	14	i	i	PRON
ejpam-5478	194	1	+	+	NOUN
ejpam-5478	194	2	1	1	NUM
ejpam-5478	194	3	2	2	NUM
ejpam-5478	194	4	b(q̇l	b(q̇l	NOUN
ejpam-5478	194	5	)	)	PUNCT
ejpam-5478	194	6	2	2	NUM
ejpam-5478	195	1	+	+	CCONJ
ejpam-5478	195	2	aqiq	aqiq	NOUN
ejpam-5478	195	3	(	(	PUNCT
ejpam-5478	195	4	4	4	NUM
ejpam-5478	195	5	)	)	PUNCT
ejpam-5478	195	6	i	i	NOUN
ejpam-5478	195	7	=	=	NOUN
ejpam-5478	195	8	0	0	PUNCT
ejpam-5478	195	9	(	(	PUNCT
ejpam-5478	195	10	13	13	NUM
ejpam-5478	195	11	)	)	PUNCT
ejpam-5478	195	12	it	it	PRON
ejpam-5478	195	13	is	be	AUX
ejpam-5478	195	14	worth	worth	ADJ
ejpam-5478	195	15	noting	note	VERB
ejpam-5478	195	16	that	that	SCONJ
ejpam-5478	195	17	the	the	DET
ejpam-5478	195	18	results	result	NOUN
ejpam-5478	195	19	in	in	ADP
ejpam-5478	195	20	equation	equation	NOUN
ejpam-5478	195	21	13	13	NUM
ejpam-5478	195	22	are	be	AUX
ejpam-5478	195	23	consistent	consistent	ADJ
ejpam-5478	195	24	with	with	ADP
ejpam-5478	195	25	those	those	PRON
ejpam-5478	195	26	found	find	VERB
ejpam-5478	195	27	in	in	ADP
ejpam-5478	195	28	muslih	muslih	PROPN
ejpam-5478	195	29	et	et	PROPN
ejpam-5478	195	30	al	al	PROPN
ejpam-5478	196	1	[	[	X
ejpam-5478	196	2	27	27	NUM
ejpam-5478	196	3	]	]	PUNCT
ejpam-5478	196	4	.	.	PUNCT
ejpam-5478	197	1	besides	besides	SCONJ
ejpam-5478	197	2	,	,	PUNCT
ejpam-5478	197	3	the	the	DET
ejpam-5478	197	4	path	path	NOUN
ejpam-5478	197	5	integral	integral	ADJ
ejpam-5478	197	6	is	be	AUX
ejpam-5478	197	7	given	give	VERB
ejpam-5478	197	8	by	by	ADP
ejpam-5478	197	9	k	k	PROPN
ejpam-5478	197	10	=	=	SYM
ejpam-5478	197	11	∫	∫	PROPN
ejpam-5478	197	12	dqe	dqe	VERB
ejpam-5478	197	13	i	i	PRON
ejpam-5478	197	14	(	(	PUNCT
ejpam-5478	197	15	1	1	NUM
ejpam-5478	197	16	2	2	NUM
ejpam-5478	197	17	ax(d2α	ax(d2α	PROPN
ejpam-5478	197	18	s|tx	s|tx	NOUN
ejpam-5478	197	19	)	)	PUNCT
ejpam-5478	197	20	2−	2−	NUM
ejpam-5478	197	21	1	1	NUM
ejpam-5478	197	22	2	2	NUM
ejpam-5478	197	23	bx(dα	bx(dα	VERB
ejpam-5478	197	24	s|tx	s|tx	NOUN
ejpam-5478	197	25	)	)	PUNCT
ejpam-5478	197	26	2)dt	2)dt	PROPN
ejpam-5478	197	27	(	(	PUNCT
ejpam-5478	197	28	14	14	NUM
ejpam-5478	197	29	)	)	PUNCT
ejpam-5478	197	30	the	the	DET
ejpam-5478	197	31	path	path	NOUN
ejpam-5478	197	32	integral	integral	ADJ
ejpam-5478	197	33	(	(	PUNCT
ejpam-5478	197	34	14	14	NUM
ejpam-5478	197	35	)	)	PUNCT
ejpam-5478	197	36	,	,	PUNCT
ejpam-5478	197	37	is	be	AUX
ejpam-5478	197	38	an	an	DET
ejpam-5478	197	39	integration	integration	NOUN
ejpam-5478	197	40	over	over	ADP
ejpam-5478	197	41	the	the	DET
ejpam-5478	197	42	canonical	canonical	ADJ
ejpam-5478	197	43	coordinate	coordinate	NOUN
ejpam-5478	197	44	x	x	NOUN
ejpam-5478	197	45	,	,	PUNCT
ejpam-5478	197	46	without	without	ADP
ejpam-5478	197	47	any	any	DET
ejpam-5478	197	48	need	need	NOUN
ejpam-5478	197	49	to	to	ADP
ejpam-5478	197	50	any	any	DET
ejpam-5478	197	51	integration	integration	NOUN
ejpam-5478	197	52	over	over	ADP
ejpam-5478	197	53	the	the	DET
ejpam-5478	197	54	velocity	velocity	NOUN
ejpam-5478	197	55	x	x	PUNCT
ejpam-5478	197	56	=	=	NOUN
ejpam-5478	197	57	dα	dα	X
ejpam-5478	197	58	s|tx	s|tx	NOUN
ejpam-5478	197	59	as	as	SCONJ
ejpam-5478	197	60	given	give	VERB
ejpam-5478	197	61	by	by	ADP
ejpam-5478	197	62	ostrogradskii	ostrogradskii	ADJ
ejpam-5478	197	63	formulation	formulation	NOUN
ejpam-5478	197	64	.	.	PUNCT
ejpam-5478	198	1	5	5	NUM
ejpam-5478	198	2	.	.	X
ejpam-5478	198	3	higher	high	ADJ
ejpam-5478	198	4	-	-	PUNCT
ejpam-5478	198	5	order	order	NOUN
ejpam-5478	198	6	calculus	calculus	NOUN
ejpam-5478	198	7	:	:	PUNCT
ejpam-5478	198	8	applications	application	NOUN
ejpam-5478	198	9	and	and	CCONJ
ejpam-5478	198	10	recommendations	recommendation	NOUN
ejpam-5478	198	11	for	for	ADP
ejpam-5478	198	12	future	future	ADJ
ejpam-5478	198	13	work	work	NOUN
ejpam-5478	198	14	understanding	understand	VERB
ejpam-5478	198	15	conformable	conformable	ADJ
ejpam-5478	198	16	calculus	calculus	NOUN
ejpam-5478	198	17	is	be	AUX
ejpam-5478	198	18	crucial	crucial	ADJ
ejpam-5478	198	19	due	due	ADP
ejpam-5478	198	20	to	to	ADP
ejpam-5478	198	21	its	its	PRON
ejpam-5478	198	22	high	high	ADJ
ejpam-5478	198	23	potential	potential	ADJ
ejpam-5478	198	24	value	value	NOUN
ejpam-5478	198	25	,	,	PUNCT
ejpam-5478	198	26	especially	especially	ADV
ejpam-5478	198	27	in	in	ADP
ejpam-5478	198	28	higher	high	ADJ
ejpam-5478	198	29	order	order	NOUN
ejpam-5478	198	30	derivatives	derivative	NOUN
ejpam-5478	198	31	,	,	PUNCT
ejpam-5478	198	32	hamiltonian	hamiltonian	ADJ
ejpam-5478	198	33	systems	system	NOUN
ejpam-5478	198	34	,	,	PUNCT
ejpam-5478	198	35	nonlinear	nonlinear	ADJ
ejpam-5478	198	36	motion	motion	NOUN
ejpam-5478	198	37	,	,	PUNCT
ejpam-5478	198	38	and	and	CCONJ
ejpam-5478	198	39	differential	differential	ADJ
ejpam-5478	198	40	equations	equation	NOUN
ejpam-5478	198	41	.	.	PUNCT
ejpam-5478	199	1	the	the	DET
ejpam-5478	199	2	hamiltonian	hamiltonian	ADJ
ejpam-5478	199	3	formalism	formalism	NOUN
ejpam-5478	199	4	for	for	ADP
ejpam-5478	199	5	fractional	fractional	ADJ
ejpam-5478	199	6	differential	differential	ADJ
ejpam-5478	199	7	equations	equation	NOUN
ejpam-5478	199	8	is	be	AUX
ejpam-5478	199	9	essential	essential	ADJ
ejpam-5478	199	10	for	for	ADP
ejpam-5478	199	11	comprehending	comprehend	VERB
ejpam-5478	199	12	the	the	DET
ejpam-5478	199	13	dynamics	dynamic	NOUN
ejpam-5478	199	14	of	of	ADP
ejpam-5478	199	15	intricate	intricate	ADJ
ejpam-5478	199	16	physical	physical	ADJ
ejpam-5478	199	17	systems	system	NOUN
ejpam-5478	199	18	,	,	PUNCT
ejpam-5478	199	19	particularly	particularly	ADV
ejpam-5478	199	20	at	at	ADP
ejpam-5478	199	21	the	the	DET
ejpam-5478	199	22	nanoscale	nanoscale	NOUN
ejpam-5478	199	23	.	.	PUNCT
ejpam-5478	200	1	this	this	DET
ejpam-5478	200	2	approach	approach	NOUN
ejpam-5478	200	3	enables	enable	VERB
ejpam-5478	200	4	the	the	DET
ejpam-5478	200	5	exploration	exploration	NOUN
ejpam-5478	200	6	of	of	ADP
ejpam-5478	200	7	fractional	fractional	ADJ
ejpam-5478	200	8	derivatives	derivative	NOUN
ejpam-5478	200	9	of	of	ADP
ejpam-5478	200	10	point	point	NOUN
ejpam-5478	200	11	particles	particle	NOUN
ejpam-5478	200	12	,	,	PUNCT
ejpam-5478	200	13	offering	offer	VERB
ejpam-5478	200	14	valuable	valuable	ADJ
ejpam-5478	200	15	insights	insight	NOUN
ejpam-5478	200	16	into	into	ADP
ejpam-5478	200	17	the	the	DET
ejpam-5478	200	18	movements	movement	NOUN
ejpam-5478	200	19	of	of	ADP
ejpam-5478	200	20	nanoscale	nanoscale	NOUN
ejpam-5478	200	21	materials	material	NOUN
ejpam-5478	200	22	and	and	CCONJ
ejpam-5478	200	23	particles	particle	NOUN
ejpam-5478	200	24	.	.	PUNCT
ejpam-5478	201	1	these	these	DET
ejpam-5478	201	2	practical	practical	ADJ
ejpam-5478	201	3	implications	implication	NOUN
ejpam-5478	201	4	highlight	highlight	VERB
ejpam-5478	201	5	the	the	DET
ejpam-5478	201	6	importance	importance	NOUN
ejpam-5478	201	7	of	of	ADP
ejpam-5478	201	8	derivatives	derivative	NOUN
ejpam-5478	201	9	in	in	ADP
ejpam-5478	201	10	understanding	understand	VERB
ejpam-5478	201	11	complex	complex	ADJ
ejpam-5478	201	12	systems	system	NOUN
ejpam-5478	201	13	in	in	ADP
ejpam-5478	201	14	engineering	engineering	NOUN
ejpam-5478	201	15	and	and	CCONJ
ejpam-5478	201	16	applied	applied	ADJ
ejpam-5478	201	17	physics	physic	NOUN
ejpam-5478	201	18	.	.	PUNCT
ejpam-5478	202	1	this	this	DET
ejpam-5478	202	2	method	method	NOUN
ejpam-5478	202	3	helps	help	VERB
ejpam-5478	202	4	researchers	researcher	NOUN
ejpam-5478	202	5	delve	delve	VERB
ejpam-5478	202	6	deeper	deeply	ADV
ejpam-5478	202	7	into	into	ADP
ejpam-5478	202	8	the	the	DET
ejpam-5478	202	9	stability	stability	NOUN
ejpam-5478	202	10	,	,	PUNCT
ejpam-5478	202	11	oscillation	oscillation	NOUN
ejpam-5478	202	12	,	,	PUNCT
ejpam-5478	202	13	and	and	CCONJ
ejpam-5478	202	14	periodicity	periodicity	NOUN
ejpam-5478	202	15	of	of	ADP
ejpam-5478	202	16	systems	system	NOUN
ejpam-5478	202	17	exhibiting	exhibit	VERB
ejpam-5478	202	18	memory	memory	NOUN
ejpam-5478	202	19	effects	effect	NOUN
ejpam-5478	202	20	or	or	CCONJ
ejpam-5478	202	21	long	long	ADJ
ejpam-5478	202	22	-	-	PUNCT
ejpam-5478	202	23	range	range	NOUN
ejpam-5478	202	24	interactions	interaction	NOUN
ejpam-5478	202	25	.	.	PUNCT
ejpam-5478	203	1	by	by	ADP
ejpam-5478	203	2	incorporating	incorporate	VERB
ejpam-5478	203	3	the	the	DET
ejpam-5478	203	4	hamiltonian	hamiltonian	ADJ
ejpam-5478	203	5	method	method	NOUN
ejpam-5478	203	6	into	into	ADP
ejpam-5478	203	7	the	the	DET
ejpam-5478	203	8	study	study	NOUN
ejpam-5478	203	9	of	of	ADP
ejpam-5478	203	10	conformable	conformable	ADJ
ejpam-5478	203	11	derivatives	derivative	NOUN
ejpam-5478	203	12	,	,	PUNCT
ejpam-5478	203	13	we	we	PRON
ejpam-5478	203	14	can	can	AUX
ejpam-5478	203	15	achieve	achieve	VERB
ejpam-5478	203	16	a	a	DET
ejpam-5478	203	17	more	more	ADV
ejpam-5478	203	18	comprehensive	comprehensive	ADJ
ejpam-5478	203	19	understanding	understanding	NOUN
ejpam-5478	203	20	of	of	ADP
ejpam-5478	203	21	how	how	SCONJ
ejpam-5478	203	22	systems	system	NOUN
ejpam-5478	203	23	respond	respond	VERB
ejpam-5478	203	24	to	to	ADP
ejpam-5478	203	25	external	external	ADJ
ejpam-5478	203	26	influences	influence	NOUN
ejpam-5478	203	27	and	and	CCONJ
ejpam-5478	203	28	disturbances	disturbance	NOUN
ejpam-5478	203	29	.	.	PUNCT
ejpam-5478	204	1	further	further	ADJ
ejpam-5478	204	2	research	research	NOUN
ejpam-5478	204	3	on	on	ADP
ejpam-5478	204	4	conformable	conformable	ADJ
ejpam-5478	204	5	derivatives	derivative	NOUN
ejpam-5478	204	6	and	and	CCONJ
ejpam-5478	204	7	generalized	generalized	ADJ
ejpam-5478	204	8	point	point	NOUN
ejpam-5478	204	9	particles	particle	NOUN
ejpam-5478	204	10	is	be	AUX
ejpam-5478	204	11	vital	vital	ADJ
ejpam-5478	204	12	for	for	ADP
ejpam-5478	204	13	advancing	advance	VERB
ejpam-5478	204	14	our	our	PRON
ejpam-5478	204	15	understanding	understanding	NOUN
ejpam-5478	204	16	of	of	ADP
ejpam-5478	204	17	these	these	DET
ejpam-5478	204	18	complex	complex	ADJ
ejpam-5478	204	19	systems	system	NOUN
ejpam-5478	204	20	.	.	PUNCT
ejpam-5478	205	1	the	the	DET
ejpam-5478	205	2	insights	insight	NOUN
ejpam-5478	205	3	gained	gain	VERB
ejpam-5478	205	4	from	from	ADP
ejpam-5478	205	5	such	such	ADJ
ejpam-5478	205	6	studies	study	NOUN
ejpam-5478	205	7	have	have	VERB
ejpam-5478	205	8	the	the	DET
ejpam-5478	205	9	potential	potential	NOUN
ejpam-5478	205	10	to	to	PART
ejpam-5478	205	11	revolutionize	revolutionize	VERB
ejpam-5478	205	12	fields	field	NOUN
ejpam-5478	205	13	like	like	ADP
ejpam-5478	205	14	nanotechnology	nanotechnology	PROPN
ejpam-5478	205	15	,	,	PUNCT
ejpam-5478	205	16	biomechanics	biomechanic	NOUN
ejpam-5478	205	17	,	,	PUNCT
ejpam-5478	205	18	and	and	CCONJ
ejpam-5478	205	19	advanced	advanced	ADJ
ejpam-5478	205	20	engineering	engineering	NOUN
ejpam-5478	205	21	,	,	PUNCT
ejpam-5478	205	22	offering	offer	VERB
ejpam-5478	205	23	innovative	innovative	ADJ
ejpam-5478	205	24	solutions	solution	NOUN
ejpam-5478	205	25	and	and	CCONJ
ejpam-5478	205	26	a	a	DET
ejpam-5478	205	27	deeper	deep	ADJ
ejpam-5478	205	28	comprehension	comprehension	NOUN
ejpam-5478	205	29	of	of	ADP
ejpam-5478	205	30	the	the	DET
ejpam-5478	205	31	fundamental	fundamental	ADJ
ejpam-5478	205	32	principles	principle	NOUN
ejpam-5478	205	33	governing	govern	VERB
ejpam-5478	205	34	these	these	DET
ejpam-5478	205	35	intricate	intricate	ADJ
ejpam-5478	205	36	phenomena	phenomenon	NOUN
ejpam-5478	205	37	.	.	PUNCT
ejpam-5478	206	1	y.	y.	PROPN
ejpam-5478	206	2	m.	m.	PROPN
ejpam-5478	206	3	alawaideh	alawaideh	PROPN
ejpam-5478	206	4	et	et	PROPN
ejpam-5478	206	5	al	al	PROPN
ejpam-5478	206	6	.	.	PUNCT
ejpam-5478	206	7	/	/	SYM
ejpam-5478	206	8	eur	eur	PROPN
ejpam-5478	206	9	.	.	PUNCT
ejpam-5478	207	1	j.	j.	PROPN
ejpam-5478	207	2	pure	pure	PROPN
ejpam-5478	207	3	appl	appl	PROPN
ejpam-5478	207	4	.	.	PROPN
ejpam-5478	207	5	math	math	PROPN
ejpam-5478	207	6	,	,	PUNCT
ejpam-5478	207	7	18	18	NUM
ejpam-5478	207	8	(	(	PUNCT
ejpam-5478	207	9	1	1	NUM
ejpam-5478	207	10	)	)	PUNCT
ejpam-5478	207	11	(	(	PUNCT
ejpam-5478	207	12	2025	2025	NUM
ejpam-5478	207	13	)	)	PUNCT
ejpam-5478	207	14	,	,	PUNCT
ejpam-5478	207	15	5478	5478	NUM
ejpam-5478	207	16	10	10	NUM
ejpam-5478	207	17	of	of	ADP
ejpam-5478	207	18	14	14	NUM
ejpam-5478	207	19	6	6	NUM
ejpam-5478	207	20	.	.	PUNCT
ejpam-5478	208	1	conclusion	conclusion	NOUN
ejpam-5478	208	2	in	in	ADP
ejpam-5478	208	3	this	this	DET
ejpam-5478	208	4	research	research	NOUN
ejpam-5478	208	5	,	,	PUNCT
ejpam-5478	208	6	we	we	PRON
ejpam-5478	208	7	investigated	investigate	VERB
ejpam-5478	208	8	two	two	NUM
ejpam-5478	208	9	systems	system	NOUN
ejpam-5478	208	10	using	use	VERB
ejpam-5478	208	11	the	the	DET
ejpam-5478	208	12	conformable	conformable	ADJ
ejpam-5478	208	13	version	version	NOUN
ejpam-5478	208	14	of	of	ADP
ejpam-5478	208	15	the	the	DET
ejpam-5478	208	16	calculus	calculus	NOUN
ejpam-5478	208	17	of	of	ADP
ejpam-5478	208	18	variations	variation	NOUN
ejpam-5478	208	19	to	to	PART
ejpam-5478	208	20	derive	derive	VERB
ejpam-5478	208	21	the	the	DET
ejpam-5478	208	22	fractional	fractional	ADJ
ejpam-5478	208	23	euler	euler	VERB
ejpam-5478	208	24	-	-	PUNCT
ejpam-5478	208	25	lagrange	lagrange	NOUN
ejpam-5478	208	26	equation	equation	NOUN
ejpam-5478	208	27	.	.	PUNCT
ejpam-5478	209	1	it	it	PRON
ejpam-5478	209	2	applies	apply	VERB
ejpam-5478	209	3	this	this	DET
ejpam-5478	209	4	calculus	calculus	NOUN
ejpam-5478	209	5	to	to	ADP
ejpam-5478	209	6	the	the	DET
ejpam-5478	209	7	conformable	conformable	ADJ
ejpam-5478	209	8	version	version	NOUN
ejpam-5478	209	9	of	of	ADP
ejpam-5478	209	10	classical	classical	ADJ
ejpam-5478	209	11	mechanics	mechanic	NOUN
ejpam-5478	209	12	,	,	PUNCT
ejpam-5478	209	13	introducing	introduce	VERB
ejpam-5478	209	14	the	the	DET
ejpam-5478	209	15	conformable	conformable	ADJ
ejpam-5478	209	16	lagrangian	lagrangian	ADJ
ejpam-5478	209	17	and	and	CCONJ
ejpam-5478	209	18	deriving	derive	VERB
ejpam-5478	209	19	the	the	DET
ejpam-5478	209	20	equation	equation	NOUN
ejpam-5478	209	21	of	of	ADP
ejpam-5478	209	22	motion	motion	NOUN
ejpam-5478	209	23	.	.	PUNCT
ejpam-5478	210	1	the	the	DET
ejpam-5478	210	2	path	path	NOUN
ejpam-5478	210	3	integral	integral	ADJ
ejpam-5478	210	4	quantization	quantization	NOUN
ejpam-5478	210	5	was	be	AUX
ejpam-5478	210	6	obtained	obtain	VERB
ejpam-5478	210	7	directly	directly	ADV
ejpam-5478	210	8	as	as	ADP
ejpam-5478	210	9	an	an	DET
ejpam-5478	210	10	integration	integration	NOUN
ejpam-5478	210	11	over	over	ADP
ejpam-5478	210	12	the	the	DET
ejpam-5478	210	13	canonical	canonical	ADJ
ejpam-5478	210	14	coordinate	coordinate	NOUN
ejpam-5478	210	15	qi	qi	PROPN
ejpam-5478	210	16	without	without	ADP
ejpam-5478	210	17	the	the	DET
ejpam-5478	210	18	need	need	NOUN
ejpam-5478	210	19	to	to	PART
ejpam-5478	210	20	integrate	integrate	VERB
ejpam-5478	210	21	over	over	ADP
ejpam-5478	210	22	the	the	DET
ejpam-5478	210	23	variable	variable	NOUN
ejpam-5478	210	24	dα	dα	ADV
ejpam-5478	210	25	t	t	PROPN
ejpam-5478	210	26	qi	qi	PROPN
ejpam-5478	210	27	.	.	PUNCT
ejpam-5478	211	1	the	the	DET
ejpam-5478	211	2	classical	classical	ADJ
ejpam-5478	211	3	equations	equation	NOUN
ejpam-5478	211	4	of	of	ADP
ejpam-5478	211	5	motion	motion	NOUN
ejpam-5478	211	6	obtained	obtain	VERB
ejpam-5478	211	7	in	in	ADP
ejpam-5478	211	8	this	this	DET
ejpam-5478	211	9	work	work	NOUN
ejpam-5478	211	10	perfectly	perfectly	ADV
ejpam-5478	211	11	matched	match	VERB
ejpam-5478	211	12	those	those	PRON
ejpam-5478	211	13	obtained	obtain	VERB
ejpam-5478	211	14	through	through	ADP
ejpam-5478	211	15	the	the	DET
ejpam-5478	211	16	lagrangian	lagrangian	ADJ
ejpam-5478	211	17	formulation	formulation	NOUN
ejpam-5478	211	18	.	.	PUNCT
ejpam-5478	212	1	the	the	DET
ejpam-5478	212	2	hamiltonian	hamiltonian	ADJ
ejpam-5478	212	3	method	method	NOUN
ejpam-5478	212	4	for	for	ADP
ejpam-5478	212	5	generalized	generalized	ADJ
ejpam-5478	212	6	conformable	conformable	ADJ
ejpam-5478	212	7	differential	differential	NOUN
ejpam-5478	212	8	equations	equation	NOUN
ejpam-5478	212	9	with	with	ADP
ejpam-5478	212	10	higher	high	ADJ
ejpam-5478	212	11	-	-	PUNCT
ejpam-5478	212	12	order	order	NOUN
ejpam-5478	212	13	derivatives	derivative	NOUN
ejpam-5478	212	14	offers	offer	VERB
ejpam-5478	212	15	a	a	DET
ejpam-5478	212	16	structured	structured	ADJ
ejpam-5478	212	17	framework	framework	NOUN
ejpam-5478	212	18	for	for	ADP
ejpam-5478	212	19	studying	study	VERB
ejpam-5478	212	20	nonlinear	nonlinear	ADJ
ejpam-5478	212	21	dynamics	dynamic	NOUN
ejpam-5478	212	22	and	and	CCONJ
ejpam-5478	212	23	invariance	invariance	NOUN
ejpam-5478	212	24	principles	principle	NOUN
ejpam-5478	212	25	in	in	ADP
ejpam-5478	212	26	complex	complex	ADJ
ejpam-5478	212	27	systems	system	NOUN
ejpam-5478	212	28	involving	involve	VERB
ejpam-5478	212	29	controlled	control	VERB
ejpam-5478	212	30	lagrangians	lagrangian	NOUN
ejpam-5478	212	31	with	with	ADP
ejpam-5478	212	32	higher	high	ADJ
ejpam-5478	212	33	-	-	PUNCT
ejpam-5478	212	34	order	order	NOUN
ejpam-5478	212	35	derivatives	derivative	NOUN
ejpam-5478	212	36	.	.	PUNCT
ejpam-5478	213	1	this	this	DET
ejpam-5478	213	2	research	research	NOUN
ejpam-5478	213	3	enhances	enhance	VERB
ejpam-5478	213	4	theoretical	theoretical	ADJ
ejpam-5478	213	5	applications	application	NOUN
ejpam-5478	213	6	in	in	ADP
ejpam-5478	213	7	this	this	DET
ejpam-5478	213	8	domain	domain	NOUN
ejpam-5478	213	9	,	,	PUNCT
ejpam-5478	213	10	demonstrating	demonstrate	VERB
ejpam-5478	213	11	invariance	invariance	NOUN
ejpam-5478	213	12	results	result	NOUN
ejpam-5478	213	13	concerning	concern	VERB
ejpam-5478	213	14	state	state	NOUN
ejpam-5478	213	15	variables	variable	NOUN
ejpam-5478	213	16	and	and	CCONJ
ejpam-5478	213	17	exploring	explore	VERB
ejpam-5478	213	18	a	a	DET
ejpam-5478	213	19	natural	natural	ADJ
ejpam-5478	213	20	hamiltonian	hamiltonian	ADJ
ejpam-5478	213	21	formulation	formulation	NOUN
ejpam-5478	213	22	for	for	ADP
ejpam-5478	213	23	composite	composite	ADJ
ejpam-5478	213	24	higher	high	ADJ
ejpam-5478	213	25	derivative	derivative	ADJ
ejpam-5478	213	26	theories	theory	NOUN
ejpam-5478	213	27	involving	involve	VERB
ejpam-5478	213	28	time	time	NOUN
ejpam-5478	213	29	derivatives	derivative	NOUN
ejpam-5478	213	30	.	.	PUNCT
ejpam-5478	214	1	the	the	DET
ejpam-5478	214	2	approach	approach	NOUN
ejpam-5478	214	3	,	,	PUNCT
ejpam-5478	214	4	along	along	ADP
ejpam-5478	214	5	with	with	ADP
ejpam-5478	214	6	a	a	DET
ejpam-5478	214	7	numerical	numerical	ADJ
ejpam-5478	214	8	example	example	NOUN
ejpam-5478	214	9	,	,	PUNCT
ejpam-5478	214	10	enables	enable	VERB
ejpam-5478	214	11	us	we	PRON
ejpam-5478	214	12	to	to	PART
ejpam-5478	214	13	identify	identify	VERB
ejpam-5478	214	14	both	both	CCONJ
ejpam-5478	214	15	the	the	DET
ejpam-5478	214	16	static	static	ADJ
ejpam-5478	214	17	and	and	CCONJ
ejpam-5478	214	18	dynamic	dynamic	ADJ
ejpam-5478	214	19	parameters	parameter	NOUN
ejpam-5478	214	20	of	of	ADP
ejpam-5478	214	21	particles	particle	NOUN
ejpam-5478	214	22	or	or	CCONJ
ejpam-5478	214	23	structures	structure	NOUN
ejpam-5478	214	24	in	in	ADP
ejpam-5478	214	25	motion	motion	NOUN
ejpam-5478	214	26	.	.	PUNCT
ejpam-5478	215	1	this	this	PRON
ejpam-5478	215	2	forms	form	VERB
ejpam-5478	215	3	the	the	DET
ejpam-5478	215	4	foundation	foundation	NOUN
ejpam-5478	215	5	for	for	ADP
ejpam-5478	215	6	a	a	DET
ejpam-5478	215	7	new	new	ADJ
ejpam-5478	215	8	research	research	NOUN
ejpam-5478	215	9	project	project	NOUN
ejpam-5478	215	10	we	we	PRON
ejpam-5478	215	11	are	be	AUX
ejpam-5478	215	12	currently	currently	ADV
ejpam-5478	215	13	developing	develop	VERB
ejpam-5478	215	14	.	.	PUNCT
ejpam-5478	216	1	references	reference	NOUN
ejpam-5478	216	2	[	[	X
ejpam-5478	216	3	1	1	NUM
ejpam-5478	216	4	]	]	PUNCT
ejpam-5478	216	5	o	o	X
ejpam-5478	216	6	p	p	PROPN
ejpam-5478	216	7	agrawal	agrawal	PROPN
ejpam-5478	216	8	,	,	PUNCT
ejpam-5478	216	9	j	j	PROPN
ejpam-5478	216	10	gregory	gregory	PROPN
ejpam-5478	216	11	,	,	PUNCT
ejpam-5478	216	12	and	and	CCONJ
ejpam-5478	216	13	k	k	PROPN
ejpam-5478	216	14	pericak	pericak	ADJ
ejpam-5478	216	15	-	-	PUNCT
ejpam-5478	216	16	spector	spector	NOUN
ejpam-5478	216	17	.	.	PUNCT
ejpam-5478	217	1	a	a	DET
ejpam-5478	217	2	bliss	bliss	ADJ
ejpam-5478	217	3	-	-	PUNCT
ejpam-5478	217	4	type	type	NOUN
ejpam-5478	217	5	multiplier	multipli	ADJ
ejpam-5478	217	6	rule	rule	NOUN
ejpam-5478	217	7	for	for	ADP
ejpam-5478	217	8	constrained	constrain	VERB
ejpam-5478	217	9	variational	variational	ADJ
ejpam-5478	217	10	problems	problem	NOUN
ejpam-5478	217	11	with	with	ADP
ejpam-5478	217	12	time	time	NOUN
ejpam-5478	217	13	delay	delay	NOUN
ejpam-5478	217	14	.	.	PUNCT
ejpam-5478	218	1	journal	journal	PROPN
ejpam-5478	218	2	of	of	ADP
ejpam-5478	218	3	mathematical	mathematical	ADJ
ejpam-5478	218	4	analysis	analysis	NOUN
ejpam-5478	218	5	and	and	CCONJ
ejpam-5478	218	6	applications	application	NOUN
ejpam-5478	218	7	,	,	PUNCT
ejpam-5478	218	8	210:702–711	210:702–711	NUM
ejpam-5478	218	9	.	.	PUNCT
ejpam-5478	218	10	,	,	PUNCT
ejpam-5478	218	11	1997	1997	NUM
ejpam-5478	218	12	.	.	PUNCT
ejpam-5478	219	1	[	[	X
ejpam-5478	219	2	2	2	NUM
ejpam-5478	219	3	]	]	SYM
ejpam-5478	219	4	m	m	VERB
ejpam-5478	219	5	al	al	PROPN
ejpam-5478	219	6	-	-	PUNCT
ejpam-5478	219	7	masaeed	masaeed	NOUN
ejpam-5478	219	8	,	,	PUNCT
ejpam-5478	219	9	e	e	NOUN
ejpam-5478	219	10	m	m	NOUN
ejpam-5478	219	11	rabei	rabei	NOUN
ejpam-5478	219	12	,	,	PUNCT
ejpam-5478	219	13	and	and	CCONJ
ejpam-5478	219	14	a	a	DET
ejpam-5478	219	15	al	al	PROPN
ejpam-5478	219	16	-	-	PUNCT
ejpam-5478	219	17	jamel	jamel	PROPN
ejpam-5478	219	18	.	.	PUNCT
ejpam-5478	220	1	extension	extension	NOUN
ejpam-5478	220	2	of	of	ADP
ejpam-5478	220	3	the	the	DET
ejpam-5478	220	4	variational	variational	ADJ
ejpam-5478	220	5	method	method	NOUN
ejpam-5478	220	6	to	to	PART
ejpam-5478	220	7	conformable	conformable	VERB
ejpam-5478	220	8	quantum	quantum	ADJ
ejpam-5478	220	9	mechanics	mechanic	NOUN
ejpam-5478	220	10	.	.	PUNCT
ejpam-5478	221	1	mathematical	mathematical	ADJ
ejpam-5478	221	2	methods	method	NOUN
ejpam-5478	221	3	in	in	ADP
ejpam-5478	221	4	the	the	DET
ejpam-5478	221	5	applied	apply	VERB
ejpam-5478	221	6	sciences	science	NOUN
ejpam-5478	221	7	,	,	PUNCT
ejpam-5478	221	8	45(5):2910–2920	45(5):2910–2920	NUM
ejpam-5478	221	9	,	,	PUNCT
ejpam-5478	221	10	2021	2021	NUM
ejpam-5478	221	11	.	.	PUNCT
ejpam-5478	222	1	[	[	X
ejpam-5478	222	2	3	3	X
ejpam-5478	222	3	]	]	X
ejpam-5478	222	4	y	y	PROPN
ejpam-5478	222	5	alawaideh	alawaideh	PROPN
ejpam-5478	222	6	,	,	PUNCT
ejpam-5478	222	7	b	b	PROPN
ejpam-5478	222	8	al	al	PROPN
ejpam-5478	222	9	-	-	PUNCT
ejpam-5478	222	10	khamiseh	khamiseh	PROPN
ejpam-5478	222	11	,	,	PUNCT
ejpam-5478	222	12	and	and	CCONJ
ejpam-5478	222	13	w	w	PROPN
ejpam-5478	222	14	al	al	PROPN
ejpam-5478	222	15	-	-	PUNCT
ejpam-5478	222	16	awaida	awaida	PROPN
ejpam-5478	222	17	.	.	PUNCT
ejpam-5478	223	1	a	a	DET
ejpam-5478	223	2	new	new	ADJ
ejpam-5478	223	3	approach	approach	NOUN
ejpam-5478	223	4	for	for	ADP
ejpam-5478	223	5	the	the	DET
ejpam-5478	223	6	generalized	generalized	ADJ
ejpam-5478	223	7	dirac	dirac	NOUN
ejpam-5478	223	8	lagrangian	lagrangian	ADJ
ejpam-5478	223	9	density	density	NOUN
ejpam-5478	223	10	with	with	ADP
ejpam-5478	223	11	atangana	atangana	PROPN
ejpam-5478	223	12	–	–	PUNCT
ejpam-5478	223	13	baleanu	baleanu	ADJ
ejpam-5478	223	14	fractional	fractional	ADJ
ejpam-5478	223	15	derivative	derivative	NOUN
ejpam-5478	223	16	.	.	PUNCT
ejpam-5478	224	1	journal	journal	PROPN
ejpam-5478	224	2	—	—	PUNCT
ejpam-5478	224	3	mesa	mesa	PROPN
ejpam-5478	224	4	,	,	PUNCT
ejpam-5478	224	5	13:497–509	13:497–509	PROPN
ejpam-5478	224	6	.	.	PROPN
ejpam-5478	224	7	,	,	PUNCT
ejpam-5478	224	8	2022	2022	NUM
ejpam-5478	224	9	.	.	PUNCT
ejpam-5478	225	1	[	[	X
ejpam-5478	225	2	4	4	NUM
ejpam-5478	225	3	]	]	X
ejpam-5478	225	4	y	y	PROPN
ejpam-5478	225	5	alawaideh	alawaideh	PROPN
ejpam-5478	225	6	,	,	PUNCT
ejpam-5478	225	7	j	j	PROPN
ejpam-5478	225	8	khalifeh	khalifeh	PROPN
ejpam-5478	225	9	,	,	PUNCT
ejpam-5478	225	10	and	and	CCONJ
ejpam-5478	225	11	r	r	NOUN
ejpam-5478	225	12	hijjawi	hijjawi	NOUN
ejpam-5478	225	13	.	.	PUNCT
ejpam-5478	226	1	reformulation	reformulation	NOUN
ejpam-5478	226	2	of	of	ADP
ejpam-5478	226	3	degasperis	degasperis	NOUN
ejpam-5478	226	4	-	-	PUNCT
ejpam-5478	226	5	procesifield	procesifield	NOUN
ejpam-5478	226	6	by	by	ADP
ejpam-5478	226	7	functional	functional	ADJ
ejpam-5478	226	8	derivatives	derivative	NOUN
ejpam-5478	226	9	.	.	PUNCT
ejpam-5478	227	1	jordanian	jordanian	ADJ
ejpam-5478	227	2	journal	journal	PROPN
ejpam-5478	227	3	of	of	ADP
ejpam-5478	227	4	physics	physics	PROPN
ejpam-5478	227	5	,	,	PUNCT
ejpam-5478	227	6	13:67–72	13:67–72	NUM
ejpam-5478	227	7	.	.	PUNCT
ejpam-5478	227	8	,	,	PUNCT
ejpam-5478	227	9	2020	2020	NUM
ejpam-5478	227	10	.	.	PUNCT
ejpam-5478	228	1	[	[	X
ejpam-5478	228	2	5	5	X
ejpam-5478	228	3	]	]	X
ejpam-5478	228	4	y.	y.	NOUN
ejpam-5478	228	5	alawaideh	alawaideh	PROPN
ejpam-5478	228	6	,	,	PUNCT
ejpam-5478	228	7	j.	j.	PROPN
ejpam-5478	228	8	khalifeh	khalifeh	PROPN
ejpam-5478	228	9	,	,	PUNCT
ejpam-5478	228	10	and	and	CCONJ
ejpam-5478	228	11	r.	r.	PROPN
ejpam-5478	228	12	hijjawi	hijjawi	PROPN
ejpam-5478	228	13	.	.	PUNCT
ejpam-5478	229	1	hamiltonian	hamiltonian	ADJ
ejpam-5478	229	2	formulation	formulation	NOUN
ejpam-5478	229	3	for	for	ADP
ejpam-5478	229	4	continuous	continuous	ADJ
ejpam-5478	229	5	third	third	ADJ
ejpam-5478	229	6	-	-	PUNCT
ejpam-5478	229	7	order	order	NOUN
ejpam-5478	229	8	systems	system	NOUN
ejpam-5478	229	9	using	use	VERB
ejpam-5478	229	10	fractional	fractional	ADJ
ejpam-5478	229	11	derivatives	derivative	NOUN
ejpam-5478	229	12	.	.	PUNCT
ejpam-5478	230	1	jordanian	jordanian	ADJ
ejpam-5478	230	2	journal	journal	PROPN
ejpam-5478	230	3	of	of	ADP
ejpam-5478	230	4	physics	physics	PROPN
ejpam-5478	230	5	,	,	PUNCT
ejpam-5478	230	6	14:35–47	14:35–47	PROPN
ejpam-5478	230	7	.	.	PROPN
ejpam-5478	230	8	,	,	PUNCT
ejpam-5478	230	9	2021	2021	NUM
ejpam-5478	230	10	.	.	PUNCT
ejpam-5478	231	1	[	[	X
ejpam-5478	231	2	6	6	NUM
ejpam-5478	231	3	]	]	X
ejpam-5478	231	4	y	y	PROPN
ejpam-5478	231	5	m	m	NOUN
ejpam-5478	231	6	alawaideh	alawaideh	NOUN
ejpam-5478	231	7	and	and	CCONJ
ejpam-5478	231	8	b	b	PROPN
ejpam-5478	231	9	m	m	PROPN
ejpam-5478	231	10	al	al	PROPN
ejpam-5478	231	11	-	-	PUNCT
ejpam-5478	231	12	khamiseh	khamiseh	PROPN
ejpam-5478	231	13	.	.	PUNCT
ejpam-5478	232	1	the	the	DET
ejpam-5478	232	2	new	new	ADJ
ejpam-5478	232	3	formulation	formulation	NOUN
ejpam-5478	232	4	of	of	ADP
ejpam-5478	232	5	hamiltonian	hamiltonian	ADJ
ejpam-5478	232	6	second	second	ADJ
ejpam-5478	232	7	order	order	NOUN
ejpam-5478	232	8	continuous	continuous	ADJ
ejpam-5478	232	9	systems	system	NOUN
ejpam-5478	232	10	of	of	ADP
ejpam-5478	232	11	riemann	riemann	PROPN
ejpam-5478	232	12	-	-	PUNCT
ejpam-5478	232	13	liouville	liouville	VERB
ejpam-5478	232	14	fractional	fractional	ADJ
ejpam-5478	232	15	derivatives	derivative	NOUN
ejpam-5478	232	16	.	.	PUNCT
ejpam-5478	233	1	econometrica	econometrica	PROPN
ejpam-5478	233	2	,	,	PUNCT
ejpam-5478	233	3	97:125210	97:125210	NOUN
ejpam-5478	233	4	,	,	PUNCT
ejpam-5478	233	5	2022	2022	NUM
ejpam-5478	233	6	.	.	PUNCT
ejpam-5478	234	1	[	[	X
ejpam-5478	234	2	7	7	X
ejpam-5478	234	3	]	]	X
ejpam-5478	234	4	y	y	PROPN
ejpam-5478	234	5	m	m	NOUN
ejpam-5478	234	6	alawaideh	alawaideh	PROPN
ejpam-5478	234	7	,	,	PUNCT
ejpam-5478	234	8	b	b	PROPN
ejpam-5478	234	9	m	m	NOUN
ejpam-5478	234	10	alkhamiseh	alkhamiseh	ADJ
ejpam-5478	234	11	,	,	PUNCT
ejpam-5478	234	12	and	and	CCONJ
ejpam-5478	234	13	m	m	PROPN
ejpam-5478	234	14	s	s	PROPN
ejpam-5478	234	15	lotayif	lotayif	PROPN
ejpam-5478	234	16	.	.	PUNCT
ejpam-5478	235	1	reformulation	reformulation	ADJ
ejpam-5478	235	2	complex	complex	ADJ
ejpam-5478	235	3	scalar	scalar	ADJ
ejpam-5478	235	4	field	field	NOUN
ejpam-5478	235	5	interacting	interact	VERB
ejpam-5478	235	6	with	with	ADP
ejpam-5478	235	7	the	the	DET
ejpam-5478	235	8	electromagnetic	electromagnetic	ADJ
ejpam-5478	235	9	lagrangian	lagrangian	ADJ
ejpam-5478	235	10	density	density	NOUN
ejpam-5478	235	11	by	by	ADP
ejpam-5478	235	12	riemann	riemann	PROPN
ejpam-5478	235	13	-	-	PUNCT
ejpam-5478	235	14	liouville	liouville	VERB
ejpam-5478	235	15	factional	factional	ADJ
ejpam-5478	235	16	derivative	derivative	NOUN
ejpam-5478	235	17	.	.	PUNCT
ejpam-5478	236	1	information	information	NOUN
ejpam-5478	236	2	sciences	sciences	PROPN
ejpam-5478	236	3	,	,	PUNCT
ejpam-5478	236	4	2121:21	2121:21	NUM
ejpam-5478	236	5	.	.	PUNCT
ejpam-5478	236	6	,	,	PUNCT
ejpam-5478	236	7	2022	2022	NUM
ejpam-5478	236	8	.	.	PUNCT
ejpam-5478	237	1	[	[	X
ejpam-5478	237	2	8	8	NUM
ejpam-5478	237	3	]	]	X
ejpam-5478	237	4	yazen	yazen	NOUN
ejpam-5478	237	5	m	m	NOUN
ejpam-5478	237	6	alawaideh	alawaideh	PROPN
ejpam-5478	237	7	,	,	PUNCT
ejpam-5478	237	8	bashar	bashar	PROPN
ejpam-5478	237	9	m	m	PROPN
ejpam-5478	237	10	al	al	PROPN
ejpam-5478	237	11	-	-	PUNCT
ejpam-5478	237	12	khamiseh	khamiseh	PROPN
ejpam-5478	237	13	,	,	PUNCT
ejpam-5478	237	14	mohammad	mohammad	PROPN
ejpam-5478	237	15	kanan	kanan	PROPN
ejpam-5478	237	16	,	,	PUNCT
ejpam-5478	237	17	and	and	CCONJ
ejpam-5478	237	18	fekadu	fekadu	ADJ
ejpam-5478	237	19	tesgera	tesgera	NOUN
ejpam-5478	237	20	agama	agama	PROPN
ejpam-5478	237	21	.	.	PUNCT
ejpam-5478	238	1	fractional	fractional	ADJ
ejpam-5478	238	2	quantization	quantization	NOUN
ejpam-5478	238	3	of	of	ADP
ejpam-5478	238	4	podolsky	podolsky	ADJ
ejpam-5478	238	5	electrodynamics	electrodynamic	NOUN
ejpam-5478	238	6	using	use	VERB
ejpam-5478	238	7	fractional	fractional	PROPN
ejpam-5478	238	8	y.	y.	PROPN
ejpam-5478	238	9	m.	m.	PROPN
ejpam-5478	238	10	alawaideh	alawaideh	PROPN
ejpam-5478	238	11	et	et	PROPN
ejpam-5478	238	12	al	al	PROPN
ejpam-5478	238	13	.	.	PUNCT
ejpam-5478	238	14	/	/	SYM
ejpam-5478	238	15	eur	eur	PROPN
ejpam-5478	238	16	.	.	PUNCT
ejpam-5478	239	1	j.	j.	PROPN
ejpam-5478	239	2	pure	pure	PROPN
ejpam-5478	239	3	appl	appl	PROPN
ejpam-5478	239	4	.	.	PROPN
ejpam-5478	239	5	math	math	PROPN
ejpam-5478	239	6	,	,	PUNCT
ejpam-5478	239	7	18	18	NUM
ejpam-5478	239	8	(	(	PUNCT
ejpam-5478	239	9	1	1	NUM
ejpam-5478	239	10	)	)	PUNCT
ejpam-5478	239	11	(	(	PUNCT
ejpam-5478	239	12	2025	2025	NUM
ejpam-5478	239	13	)	)	PUNCT
ejpam-5478	239	14	,	,	PUNCT
ejpam-5478	239	15	5478	5478	NUM
ejpam-5478	239	16	11	11	NUM
ejpam-5478	239	17	of	of	ADP
ejpam-5478	239	18	14	14	NUM
ejpam-5478	239	19	hamilton	hamilton	PROPN
ejpam-5478	239	20	-	-	PUNCT
ejpam-5478	239	21	jacobi	jacobi	PROPN
ejpam-5478	239	22	formulation	formulation	PROPN
ejpam-5478	239	23	.	.	PUNCT
ejpam-5478	240	1	progress	progress	NOUN
ejpam-5478	240	2	in	in	ADP
ejpam-5478	240	3	fractional	fractional	ADJ
ejpam-5478	240	4	differentiation	differentiation	NOUN
ejpam-5478	240	5	and	and	CCONJ
ejpam-5478	240	6	applications	application	NOUN
ejpam-5478	240	7	,	,	PUNCT
ejpam-5478	240	8	9(2):211–221	9(2):211–221	NUM
ejpam-5478	240	9	,	,	PUNCT
ejpam-5478	240	10	2023	2023	NUM
ejpam-5478	240	11	.	.	PUNCT
ejpam-5478	241	1	211–221	211–221	NUM
ejpam-5478	241	2	.	.	PUNCT
ejpam-5478	242	1	https://doi.org/10.18576/pfda/090202	https://doi.org/10.18576/pfda/090202	NOUN
ejpam-5478	242	2	.	.	PUNCT
ejpam-5478	243	1	[	[	X
ejpam-5478	243	2	9	9	NUM
ejpam-5478	243	3	]	]	X
ejpam-5478	243	4	bashar	bashar	PROPN
ejpam-5478	243	5	alkhamiseh	alkhamiseh	PROPN
ejpam-5478	243	6	and	and	CCONJ
ejpam-5478	243	7	yazen	yazen	NOUN
ejpam-5478	243	8	alawaideh	alawaideh	NOUN
ejpam-5478	243	9	.	.	PUNCT
ejpam-5478	244	1	electromagnetic	electromagnetic	ADJ
ejpam-5478	244	2	interaction	interaction	NOUN
ejpam-5478	244	3	into	into	ADP
ejpam-5478	244	4	the	the	DET
ejpam-5478	244	5	lagrangian	lagrangian	ADJ
ejpam-5478	244	6	density	density	NOUN
ejpam-5478	244	7	fermi	fermi	NOUN
ejpam-5478	244	8	field	field	NOUN
ejpam-5478	244	9	:	:	PUNCT
ejpam-5478	244	10	fractional	fractional	ADJ
ejpam-5478	244	11	formulation	formulation	NOUN
ejpam-5478	244	12	.	.	PUNCT
ejpam-5478	245	1	jordan	jordan	PROPN
ejpam-5478	245	2	journal	journal	PROPN
ejpam-5478	245	3	of	of	ADP
ejpam-5478	245	4	physics	physics	PROPN
ejpam-5478	245	5	,	,	PUNCT
ejpam-5478	245	6	16(3):299–304	16(3):299–304	PROPN
ejpam-5478	245	7	,	,	PUNCT
ejpam-5478	245	8	1998	1998	NUM
ejpam-5478	245	9	.	.	PUNCT
ejpam-5478	246	1	04	04	NUM
ejpam-5478	246	2	.	.	PUNCT
ejpam-5478	247	1	https://doi.org/10.47011/16.3.5	https://doi.org/10.47011/16.3.5	PROPN
ejpam-5478	247	2	.	.	PUNCT
ejpam-5478	248	1	[	[	X
ejpam-5478	248	2	10	10	NUM
ejpam-5478	248	3	]	]	X
ejpam-5478	248	4	a	a	DET
ejpam-5478	248	5	almalki	almalki	NOUN
ejpam-5478	248	6	,	,	PUNCT
ejpam-5478	248	7	y	y	PROPN
ejpam-5478	248	8	m	m	VERB
ejpam-5478	248	9	alawaideh	alawaideh	PROPN
ejpam-5478	248	10	,	,	PUNCT
ejpam-5478	248	11	b	b	PROPN
ejpam-5478	248	12	m	m	PROPN
ejpam-5478	248	13	al	al	PROPN
ejpam-5478	248	14	-	-	PUNCT
ejpam-5478	248	15	khamiseh	khamiseh	PROPN
ejpam-5478	248	16	,	,	PUNCT
ejpam-5478	248	17	and	and	CCONJ
ejpam-5478	248	18	s	s	PROPN
ejpam-5478	248	19	e	e	NOUN
ejpam-5478	248	20	alawaideh	alawaideh	NOUN
ejpam-5478	248	21	.	.	PUNCT
ejpam-5478	249	1	rhamilton	rhamilton	NOUN
ejpam-5478	249	2	formulation	formulation	NOUN
ejpam-5478	249	3	for	for	ADP
ejpam-5478	249	4	the	the	DET
ejpam-5478	249	5	electrodynamics	electrodynamic	NOUN
ejpam-5478	249	6	of	of	ADP
ejpam-5478	249	7	generalized	generalized	ADJ
ejpam-5478	249	8	maxwell	maxwell	PROPN
ejpam-5478	249	9	using	use	VERB
ejpam-5478	249	10	fractional	fractional	ADJ
ejpam-5478	249	11	derivatives	derivative	NOUN
ejpam-5478	249	12	.	.	PUNCT
ejpam-5478	250	1	[	[	X
ejpam-5478	250	2	11	11	NUM
ejpam-5478	250	3	]	]	PUNCT
ejpam-5478	250	4	h	h	NOUN
ejpam-5478	250	5	aykut	aykut	NOUN
ejpam-5478	250	6	,	,	PUNCT
ejpam-5478	250	7	b	b	PROPN
ejpam-5478	250	8	yılmaz	yılmaz	PROPN
ejpam-5478	250	9	,	,	PUNCT
ejpam-5478	250	10	and	and	CCONJ
ejpam-5478	250	11	d	d	ADP
ejpam-5478	250	12	baleanu	baleanu	NOUN
ejpam-5478	250	13	.	.	PUNCT
ejpam-5478	251	1	on	on	ADP
ejpam-5478	251	2	the	the	DET
ejpam-5478	251	3	geometric	geometric	ADJ
ejpam-5478	251	4	and	and	CCONJ
ejpam-5478	251	5	physical	physical	ADJ
ejpam-5478	251	6	properties	property	NOUN
ejpam-5478	251	7	of	of	ADP
ejpam-5478	251	8	conformable	conformable	ADJ
ejpam-5478	251	9	derivative	derivative	NOUN
ejpam-5478	251	10	.	.	PUNCT
ejpam-5478	252	1	mathematical	mathematical	ADJ
ejpam-5478	252	2	sciences	science	NOUN
ejpam-5478	252	3	and	and	CCONJ
ejpam-5478	252	4	applications	application	NOUN
ejpam-5478	252	5	e	e	NOUN
ejpam-5478	252	6	-	-	NOUN
ejpam-5478	252	7	notes	note	NOUN
ejpam-5478	252	8	,	,	PUNCT
ejpam-5478	252	9	12(2	12(2	NUM
ejpam-5478	252	10	):	):	PUNCT
ejpam-5478	252	11	.	.	PROPN
ejpam-5478	252	12	,	,	PUNCT
ejpam-5478	252	13	2024	2024	NUM
ejpam-5478	252	14	.	.	PUNCT
ejpam-5478	253	1	[	[	X
ejpam-5478	253	2	12	12	NUM
ejpam-5478	253	3	]	]	X
ejpam-5478	253	4	d	d	NOUN
ejpam-5478	253	5	baleanu	baleanu	NOUN
ejpam-5478	253	6	,	,	PUNCT
ejpam-5478	253	7	o	o	NOUN
ejpam-5478	253	8	defterli	defterli	NOUN
ejpam-5478	253	9	,	,	PUNCT
ejpam-5478	253	10	and	and	CCONJ
ejpam-5478	253	11	o	o	X
ejpam-5478	253	12	p	p	PROPN
ejpam-5478	253	13	agrawal	agrawal	PROPN
ejpam-5478	253	14	.	.	PUNCT
ejpam-5478	254	1	a	a	DET
ejpam-5478	254	2	central	central	ADJ
ejpam-5478	254	3	difference	difference	NOUN
ejpam-5478	254	4	numerical	numerical	ADJ
ejpam-5478	254	5	scheme	scheme	NOUN
ejpam-5478	254	6	for	for	ADP
ejpam-5478	254	7	fractional	fractional	ADJ
ejpam-5478	254	8	optimal	optimal	ADJ
ejpam-5478	254	9	control	control	NOUN
ejpam-5478	254	10	problems	problem	NOUN
ejpam-5478	254	11	.	.	PUNCT
ejpam-5478	255	1	journal	journal	NOUN
ejpam-5478	255	2	of	of	ADP
ejpam-5478	255	3	vibration	vibration	NOUN
ejpam-5478	255	4	and	and	CCONJ
ejpam-5478	255	5	control	control	NOUN
ejpam-5478	255	6	,	,	PUNCT
ejpam-5478	255	7	15:583–597	15:583–597	PROPN
ejpam-5478	255	8	.	.	PROPN
ejpam-5478	255	9	,	,	PUNCT
ejpam-5478	255	10	2009	2009	NUM
ejpam-5478	255	11	.	.	PUNCT
ejpam-5478	256	1	[	[	X
ejpam-5478	256	2	13	13	NUM
ejpam-5478	256	3	]	]	X
ejpam-5478	256	4	d	d	NOUN
ejpam-5478	256	5	baleanu	baleanu	NOUN
ejpam-5478	256	6	,	,	PUNCT
ejpam-5478	256	7	s	s	PART
ejpam-5478	256	8	i	i	PRON
ejpam-5478	256	9	muslih	muslih	VERB
ejpam-5478	256	10	,	,	PUNCT
ejpam-5478	256	11	and	and	CCONJ
ejpam-5478	256	12	k	k	PROPN
ejpam-5478	256	13	taş.	taş.	PROPN
ejpam-5478	256	14	fractional	fractional	ADJ
ejpam-5478	256	15	hamiltonian	hamiltonian	ADJ
ejpam-5478	256	16	analysis	analysis	NOUN
ejpam-5478	256	17	of	of	ADP
ejpam-5478	256	18	higher	high	ADJ
ejpam-5478	256	19	order	order	NOUN
ejpam-5478	256	20	derivatives	derivative	NOUN
ejpam-5478	256	21	systems	system	NOUN
ejpam-5478	256	22	.	.	PUNCT
ejpam-5478	257	1	journal	journal	PROPN
ejpam-5478	257	2	of	of	ADP
ejpam-5478	257	3	mathematical	mathematical	ADJ
ejpam-5478	257	4	physics	physics	NOUN
ejpam-5478	257	5	,	,	PUNCT
ejpam-5478	257	6	47(10	47(10	NUM
ejpam-5478	257	7	):	):	PUNCT
ejpam-5478	257	8	.	.	PROPN
ejpam-5478	257	9	,	,	PUNCT
ejpam-5478	257	10	2006	2006	NUM
ejpam-5478	257	11	.	.	PUNCT
ejpam-5478	258	1	[	[	X
ejpam-5478	258	2	14	14	NUM
ejpam-5478	258	3	]	]	SYM
ejpam-5478	258	4	j	j	PROPN
ejpam-5478	258	5	l	l	NOUN
ejpam-5478	258	6	basdevant	basdevant	NOUN
ejpam-5478	258	7	and	and	CCONJ
ejpam-5478	258	8	j	j	PROPN
ejpam-5478	258	9	dalibard	dalibard	NOUN
ejpam-5478	258	10	.	.	PUNCT
ejpam-5478	259	1	the	the	DET
ejpam-5478	259	2	lagrangian	lagrangian	ADJ
ejpam-5478	259	3	and	and	CCONJ
ejpam-5478	259	4	hamiltonian	hamiltonian	ADJ
ejpam-5478	259	5	formalisms	formalism	NOUN
ejpam-5478	259	6	,	,	PUNCT
ejpam-5478	259	7	lorentz	lorentz	PROPN
ejpam-5478	259	8	force	force	NOUN
ejpam-5478	259	9	in	in	ADP
ejpam-5478	259	10	quantum	quantum	ADJ
ejpam-5478	259	11	mechanics	mechanic	NOUN
ejpam-5478	259	12	.	.	PUNCT
ejpam-5478	260	1	quantum	quantum	ADJ
ejpam-5478	260	2	mechanics	mechanic	NOUN
ejpam-5478	260	3	,	,	PUNCT
ejpam-5478	260	4	pages	page	NOUN
ejpam-5478	260	5	293–308	293–308	NUM
ejpam-5478	260	6	.	.	PROPN
ejpam-5478	260	7	,	,	PUNCT
ejpam-5478	260	8	2002	2002	NUM
ejpam-5478	260	9	.	.	PUNCT
ejpam-5478	261	1	[	[	X
ejpam-5478	261	2	15	15	NUM
ejpam-5478	261	3	]	]	X
ejpam-5478	261	4	j	j	PROPN
ejpam-5478	261	5	r	r	PROPN
ejpam-5478	261	6	cary	cary	PROPN
ejpam-5478	261	7	and	and	CCONJ
ejpam-5478	261	8	a	a	DET
ejpam-5478	261	9	j	j	PROPN
ejpam-5478	261	10	brizard	brizard	ADJ
ejpam-5478	261	11	.	.	PUNCT
ejpam-5478	262	1	hamiltonian	hamiltonian	ADJ
ejpam-5478	262	2	theory	theory	NOUN
ejpam-5478	262	3	of	of	ADP
ejpam-5478	262	4	guiding	guide	VERB
ejpam-5478	262	5	-	-	PUNCT
ejpam-5478	262	6	center	center	NOUN
ejpam-5478	262	7	motion	motion	NOUN
ejpam-5478	262	8	.	.	PUNCT
ejpam-5478	263	1	reviews	review	NOUN
ejpam-5478	263	2	of	of	ADP
ejpam-5478	263	3	modern	modern	ADJ
ejpam-5478	263	4	physics	physic	NOUN
ejpam-5478	263	5	,	,	PUNCT
ejpam-5478	263	6	81((2)):693–738	81((2)):693–738	NOUN
ejpam-5478	263	7	.	.	PUNCT
ejpam-5478	264	1	https://doi.org/10.1103/revmodphys.81.693	https://doi.org/10.1103/revmodphys.81.693	PROPN
ejpam-5478	264	2	,	,	PUNCT
ejpam-5478	264	3	2009	2009	NUM
ejpam-5478	264	4	.	.	PUNCT
ejpam-5478	265	1	[	[	X
ejpam-5478	265	2	16	16	NUM
ejpam-5478	265	3	]	]	X
ejpam-5478	265	4	i	i	PRON
ejpam-5478	265	5	cho	cho	VERB
ejpam-5478	265	6	and	and	CCONJ
ejpam-5478	265	7	o	o	NOUN
ejpam-5478	265	8	k	k	PROPN
ejpam-5478	265	9	kwon	kwon	PROPN
ejpam-5478	265	10	.	.	PUNCT
ejpam-5478	266	1	generalized	generalize	VERB
ejpam-5478	266	2	lee	lee	PROPN
ejpam-5478	266	3	-	-	PUNCT
ejpam-5478	266	4	wick	wick	NOUN
ejpam-5478	266	5	formulation	formulation	NOUN
ejpam-5478	266	6	from	from	ADP
ejpam-5478	266	7	higher	high	ADJ
ejpam-5478	266	8	derivative	derivative	ADJ
ejpam-5478	266	9	field	field	NOUN
ejpam-5478	266	10	theories	theory	NOUN
ejpam-5478	266	11	.	.	PUNCT
ejpam-5478	267	1	physical	physical	ADJ
ejpam-5478	267	2	review	review	PROPN
ejpam-5478	267	3	,	,	PUNCT
ejpam-5478	267	4	d82:025013	d82:025013	PROPN
ejpam-5478	267	5	.	.	PROPN
ejpam-5478	267	6	,	,	PUNCT
ejpam-5478	267	7	2010	2010	NUM
ejpam-5478	267	8	.	.	PUNCT
ejpam-5478	268	1	[	[	X
ejpam-5478	268	2	17	17	NUM
ejpam-5478	268	3	]	]	X
ejpam-5478	268	4	e	e	NOUN
ejpam-5478	268	5	m	m	PROPN
ejpam-5478	268	6	rabei	rabei	VERB
ejpam-5478	268	7	h	h	NOUN
ejpam-5478	268	8	a	a	DET
ejpam-5478	268	9	el	el	PROPN
ejpam-5478	268	10	-	-	PUNCT
ejpam-5478	268	11	zalan	zalan	NOUN
ejpam-5478	268	12	,	,	PUNCT
ejpam-5478	268	13	s	s	VERB
ejpam-5478	268	14	i	i	PRON
ejpam-5478	268	15	muslih	muslih	VERB
ejpam-5478	268	16	and	and	CCONJ
ejpam-5478	268	17	d	d	X
ejpam-5478	268	18	baleanu	baleanu	NOUN
ejpam-5478	268	19	.	.	PUNCT
ejpam-5478	269	1	hamilton	hamilton	PROPN
ejpam-5478	269	2	formulation	formulation	PROPN
ejpam-5478	269	3	for	for	ADP
ejpam-5478	269	4	continuous	continuous	ADJ
ejpam-5478	269	5	systems	system	NOUN
ejpam-5478	269	6	with	with	ADP
ejpam-5478	269	7	second	second	ADJ
ejpam-5478	269	8	order	order	NOUN
ejpam-5478	269	9	derivatives	derivative	NOUN
ejpam-5478	269	10	,	,	PUNCT
ejpam-5478	269	11	.	.	PUNCT
ejpam-5478	270	1	international	international	ADJ
ejpam-5478	270	2	journal	journal	PROPN
ejpam-5478	270	3	of	of	ADP
ejpam-5478	270	4	theoretical	theoretical	ADJ
ejpam-5478	270	5	physics	physics	NOUN
ejpam-5478	270	6	,	,	PUNCT
ejpam-5478	270	7	47:2195–2202	47:2195–2202	PROPN
ejpam-5478	270	8	.	.	PROPN
ejpam-5478	270	9	,	,	PUNCT
ejpam-5478	270	10	2008	2008	NUM
ejpam-5478	270	11	.	.	PUNCT
ejpam-5478	271	1	[	[	X
ejpam-5478	271	2	18	18	NUM
ejpam-5478	271	3	]	]	X
ejpam-5478	271	4	r	r	NOUN
ejpam-5478	271	5	khalil	khalil	PROPN
ejpam-5478	271	6	,	,	PUNCT
ejpam-5478	271	7	m	m	PROPN
ejpam-5478	271	8	al	al	PROPN
ejpam-5478	271	9	horani	horani	PROPN
ejpam-5478	271	10	,	,	PUNCT
ejpam-5478	271	11	a	a	DET
ejpam-5478	271	12	yousef	yousef	PROPN
ejpam-5478	271	13	,	,	PUNCT
ejpam-5478	271	14	and	and	CCONJ
ejpam-5478	271	15	m	m	PROPN
ejpam-5478	271	16	j	j	PROPN
ejpam-5478	271	17	sababheh	sababheh	NOUN
ejpam-5478	271	18	.	.	PUNCT
ejpam-5478	272	1	fractional	fractional	ADJ
ejpam-5478	272	2	hamiltonian	hamiltonian	ADJ
ejpam-5478	272	3	analysis	analysis	NOUN
ejpam-5478	272	4	of	of	ADP
ejpam-5478	272	5	higher	high	ADJ
ejpam-5478	272	6	order	order	NOUN
ejpam-5478	272	7	derivatives	derivative	NOUN
ejpam-5478	272	8	systems	system	NOUN
ejpam-5478	272	9	.	.	PUNCT
ejpam-5478	273	1	comput	comput	NOUN
ejpam-5478	273	2	.	.	PUNCT
ejpam-5478	274	1	appl	appl	PROPN
ejpam-5478	274	2	.	.	PROPN
ejpam-5478	274	3	math	math	PROPN
ejpam-5478	274	4	,	,	PUNCT
ejpam-5478	274	5	264:6570	264:6570	NUM
ejpam-5478	274	6	,	,	PUNCT
ejpam-5478	274	7	2014	2014	NUM
ejpam-5478	274	8	.	.	PUNCT
ejpam-5478	275	1	[	[	X
ejpam-5478	275	2	19	19	NUM
ejpam-5478	275	3	]	]	X
ejpam-5478	275	4	m	m	PROPN
ejpam-5478	275	5	klimek	klimek	PROPN
ejpam-5478	275	6	.	.	PUNCT
ejpam-5478	276	1	fractional	fractional	ADJ
ejpam-5478	276	2	sequential	sequential	ADJ
ejpam-5478	276	3	mechanics	mechanic	NOUN
ejpam-5478	276	4	—	—	PUNCT
ejpam-5478	276	5	models	model	NOUN
ejpam-5478	276	6	with	with	ADP
ejpam-5478	276	7	symmetric	symmetric	ADJ
ejpam-5478	276	8	fractional	fractional	ADJ
ejpam-5478	276	9	derivative	derivative	NOUN
ejpam-5478	276	10	.	.	PUNCT
ejpam-5478	277	1	czechoslovak	czechoslovak	ADJ
ejpam-5478	277	2	journal	journal	PROPN
ejpam-5478	277	3	of	of	ADP
ejpam-5478	277	4	physics	physics	PROPN
ejpam-5478	277	5	,	,	PUNCT
ejpam-5478	277	6	51:1348–1354	51:1348–1354	PROPN
ejpam-5478	277	7	,	,	PUNCT
ejpam-5478	277	8	2001	2001	NUM
ejpam-5478	277	9	.	.	PUNCT
ejpam-5478	278	1	[	[	X
ejpam-5478	278	2	20	20	NUM
ejpam-5478	278	3	]	]	X
ejpam-5478	278	4	j	j	PROPN
ejpam-5478	278	5	t	t	PROPN
ejpam-5478	278	6	machado	machado	PROPN
ejpam-5478	278	7	.	.	PUNCT
ejpam-5478	279	1	fractional	fractional	ADJ
ejpam-5478	279	2	derivatives	derivative	NOUN
ejpam-5478	279	3	:	:	PUNCT
ejpam-5478	279	4	probability	probability	NOUN
ejpam-5478	279	5	interpretation	interpretation	NOUN
ejpam-5478	279	6	and	and	CCONJ
ejpam-5478	279	7	frequency	frequency	NOUN
ejpam-5478	279	8	response	response	NOUN
ejpam-5478	279	9	of	of	ADP
ejpam-5478	279	10	rational	rational	ADJ
ejpam-5478	279	11	approximations	approximation	NOUN
ejpam-5478	279	12	.	.	PUNCT
ejpam-5478	280	1	communications	communication	NOUN
ejpam-5478	280	2	in	in	ADP
ejpam-5478	280	3	nonlinear	nonlinear	ADJ
ejpam-5478	280	4	science	science	NOUN
ejpam-5478	280	5	and	and	CCONJ
ejpam-5478	280	6	numerical	numerical	PROPN
ejpam-5478	280	7	simulation	simulation	PROPN
ejpam-5478	280	8	,	,	PUNCT
ejpam-5478	280	9	14:3492–3497	14:3492–3497	NUM
ejpam-5478	280	10	,	,	PUNCT
ejpam-5478	280	11	1989	1989	NUM
ejpam-5478	280	12	.	.	PUNCT
ejpam-5478	281	1	[	[	X
ejpam-5478	281	2	21	21	NUM
ejpam-5478	281	3	]	]	X
ejpam-5478	281	4	a	a	DET
ejpam-5478	281	5	martynyuk	martynyuk	NOUN
ejpam-5478	281	6	and	and	CCONJ
ejpam-5478	281	7	y	y	PROPN
ejpam-5478	281	8	a	a	DET
ejpam-5478	281	9	chernienko	chernienko	NOUN
ejpam-5478	281	10	.	.	PUNCT
ejpam-5478	282	1	boundedness	boundedness	NOUN
ejpam-5478	282	2	of	of	ADP
ejpam-5478	282	3	solutions	solution	NOUN
ejpam-5478	282	4	of	of	ADP
ejpam-5478	282	5	conformable	conformable	ADJ
ejpam-5478	282	6	fractional	fractional	ADJ
ejpam-5478	282	7	equations	equation	NOUN
ejpam-5478	282	8	of	of	ADP
ejpam-5478	282	9	perturbed	perturb	VERB
ejpam-5478	282	10	motion	motion	NOUN
ejpam-5478	282	11	.	.	PUNCT
ejpam-5478	283	1	international	international	ADJ
ejpam-5478	283	2	applied	apply	VERB
ejpam-5478	283	3	mechanics	mechanic	NOUN
ejpam-5478	283	4	,	,	PUNCT
ejpam-5478	283	5	56:572–580	56:572–580	PROPN
ejpam-5478	283	6	.	.	PROPN
ejpam-5478	283	7	,	,	PUNCT
ejpam-5478	283	8	2020	2020	NUM
ejpam-5478	283	9	.	.	PUNCT
ejpam-5478	284	1	[	[	X
ejpam-5478	284	2	22	22	NUM
ejpam-5478	284	3	]	]	SYM
ejpam-5478	284	4	s	s	X
ejpam-5478	284	5	i	i	PRON
ejpam-5478	284	6	muslih	muslih	ADJ
ejpam-5478	284	7	and	and	CCONJ
ejpam-5478	284	8	h	h	DET
ejpam-5478	284	9	a	a	DET
ejpam-5478	284	10	el	el	PROPN
ejpam-5478	284	11	-	-	PUNCT
ejpam-5478	284	12	zalan	zalan	NOUN
ejpam-5478	284	13	.	.	PUNCT
ejpam-5478	285	1	rhamiltonian	rhamiltonian	ADJ
ejpam-5478	285	2	formulation	formulation	NOUN
ejpam-5478	285	3	of	of	ADP
ejpam-5478	285	4	systems	system	NOUN
ejpam-5478	285	5	with	with	ADP
ejpam-5478	285	6	higher	high	ADJ
ejpam-5478	285	7	order	order	NOUN
ejpam-5478	285	8	derivatives	derivative	NOUN
ejpam-5478	285	9	.	.	PUNCT
ejpam-5478	286	1	international	international	ADJ
ejpam-5478	286	2	journal	journal	NOUN
ejpam-5478	286	3	of	of	ADP
ejpam-5478	286	4	theoretical	theoretical	ADJ
ejpam-5478	286	5	physics	physics	NOUN
ejpam-5478	286	6	,	,	PUNCT
ejpam-5478	286	7	47:3150–3158	47:3150–3158	PROPN
ejpam-5478	286	8	.	.	PROPN
ejpam-5478	286	9	,	,	PUNCT
ejpam-5478	286	10	2007	2007	NUM
ejpam-5478	286	11	.	.	PUNCT
ejpam-5478	287	1	[	[	X
ejpam-5478	287	2	23	23	NUM
ejpam-5478	287	3	]	]	X
ejpam-5478	287	4	t	t	PROPN
ejpam-5478	287	5	f	f	PROPN
ejpam-5478	287	6	nonnenmacher	nonnenmacher	PROPN
ejpam-5478	287	7	.	.	PUNCT
ejpam-5478	288	1	fractional	fractional	ADJ
ejpam-5478	288	2	integral	integral	ADJ
ejpam-5478	288	3	and	and	CCONJ
ejpam-5478	288	4	differential	differential	ADJ
ejpam-5478	288	5	equations	equation	NOUN
ejpam-5478	288	6	for	for	ADP
ejpam-5478	288	7	a	a	DET
ejpam-5478	288	8	class	class	NOUN
ejpam-5478	288	9	of	of	ADP
ejpam-5478	288	10	levy	levy	NOUN
ejpam-5478	288	11	-	-	PUNCT
ejpam-5478	288	12	type	type	NOUN
ejpam-5478	288	13	probability	probability	NOUN
ejpam-5478	288	14	densities	density	NOUN
ejpam-5478	288	15	.	.	PUNCT
ejpam-5478	289	1	journal	journal	PROPN
ejpam-5478	289	2	of	of	ADP
ejpam-5478	289	3	physics	physics	PROPN
ejpam-5478	289	4	a	a	PRON
ejpam-5478	289	5	:	:	PUNCT
ejpam-5478	289	6	mathematical	mathematical	ADJ
ejpam-5478	289	7	and	and	CCONJ
ejpam-5478	289	8	general	general	ADJ
ejpam-5478	289	9	,	,	PUNCT
ejpam-5478	289	10	23	23	NUM
ejpam-5478	289	11	:	:	PUNCT
ejpam-5478	289	12	l697s	l697s	PROPN
ejpam-5478	289	13	.	.	PUNCT
ejpam-5478	289	14	,	,	PUNCT
ejpam-5478	289	15	1990	1990	NUM
ejpam-5478	289	16	.	.	PUNCT
ejpam-5478	290	1	[	[	X
ejpam-5478	290	2	24	24	NUM
ejpam-5478	290	3	]	]	X
ejpam-5478	290	4	m	m	PROPN
ejpam-5478	290	5	s	s	NOUN
ejpam-5478	290	6	rashid	rashid	PROPN
ejpam-5478	290	7	and	and	CCONJ
ejpam-5478	290	8	s	s	PROPN
ejpam-5478	290	9	khalil	khalil	PROPN
ejpam-5478	290	10	.	.	PUNCT
ejpam-5478	291	1	hamiltonian	hamiltonian	ADJ
ejpam-5478	291	2	description	description	NOUN
ejpam-5478	291	3	of	of	ADP
ejpam-5478	291	4	higher	high	ADJ
ejpam-5478	291	5	order	order	NOUN
ejpam-5478	291	6	lagrangians	lagrangians	PROPN
ejpam-5478	291	7	.	.	PUNCT
ejpam-5478	292	1	iny	iny	PROPN
ejpam-5478	292	2	.	.	PUNCT
ejpam-5478	292	3	m.	m.	NOUN
ejpam-5478	292	4	alawaideh	alawaideh	PROPN
ejpam-5478	292	5	et	et	PROPN
ejpam-5478	292	6	al	al	PROPN
ejpam-5478	292	7	.	.	PUNCT
ejpam-5478	292	8	/	/	SYM
ejpam-5478	292	9	eur	eur	PROPN
ejpam-5478	292	10	.	.	PUNCT
ejpam-5478	293	1	j.	j.	PROPN
ejpam-5478	293	2	pure	pure	PROPN
ejpam-5478	293	3	appl	appl	PROPN
ejpam-5478	293	4	.	.	PROPN
ejpam-5478	293	5	math	math	PROPN
ejpam-5478	293	6	,	,	PUNCT
ejpam-5478	293	7	18	18	NUM
ejpam-5478	293	8	(	(	PUNCT
ejpam-5478	293	9	1	1	NUM
ejpam-5478	293	10	)	)	PUNCT
ejpam-5478	293	11	(	(	PUNCT
ejpam-5478	293	12	2025	2025	NUM
ejpam-5478	293	13	)	)	PUNCT
ejpam-5478	293	14	,	,	PUNCT
ejpam-5478	293	15	5478	5478	NUM
ejpam-5478	293	16	12	12	NUM
ejpam-5478	293	17	of	of	ADP
ejpam-5478	293	18	14	14	NUM
ejpam-5478	293	19	ternational	ternational	ADJ
ejpam-5478	293	20	journal	journal	NOUN
ejpam-5478	293	21	of	of	ADP
ejpam-5478	293	22	modern	modern	ADJ
ejpam-5478	293	23	physics	physics	PROPN
ejpam-5478	293	24	a	a	PRON
ejpam-5478	293	25	,	,	PUNCT
ejpam-5478	293	26	25(11):4551–4559	25(11):4551–4559	NUM
ejpam-5478	293	27	.	.	PUNCT
ejpam-5478	293	28	https://doi.org/10.1142/s0217751x96002108	https://doi.org/10.1142/s0217751x96002108	NOUN
ejpam-5478	293	29	,	,	PUNCT
ejpam-5478	293	30	1996	1996	NUM
ejpam-5478	293	31	.	.	PUNCT
ejpam-5478	294	1	[	[	X
ejpam-5478	294	2	25	25	NUM
ejpam-5478	294	3	]	]	X
ejpam-5478	294	4	f	f	PROPN
ejpam-5478	294	5	riewe	riewe	PROPN
ejpam-5478	294	6	.	.	PUNCT
ejpam-5478	295	1	nonconservativelagrangian	nonconservativelagrangian	ADJ
ejpam-5478	295	2	and	and	CCONJ
ejpam-5478	295	3	hamiltonian	hamiltonian	ADJ
ejpam-5478	295	4	mechanics	mechanic	NOUN
ejpam-5478	295	5	.	.	PUNCT
ejpam-5478	296	1	physical	physical	ADJ
ejpam-5478	296	2	review	review	PROPN
ejpam-5478	296	3	e	e	PROPN
ejpam-5478	296	4	,	,	PUNCT
ejpam-5478	296	5	53:1890	53:1890	PROPN
ejpam-5478	296	6	.	.	PROPN
ejpam-5478	296	7	,	,	PUNCT
ejpam-5478	296	8	1996	1996	NUM
ejpam-5478	296	9	.	.	PUNCT
ejpam-5478	297	1	[	[	X
ejpam-5478	297	2	26	26	NUM
ejpam-5478	297	3	]	]	X
ejpam-5478	297	4	c	c	PROPN
ejpam-5478	297	5	won	won	PROPN
ejpam-5478	297	6	sang	sing	VERB
ejpam-5478	297	7	.	.	PUNCT
ejpam-5478	298	1	fractional	fractional	PROPN
ejpam-5478	298	2	newton	newton	PROPN
ejpam-5478	298	3	mechanics	mechanic	NOUN
ejpam-5478	298	4	with	with	ADP
ejpam-5478	298	5	conformable	conformable	ADJ
ejpam-5478	298	6	fractional	fractional	ADJ
ejpam-5478	298	7	derivative	derivative	NOUN
ejpam-5478	298	8	.	.	PUNCT
ejpam-5478	299	1	jour	jour	PROPN
ejpam-5478	299	2	la	la	PROPN
ejpam-5478	299	3	bibliographienal	bibliographienal	PROPN
ejpam-5478	299	4	of	of	ADP
ejpam-5478	299	5	computational	computational	ADJ
ejpam-5478	299	6	and	and	CCONJ
ejpam-5478	299	7	applied	applied	ADJ
ejpam-5478	299	8	mathematics	mathematic	NOUN
ejpam-5478	299	9	,	,	PUNCT
ejpam-5478	299	10	290:150–158	290:150–158	NUM
ejpam-5478	299	11	.	.	PUNCT
ejpam-5478	299	12	,	,	PUNCT
ejpam-5478	299	13	2015	2015	NUM
ejpam-5478	299	14	.	.	PUNCT
ejpam-5478	300	1	[	[	X
ejpam-5478	300	2	27	27	NUM
ejpam-5478	300	3	]	]	X
ejpam-5478	300	4	c.	c.	PROPN
ejpam-5478	300	5	won	won	PROPN
ejpam-5478	300	6	sang	sing	VERB
ejpam-5478	300	7	.	.	PUNCT
ejpam-5478	301	1	fractional	fractional	PROPN
ejpam-5478	301	2	newton	newton	PROPN
ejpam-5478	301	3	mechanics	mechanic	NOUN
ejpam-5478	301	4	with	with	ADP
ejpam-5478	301	5	conformable	conformable	ADJ
ejpam-5478	301	6	fractional	fractional	ADJ
ejpam-5478	301	7	derivative	derivative	NOUN
ejpam-5478	301	8	.	.	PUNCT
ejpam-5478	302	1	jour	jour	PROPN
ejpam-5478	302	2	la	la	PROPN
ejpam-5478	302	3	bibliographienal	bibliographienal	PROPN
ejpam-5478	302	4	of	of	ADP
ejpam-5478	302	5	computational	computational	ADJ
ejpam-5478	302	6	and	and	CCONJ
ejpam-5478	302	7	applied	applied	ADJ
ejpam-5478	302	8	mathematics	mathematic	NOUN
ejpam-5478	302	9	,	,	PUNCT
ejpam-5478	302	10	2015	2015	NUM
ejpam-5478	302	11	.	.	PUNCT
ejpam-5478	303	1	[	[	X
ejpam-5478	303	2	28	28	NUM
ejpam-5478	303	3	]	]	X
ejpam-5478	303	4	j	j	PROPN
ejpam-5478	303	5	a	a	DET
ejpam-5478	303	6	malham	malham	PROPN
ejpam-5478	303	7	simon	simon	PROPN
ejpam-5478	303	8	.	.	PUNCT
ejpam-5478	304	1	an	an	DET
ejpam-5478	304	2	introduction	introduction	NOUN
ejpam-5478	304	3	to	to	ADP
ejpam-5478	304	4	lagrangian	lagrangian	ADJ
ejpam-5478	304	5	and	and	CCONJ
ejpam-5478	304	6	hamiltonian	hamiltonian	ADJ
ejpam-5478	304	7	mechanics	mechanic	NOUN
ejpam-5478	304	8	.	.	PUNCT
ejpam-5478	305	1	maxwell	maxwell	PROPN
ejpam-5478	305	2	institute	institute	PROPN
ejpam-5478	305	3	for	for	ADP
ejpam-5478	305	4	mathematical	mathematical	ADJ
ejpam-5478	305	5	sciences	sciences	PROPN
ejpam-5478	305	6	school	school	NOUN
ejpam-5478	305	7	of	of	ADP
ejpam-5478	305	8	mathematical	mathematical	ADJ
ejpam-5478	305	9	and	and	CCONJ
ejpam-5478	305	10	computer	computer	NOUN
ejpam-5478	305	11	sciences	science	NOUN
ejpam-5478	305	12	heriot	heriot	NOUN
ejpam-5478	305	13	-	-	PUNCT
ejpam-5478	305	14	watt	watt	NOUN
ejpam-5478	305	15	university	university	NOUN
ejpam-5478	305	16	,	,	PUNCT
ejpam-5478	305	17	edinburgh	edinburgh	NOUN
ejpam-5478	305	18	eh14	eh14	PROPN
ejpam-5478	305	19	4as	4as	NOUN
ejpam-5478	305	20	,	,	PUNCT
ejpam-5478	305	21	page	page	NOUN
ejpam-5478	305	22	.	.	PUNCT
ejpam-5478	305	23	,	,	PUNCT
ejpam-5478	305	24	uk	uk	PROPN
ejpam-5478	305	25	(	(	PUNCT
ejpam-5478	305	26	2014	2014	NUM
ejpam-5478	305	27	)	)	PUNCT
ejpam-5478	305	28	.	.	PUNCT
ejpam-5478	306	1	[	[	X
ejpam-5478	306	2	29	29	NUM
ejpam-5478	306	3	]	]	SYM
ejpam-5478	306	4	v	v	NUM
ejpam-5478	306	5	sinitsyn	sinitsyn	PROPN
ejpam-5478	306	6	.	.	PUNCT
ejpam-5478	307	1	on	on	ADP
ejpam-5478	307	2	the	the	DET
ejpam-5478	307	3	hamilton	hamilton	PROPN
ejpam-5478	307	4	-	-	PUNCT
ejpam-5478	307	5	ostrogradskii	ostrogradskii	ADJ
ejpam-5478	307	6	principle	principle	NOUN
ejpam-5478	307	7	in	in	ADP
ejpam-5478	307	8	the	the	DET
ejpam-5478	307	9	case	case	NOUN
ejpam-5478	307	10	of	of	ADP
ejpam-5478	307	11	impulsive	impulsive	ADJ
ejpam-5478	307	12	motions	motion	NOUN
ejpam-5478	307	13	of	of	ADP
ejpam-5478	307	14	dynamic	dynamic	ADJ
ejpam-5478	307	15	systems	system	NOUN
ejpam-5478	307	16	.	.	PUNCT
ejpam-5478	308	1	journal	journal	NOUN
ejpam-5478	308	2	of	of	ADP
ejpam-5478	308	3	applied	apply	VERB
ejpam-5478	308	4	mathematics	mathematic	NOUN
ejpam-5478	308	5	and	and	CCONJ
ejpam-5478	308	6	mechanics	mechanic	NOUN
ejpam-5478	308	7	,	,	PUNCT
ejpam-5478	308	8	45(3):356–359	45(3):356–359	NOUN
ejpam-5478	308	9	.	.	PUNCT
ejpam-5478	309	1	https://doi.org/10.1016/0021–8928(81)90066–6	https://doi.org/10.1016/0021–8928(81)90066–6	NOUN
ejpam-5478	309	2	,	,	PUNCT
ejpam-5478	309	3	1981	1981	NUM
ejpam-5478	309	4	.	.	PUNCT
ejpam-5478	310	1	[	[	X
ejpam-5478	310	2	30	30	NUM
ejpam-5478	310	3	]	]	X
ejpam-5478	310	4	abdeljawad	abdeljawad	NOUN
ejpam-5478	310	5	t.	t.	NOUN
ejpam-5478	310	6	on	on	ADP
ejpam-5478	310	7	conformable	conformable	ADJ
ejpam-5478	310	8	fractional	fractional	ADJ
ejpam-5478	310	9	calculus	calculus	NOUN
ejpam-5478	310	10	.	.	PUNCT
ejpam-5478	311	1	journal	journal	PROPN
ejpam-5478	311	2	of	of	ADP
ejpam-5478	311	3	computational	computational	ADJ
ejpam-5478	311	4	and	and	CCONJ
ejpam-5478	311	5	applied	applied	ADJ
ejpam-5478	311	6	mathematics	mathematic	NOUN
ejpam-5478	311	7	,	,	PUNCT
ejpam-5478	311	8	2014	2014	NUM
ejpam-5478	311	9	.	.	PUNCT
ejpam-5478	312	1	[	[	X
ejpam-5478	312	2	31	31	NUM
ejpam-5478	312	3	]	]	X
ejpam-5478	312	4	g	g	PROPN
ejpam-5478	312	5	m	m	PROPN
ejpam-5478	312	6	zaslavsky	zaslavsky	PROPN
ejpam-5478	312	7	.	.	PUNCT
ejpam-5478	313	1	chaos	chaos	NOUN
ejpam-5478	313	2	,	,	PUNCT
ejpam-5478	313	3	fractional	fractional	ADJ
ejpam-5478	313	4	kinetics	kinetic	NOUN
ejpam-5478	313	5	,	,	PUNCT
ejpam-5478	313	6	and	and	CCONJ
ejpam-5478	313	7	anomalous	anomalous	ADJ
ejpam-5478	313	8	transport	transport	NOUN
ejpam-5478	313	9	.	.	PUNCT
ejpam-5478	314	1	physics	physics	NOUN
ejpam-5478	314	2	reports	report	NOUN
ejpam-5478	314	3	,	,	PUNCT
ejpam-5478	314	4	371:461–580	371:461–580	NUM
ejpam-5478	314	5	.	.	NUM
ejpam-5478	314	6	,	,	PUNCT
ejpam-5478	314	7	2002	2002	NUM
ejpam-5478	314	8	.	.	PUNCT
ejpam-5478	315	1	appendix	appendix	NOUN
ejpam-5478	315	2	in	in	ADP
ejpam-5478	315	3	this	this	DET
ejpam-5478	315	4	appendix	appendix	NOUN
ejpam-5478	315	5	,	,	PUNCT
ejpam-5478	315	6	we	we	PRON
ejpam-5478	315	7	shift	shift	VERB
ejpam-5478	315	8	from	from	ADP
ejpam-5478	315	9	the	the	DET
ejpam-5478	315	10	lagrangian	lagrangian	ADJ
ejpam-5478	315	11	approach	approach	NOUN
ejpam-5478	315	12	to	to	ADP
ejpam-5478	315	13	the	the	DET
ejpam-5478	315	14	hamiltonian	hamiltonian	ADJ
ejpam-5478	315	15	approach	approach	NOUN
ejpam-5478	315	16	,	,	PUNCT
ejpam-5478	315	17	we	we	PRON
ejpam-5478	315	18	introduce	introduce	VERB
ejpam-5478	315	19	paired	pair	VERB
ejpam-5478	315	20	generalized	generalized	ADJ
ejpam-5478	315	21	momenta	momenta	NOUN
ejpam-5478	315	22	(	(	PUNCT
ejpam-5478	315	23	pi	pi	NOUN
ejpam-5478	315	24	and	and	CCONJ
ejpam-5478	315	25	φ	φ	NUM
ejpam-5478	315	26	)	)	PUNCT
ejpam-5478	315	27	associated	associate	VERB
ejpam-5478	315	28	with	with	ADP
ejpam-5478	315	29	and	and	CCONJ
ejpam-5478	315	30	associated	associate	VERB
ejpam-5478	315	31	in	in	ADP
ejpam-5478	315	32	conjunction	conjunction	NOUN
ejpam-5478	315	33	with	with	ADP
ejpam-5478	315	34	their	their	PRON
ejpam-5478	315	35	respective	respective	ADJ
ejpam-5478	315	36	generalized	generalized	ADJ
ejpam-5478	315	37	coordinates	coordinate	NOUN
ejpam-5478	315	38	.	.	PUNCT
ejpam-5478	316	1	pi	pi	NOUN
ejpam-5478	317	1	=	=	NOUN
ejpam-5478	317	2	dα	dα	ADJ
ejpam-5478	317	3	s|t	s|t	NOUN
ejpam-5478	317	4	∂l	∂l	PROPN
ejpam-5478	317	5	∂dα	∂dα	PROPN
ejpam-5478	317	6	s|tqi	s|tqi	PROPN
ejpam-5478	317	7	+	+	NOUN
ejpam-5478	317	8	d2α	d2α	NOUN
ejpam-5478	317	9	s|t	s|t	NOUN
ejpam-5478	317	10	∂l	∂l	PROPN
ejpam-5478	317	11	∂(d2α	∂(d2α	PROPN
ejpam-5478	317	12	s|tqi	s|tqi	PROPN
ejpam-5478	317	13	)	)	PUNCT
ejpam-5478	317	14	πi	πi	ADP
ejpam-5478	317	15	=	=	SYM
ejpam-5478	317	16	∂l	∂l	PROPN
ejpam-5478	317	17	∂(dα	∂(dα	NOUN
ejpam-5478	317	18	s|tqi	s|tqi	PROPN
ejpam-5478	317	19	)	)	PUNCT
ejpam-5478	317	20	we	we	PRON
ejpam-5478	317	21	expand	expand	VERB
ejpam-5478	317	22	the	the	DET
ejpam-5478	317	23	phase	phase	NOUN
ejpam-5478	317	24	space	space	NOUN
ejpam-5478	317	25	to	to	PART
ejpam-5478	317	26	include	include	VERB
ejpam-5478	317	27	the	the	DET
ejpam-5478	317	28	canonical	canonical	ADJ
ejpam-5478	317	29	variables	variable	NOUN
ejpam-5478	317	30	(	(	PUNCT
ejpam-5478	317	31	qi	qi	PROPN
ejpam-5478	317	32	,	,	PUNCT
ejpam-5478	317	33	pi	pi	NOUN
ejpam-5478	317	34	)	)	PUNCT
ejpam-5478	317	35	and	and	CCONJ
ejpam-5478	317	36	their	their	PRON
ejpam-5478	317	37	associated	associated	ADJ
ejpam-5478	317	38	counterparts	counterpart	NOUN
ejpam-5478	317	39	(	(	PUNCT
ejpam-5478	317	40	ql	ql	INTJ
ejpam-5478	317	41	,	,	PUNCT
ejpam-5478	317	42	πi	πi	ADP
ejpam-5478	317	43	)	)	PUNCT
ejpam-5478	317	44	,	,	PUNCT
ejpam-5478	317	45	where	where	SCONJ
ejpam-5478	317	46	(	(	PUNCT
ejpam-5478	317	47	ql	ql	X
ejpam-5478	317	48	=	=	ADJ
ejpam-5478	317	49	dα	dα	ADJ
ejpam-5478	317	50	s|t	s|t	NOUN
ejpam-5478	317	51	)	)	PUNCT
ejpam-5478	317	52	.	.	PUNCT
ejpam-5478	318	1	within	within	ADP
ejpam-5478	318	2	this	this	DET
ejpam-5478	318	3	augmented	augment	VERB
ejpam-5478	318	4	phase	phase	NOUN
ejpam-5478	318	5	space	space	NOUN
ejpam-5478	318	6	,	,	PUNCT
ejpam-5478	318	7	the	the	DET
ejpam-5478	318	8	hamiltonian	hamiltonian	NOUN
ejpam-5478	318	9	is	be	AUX
ejpam-5478	318	10	expressed	express	VERB
ejpam-5478	318	11	as	as	SCONJ
ejpam-5478	318	12	follows	follow	VERB
ejpam-5478	318	13	:	:	PUNCT
ejpam-5478	318	14	h	h	NOUN
ejpam-5478	318	15	=	=	PUNCT
ejpam-5478	318	16	piqi	piqi	PROPN
ejpam-5478	318	17	+	+	CCONJ
ejpam-5478	318	18	πid	πid	VERB
ejpam-5478	318	19	2α	2α	ADJ
ejpam-5478	318	20	s|tqi	s|tqi	NOUN
ejpam-5478	318	21	−	−	PROPN
ejpam-5478	318	22	l	l	NOUN
ejpam-5478	318	23	this	this	PRON
ejpam-5478	318	24	implies	imply	VERB
ejpam-5478	318	25	that	that	SCONJ
ejpam-5478	318	26	the	the	DET
ejpam-5478	318	27	hamiltonian	hamiltonian	NOUN
ejpam-5478	318	28	can	can	AUX
ejpam-5478	318	29	be	be	AUX
ejpam-5478	318	30	expressed	express	VERB
ejpam-5478	318	31	as	as	ADP
ejpam-5478	318	32	a	a	DET
ejpam-5478	318	33	function	function	NOUN
ejpam-5478	318	34	,	,	PUNCT
ejpam-5478	318	35	as	as	SCONJ
ejpam-5478	318	36	follows	follow	VERB
ejpam-5478	318	37	:	:	PUNCT
ejpam-5478	318	38	h	h	NOUN
ejpam-5478	318	39	=	=	SYM
ejpam-5478	318	40	h(qi	h(qi	PROPN
ejpam-5478	318	41	,	,	PUNCT
ejpam-5478	318	42	pi	pi	NOUN
ejpam-5478	318	43	,	,	PUNCT
ejpam-5478	318	44	qi	qi	PROPN
ejpam-5478	318	45	,	,	PUNCT
ejpam-5478	318	46	πi	πi	ADV
ejpam-5478	318	47	,	,	PUNCT
ejpam-5478	318	48	t	t	PROPN
ejpam-5478	318	49	)	)	PUNCT
ejpam-5478	318	50	in	in	ADP
ejpam-5478	318	51	the	the	DET
ejpam-5478	318	52	generalized	generalized	ADJ
ejpam-5478	318	53	case	case	NOUN
ejpam-5478	318	54	:	:	PUNCT
ejpam-5478	318	55	l	l	NOUN
ejpam-5478	318	56	=	=	SYM
ejpam-5478	318	57	l(qi	l(qi	PROPN
ejpam-5478	318	58	,	,	PUNCT
ejpam-5478	318	59	d	d	PROPN
ejpam-5478	318	60	α	α	PROPN
ejpam-5478	318	61	s|tqi	s|tqi	PROPN
ejpam-5478	318	62	,	,	PUNCT
ejpam-5478	318	63	d	d	PROPN
ejpam-5478	318	64	2α	2α	PROPN
ejpam-5478	318	65	s|tqi	s|tqi	PROPN
ejpam-5478	318	66	,	,	PUNCT
ejpam-5478	318	67	·	·	PUNCT
ejpam-5478	318	68	·	·	PUNCT
ejpam-5478	318	69	·	·	PUNCT
ejpam-5478	318	70	,	,	PUNCT
ejpam-5478	319	1	d	d	X
ejpam-5478	319	2	nα	nα	PROPN
ejpam-5478	319	3	s|t	s|t	PROPN
ejpam-5478	319	4	qi	qi	PROPN
ejpam-5478	319	5	,	,	PUNCT
ejpam-5478	319	6	t	t	PROPN
ejpam-5478	319	7	)	)	PUNCT
ejpam-5478	319	8	y.	y.	NOUN
ejpam-5478	319	9	m.	m.	NOUN
ejpam-5478	319	10	alawaideh	alawaideh	PROPN
ejpam-5478	319	11	et	et	PROPN
ejpam-5478	319	12	al	al	PROPN
ejpam-5478	319	13	.	.	PUNCT
ejpam-5478	319	14	/	/	SYM
ejpam-5478	319	15	eur	eur	PROPN
ejpam-5478	319	16	.	.	PUNCT
ejpam-5478	320	1	j.	j.	PROPN
ejpam-5478	320	2	pure	pure	PROPN
ejpam-5478	320	3	appl	appl	PROPN
ejpam-5478	320	4	.	.	PROPN
ejpam-5478	320	5	math	math	PROPN
ejpam-5478	320	6	,	,	PUNCT
ejpam-5478	320	7	18	18	NUM
ejpam-5478	320	8	(	(	PUNCT
ejpam-5478	320	9	1	1	NUM
ejpam-5478	320	10	)	)	PUNCT
ejpam-5478	320	11	(	(	PUNCT
ejpam-5478	320	12	2025	2025	NUM
ejpam-5478	320	13	)	)	PUNCT
ejpam-5478	320	14	,	,	PUNCT
ejpam-5478	320	15	5478	5478	NUM
ejpam-5478	320	16	13	13	NUM
ejpam-5478	320	17	of	of	ADP
ejpam-5478	320	18	14	14	NUM
ejpam-5478	320	19	considering	consider	VERB
ejpam-5478	320	20	the	the	DET
ejpam-5478	320	21	variation	variation	NOUN
ejpam-5478	320	22	principle	principle	NOUN
ejpam-5478	320	23	,	,	PUNCT
ejpam-5478	320	24	it	it	PRON
ejpam-5478	320	25	is	be	AUX
ejpam-5478	320	26	evident	evident	ADJ
ejpam-5478	320	27	that	that	SCONJ
ejpam-5478	320	28	the	the	DET
ejpam-5478	320	29	euler	euler	PROPN
ejpam-5478	320	30	–	–	PUNCT
ejpam-5478	320	31	lagrange	lagrange	NOUN
ejpam-5478	320	32	equations	equation	NOUN
ejpam-5478	320	33	governing	govern	VERB
ejpam-5478	320	34	the	the	DET
ejpam-5478	320	35	motion	motion	NOUN
ejpam-5478	320	36	of	of	ADP
ejpam-5478	320	37	the	the	DET
ejpam-5478	320	38	system	system	NOUN
ejpam-5478	320	39	are	be	AUX
ejpam-5478	320	40	expressed	express	VERB
ejpam-5478	320	41	as	as	SCONJ
ejpam-5478	320	42	follows	follow	VERB
ejpam-5478	320	43	:	:	PUNCT
ejpam-5478	320	44	n∑	n∑	PROPN
ejpam-5478	320	45	i=0	i=0	PROPN
ejpam-5478	320	46	(	(	PUNCT
ejpam-5478	320	47	−1)idiα	−1)idiα	PROPN
ejpam-5478	320	48	s|tqi	s|tqi	PROPN
ejpam-5478	320	49	(	(	PUNCT
ejpam-5478	320	50	dl	dl	INTJ
ejpam-5478	320	51	dqi	dqi	ADV
ejpam-5478	320	52	)	)	PUNCT
ejpam-5478	320	53	=	=	SYM
ejpam-5478	320	54	0	0	NUM
ejpam-5478	320	55	qi	qi	NOUN
ejpam-5478	320	56	=	=	NOUN
ejpam-5478	320	57	diα	diα	NOUN
ejpam-5478	320	58	s|tq	s|tq	NOUN
ejpam-5478	320	59	i	i	PRON
ejpam-5478	320	60	i	i	VERB
ejpam-5478	320	61	=	=	NOUN
ejpam-5478	320	62	0	0	NUM
ejpam-5478	320	63	,	,	PUNCT
ejpam-5478	320	64	1	1	NUM
ejpam-5478	320	65	,	,	PUNCT
ejpam-5478	320	66	2	2	NUM
ejpam-5478	320	67	,	,	PUNCT
ejpam-5478	320	68	·	·	PUNCT
ejpam-5478	320	69	·	·	PUNCT
ejpam-5478	320	70	·	·	PUNCT
ejpam-5478	320	71	to	to	PART
ejpam-5478	320	72	streamline	streamline	VERB
ejpam-5478	320	73	the	the	DET
ejpam-5478	320	74	representation	representation	NOUN
ejpam-5478	320	75	of	of	ADP
ejpam-5478	320	76	these	these	DET
ejpam-5478	320	77	equations	equation	NOUN
ejpam-5478	320	78	through	through	ADP
ejpam-5478	320	79	ostrogradskii	ostrogradskii	PROPN
ejpam-5478	320	80	’s	’s	PART
ejpam-5478	320	81	method	method	NOUN
ejpam-5478	320	82	and	and	CCONJ
ejpam-5478	320	83	the	the	DET
ejpam-5478	320	84	introduction	introduction	NOUN
ejpam-5478	320	85	of	of	ADP
ejpam-5478	320	86	paired	pair	VERB
ejpam-5478	320	87	generalized	generalized	ADJ
ejpam-5478	320	88	momenta	momenta	NOUN
ejpam-5478	320	89	(	(	PUNCT
ejpam-5478	320	90	pi	pi	NOUN
ejpam-5478	320	91	,	,	PUNCT
ejpam-5478	320	92	πi	πi	CCONJ
ejpam-5478	320	93	)	)	PUNCT
ejpam-5478	320	94	linked	link	VERB
ejpam-5478	320	95	to	to	ADP
ejpam-5478	320	96	the	the	DET
ejpam-5478	320	97	generalized	generalized	ADJ
ejpam-5478	320	98	coordinates	coordinate	NOUN
ejpam-5478	320	99	(	(	PUNCT
ejpam-5478	320	100	qi	qi	PROPN
ejpam-5478	320	101	,	,	PUNCT
ejpam-5478	320	102	d	d	PROPN
ejpam-5478	320	103	α	α	PROPN
ejpam-5478	320	104	s|tqi	s|tqi	PROPN
ejpam-5478	320	105	)	)	PUNCT
ejpam-5478	320	106	the	the	DET
ejpam-5478	320	107	equations	equation	NOUN
ejpam-5478	320	108	can	can	AUX
ejpam-5478	320	109	be	be	AUX
ejpam-5478	320	110	reformulated	reformulate	VERB
ejpam-5478	320	111	as	as	SCONJ
ejpam-5478	320	112	follows	follow	VERB
ejpam-5478	320	113	:	:	PUNCT
ejpam-5478	320	114	pk−1	pk−1	INTJ
ejpam-5478	320	115	i	i	NOUN
ejpam-5478	320	116	=	=	SYM
ejpam-5478	320	117	∂l	∂l	PROPN
ejpam-5478	320	118	∂(dα	∂(dα	NOUN
ejpam-5478	320	119	xλ	xλ	PROPN
ejpam-5478	320	120	dα	dα	ADP
ejpam-5478	320	121	s|xλ	s|xλ	ADV
ejpam-5478	320	122	qi	qi	NOUN
ejpam-5478	320	123	)	)	PUNCT
ejpam-5478	320	124	−	−	PROPN
ejpam-5478	321	1	d	d	X
ejpam-5478	321	2	dt	dt	X
ejpam-5478	321	3	(	(	PUNCT
ejpam-5478	321	4	∂l	∂l	PROPN
ejpam-5478	321	5	∂(∂dqk+1	∂(∂dqk+1	PROPN
ejpam-5478	321	6	i	i	PROPN
ejpam-5478	321	7	)	)	PUNCT
ejpam-5478	321	8	)	)	PUNCT
ejpam-5478	321	9	,	,	PUNCT
ejpam-5478	321	10	k	k	PROPN
ejpam-5478	321	11	=	=	SYM
ejpam-5478	321	12	0	0	NUM
ejpam-5478	321	13	,	,	PUNCT
ejpam-5478	321	14	1	1	NUM
ejpam-5478	321	15	,	,	PUNCT
ejpam-5478	321	16	2	2	NUM
ejpam-5478	321	17	,	,	PUNCT
ejpam-5478	321	18	·	·	PUNCT
ejpam-5478	321	19	·	·	PUNCT
ejpam-5478	321	20	·	·	PUNCT
ejpam-5478	321	21	,	,	PUNCT
ejpam-5478	321	22	n−	n−	NOUN
ejpam-5478	321	23	1	1	NUM
ejpam-5478	321	24	,	,	PUNCT
ejpam-5478	321	25	πi	πi	ADV
ejpam-5478	321	26	=	=	SYM
ejpam-5478	321	27	dl	dl	PROPN
ejpam-5478	321	28	dqn	dqn	PROPN
ejpam-5478	321	29	.	.	PUNCT
ejpam-5478	322	1	the	the	DET
ejpam-5478	322	2	phase	phase	NOUN
ejpam-5478	322	3	space	space	NOUN
ejpam-5478	322	4	,	,	PUNCT
ejpam-5478	322	5	defined	define	VERB
ejpam-5478	322	6	by	by	ADP
ejpam-5478	322	7	the	the	DET
ejpam-5478	322	8	canonical	canonical	ADJ
ejpam-5478	322	9	variables	variable	NOUN
ejpam-5478	322	10	(	(	PUNCT
ejpam-5478	322	11	qi	qi	NOUN
ejpam-5478	322	12	and	and	CCONJ
ejpam-5478	322	13	pk−1	pk−1	PROPN
ejpam-5478	322	14	i	i	PROPN
ejpam-5478	322	15	)	)	PUNCT
ejpam-5478	322	16	and	and	CCONJ
ejpam-5478	322	17	their	their	PRON
ejpam-5478	322	18	associated	associated	ADJ
ejpam-5478	322	19	counterparts	counterpart	NOUN
ejpam-5478	322	20	(	(	PUNCT
ejpam-5478	322	21	qi	qi	PROPN
ejpam-5478	322	22	k	k	PROPN
ejpam-5478	322	23	and	and	CCONJ
ejpam-5478	322	24	πi	πi	CCONJ
ejpam-5478	322	25	)	)	PUNCT
ejpam-5478	322	26	encompasses	encompass	VERB
ejpam-5478	322	27	the	the	DET
ejpam-5478	322	28	generalized	generalized	ADJ
ejpam-5478	322	29	coordinates	coordinate	NOUN
ejpam-5478	322	30	(	(	PUNCT
ejpam-5478	322	31	qi	qi	PROPN
ejpam-5478	322	32	k	k	PROPN
ejpam-5478	322	33	and	and	CCONJ
ejpam-5478	322	34	qk+1	qk+1	NOUN
ejpam-5478	322	35	i	i	PROPN
ejpam-5478	322	36	)	)	PUNCT
ejpam-5478	322	37	.	.	PUNCT
ejpam-5478	323	1	the	the	DET
ejpam-5478	323	2	formulation	formulation	NOUN
ejpam-5478	323	3	of	of	ADP
ejpam-5478	323	4	the	the	DET
ejpam-5478	323	5	hamiltonian	hamiltonian	NOUN
ejpam-5478	323	6	is	be	AUX
ejpam-5478	323	7	as	as	SCONJ
ejpam-5478	323	8	follows	follow	VERB
ejpam-5478	323	9	:	:	PUNCT
ejpam-5478	324	1	h	h	NOUN
ejpam-5478	324	2	=	=	PUNCT
ejpam-5478	324	3	n−1∑	n−1∑	PROPN
ejpam-5478	325	1	k=1	k=1	INTJ
ejpam-5478	325	2	pkq	pkq	PROPN
ejpam-5478	325	3	k	k	PROPN
ejpam-5478	326	1	+	+	CCONJ
ejpam-5478	326	2	πiq	πiq	PROPN
ejpam-5478	326	3	n	n	NOUN
ejpam-5478	326	4	i	i	PRON
ejpam-5478	326	5	−	−	PROPN
ejpam-5478	326	6	l	l	NOUN
ejpam-5478	326	7	this	this	PRON
ejpam-5478	326	8	implies	imply	VERB
ejpam-5478	326	9	that	that	SCONJ
ejpam-5478	326	10	the	the	DET
ejpam-5478	326	11	hamiltonian	hamiltonian	NOUN
ejpam-5478	326	12	can	can	AUX
ejpam-5478	326	13	be	be	AUX
ejpam-5478	326	14	represented	represent	VERB
ejpam-5478	326	15	as	as	SCONJ
ejpam-5478	326	16	follows	follow	VERB
ejpam-5478	326	17	:	:	PUNCT
ejpam-5478	326	18	h	h	NOUN
ejpam-5478	326	19	=	=	SYM
ejpam-5478	326	20	h(qi	h(qi	PROPN
ejpam-5478	326	21	,	,	PUNCT
ejpam-5478	326	22	p	p	NOUN
ejpam-5478	326	23	k−1	k−1	PROPN
ejpam-5478	327	1	i	i	PRON
ejpam-5478	327	2	,	,	PUNCT
ejpam-5478	327	3	qk−1	qk−1	PROPN
ejpam-5478	327	4	i	i	PRON
ejpam-5478	327	5	,	,	PUNCT
ejpam-5478	327	6	πi	πi	PROPN
ejpam-5478	327	7	,	,	PUNCT
ejpam-5478	327	8	t	t	PROPN
ejpam-5478	327	9	)	)	PUNCT
ejpam-5478	327	10	,	,	PUNCT
ejpam-5478	327	11	now	now	ADV
ejpam-5478	327	12	,	,	PUNCT
ejpam-5478	327	13	the	the	DET
ejpam-5478	327	14	hamiltonian	hamiltonian	ADJ
ejpam-5478	327	15	formalism	formalism	NOUN
ejpam-5478	327	16	,	,	PUNCT
ejpam-5478	327	17	denoted	denote	VERB
ejpam-5478	327	18	as	as	ADP
ejpam-5478	327	19	h	h	NOUN
ejpam-5478	327	20	,	,	PUNCT
ejpam-5478	327	21	is	be	AUX
ejpam-5478	327	22	obtained	obtain	VERB
ejpam-5478	327	23	by	by	ADP
ejpam-5478	327	24	employing	employ	VERB
ejpam-5478	327	25	the	the	DET
ejpam-5478	327	26	legendre	legendre	PROPN
ejpam-5478	327	27	transformation	transformation	NOUN
ejpam-5478	327	28	in	in	ADP
ejpam-5478	327	29	the	the	DET
ejpam-5478	327	30	following	following	ADJ
ejpam-5478	327	31	manner	manner	NOUN
ejpam-5478	327	32	:	:	PUNCT
ejpam-5478	327	33	h	h	NOUN
ejpam-5478	327	34	=	=	PUNCT
ejpam-5478	327	35	p1d	p1d	NOUN
ejpam-5478	327	36	α	α	X
ejpam-5478	327	37	s|tqi	s|tqi	NOUN
ejpam-5478	327	38	+	+	CCONJ
ejpam-5478	327	39	p1d	p1d	NOUN
ejpam-5478	327	40	2α	2α	NOUN
ejpam-5478	327	41	s|tqi	s|tqi	NOUN
ejpam-5478	327	42	−	−	PROPN
ejpam-5478	327	43	l	l	NOUN
ejpam-5478	327	44	,	,	PUNCT
ejpam-5478	327	45	determining	determine	VERB
ejpam-5478	327	46	the	the	DET
ejpam-5478	327	47	total	total	ADJ
ejpam-5478	327	48	differential	differential	NOUN
ejpam-5478	327	49	of	of	ADP
ejpam-5478	327	50	this	this	DET
ejpam-5478	327	51	hamiltonian	hamiltonian	NOUN
ejpam-5478	327	52	leads	lead	VERB
ejpam-5478	327	53	us	we	PRON
ejpam-5478	327	54	to	to	ADP
ejpam-5478	327	55	the	the	DET
ejpam-5478	327	56	following	follow	VERB
ejpam-5478	327	57	outcome	outcome	NOUN
ejpam-5478	327	58	.	.	PUNCT
ejpam-5478	328	1	dh	dh	NOUN
ejpam-5478	328	2	=	=	PROPN
ejpam-5478	328	3	p1d(d	p1d(d	PROPN
ejpam-5478	328	4	α	α	PROPN
ejpam-5478	328	5	s|tqi	s|tqi	PROPN
ejpam-5478	328	6	)	)	PUNCT
ejpam-5478	329	1	+	+	CCONJ
ejpam-5478	329	2	dα	dα	PROPN
ejpam-5478	329	3	s|tqid(p1	s|tqid(p1	NOUN
ejpam-5478	329	4	)	)	PUNCT
ejpam-5478	330	1	+	+	CCONJ
ejpam-5478	330	2	p2d(d	p2d(d	PROPN
ejpam-5478	330	3	α	α	PROPN
ejpam-5478	330	4	s|td	s|td	PROPN
ejpam-5478	330	5	α	α	PROPN
ejpam-5478	330	6	s|tqi	s|tqi	PROPN
ejpam-5478	330	7	)	)	PUNCT
ejpam-5478	331	1	+	+	CCONJ
ejpam-5478	331	2	d2α	d2α	NOUN
ejpam-5478	331	3	s|tqid(p2	s|tqid(p2	NUM
ejpam-5478	331	4	)	)	PUNCT
ejpam-5478	332	1	−	−	PROPN
ejpam-5478	333	1	∂l	∂l	NOUN
ejpam-5478	333	2	∂qi	∂qi	PROPN
ejpam-5478	333	3	−	−	PROPN
ejpam-5478	334	1	∂l	∂l	PROPN
ejpam-5478	334	2	∂dα	∂dα	PROPN
ejpam-5478	334	3	s|tqi	s|tqi	PROPN
ejpam-5478	334	4	dα	dα	PROPN
ejpam-5478	334	5	s|tqi	s|tqi	PROPN
ejpam-5478	334	6	−	−	PROPN
ejpam-5478	334	7	∂l	∂l	PROPN
ejpam-5478	334	8	∂d2α	∂d2α	PROPN
ejpam-5478	334	9	s|tqi	s|tqi	PROPN
ejpam-5478	334	10	d2α	d2α	PROPN
ejpam-5478	334	11	s|tqi	s|tqi	PROPN
ejpam-5478	334	12	,	,	PUNCT
ejpam-5478	334	13	(	(	PUNCT
ejpam-5478	334	14	a.2	a.2	SYM
ejpam-5478	334	15	)	)	PUNCT
ejpam-5478	334	16	the	the	DET
ejpam-5478	334	17	generalized	generalize	VERB
ejpam-5478	334	18	momenta	momenta	NOUN
ejpam-5478	334	19	p1	p1	NOUN
ejpam-5478	334	20	and	and	CCONJ
ejpam-5478	334	21	p2	p2	PROPN
ejpam-5478	334	22	corresponding	correspond	VERB
ejpam-5478	334	23	to	to	ADP
ejpam-5478	334	24	dα	dα	DET
ejpam-5478	334	25	s|tqi	s|tqi	PROPN
ejpam-5478	334	26	and	and	CCONJ
ejpam-5478	334	27	d2α	d2α	PROPN
ejpam-5478	334	28	s|tqi	s|tqi	PROPN
ejpam-5478	334	29	can	can	AUX
ejpam-5478	334	30	be	be	AUX
ejpam-5478	334	31	defined	define	VERB
ejpam-5478	334	32	as	as	SCONJ
ejpam-5478	334	33	follows	follow	VERB
ejpam-5478	334	34	:	:	PUNCT
ejpam-5478	334	35	p1	p1	PROPN
ejpam-5478	334	36	=	=	SYM
ejpam-5478	334	37	∂l	∂l	PROPN
ejpam-5478	334	38	∂(dα	∂(dα	NOUN
ejpam-5478	334	39	s|tqi	s|tqi	PROPN
ejpam-5478	334	40	)	)	PUNCT
ejpam-5478	334	41	,	,	PUNCT
ejpam-5478	334	42	p2	p2	PROPN
ejpam-5478	334	43	=	=	SYM
ejpam-5478	334	44	∂l	∂l	PROPN
ejpam-5478	334	45	∂(d2α	∂(d2α	NOUN
ejpam-5478	334	46	s|tqi	s|tqi	PROPN
ejpam-5478	334	47	)	)	PUNCT
ejpam-5478	334	48	,	,	PUNCT
ejpam-5478	334	49	substituting	substitute	VERB
ejpam-5478	334	50	the	the	DET
ejpam-5478	334	51	values	value	NOUN
ejpam-5478	334	52	of	of	ADP
ejpam-5478	334	53	momenta	momenta	NOUN
ejpam-5478	334	54	p1	p1	NOUN
ejpam-5478	334	55	and	and	CCONJ
ejpam-5478	334	56	p2	p2	NOUN
ejpam-5478	334	57	into	into	ADP
ejpam-5478	334	58	(	(	PUNCT
ejpam-5478	334	59	2	2	NUM
ejpam-5478	334	60	)	)	PUNCT
ejpam-5478	334	61	,	,	PUNCT
ejpam-5478	334	62	we	we	PRON
ejpam-5478	334	63	get	get	VERB
ejpam-5478	334	64	:	:	PUNCT
ejpam-5478	334	65	dh	dh	NOUN
ejpam-5478	334	66	=	=	PROPN
ejpam-5478	334	67	p1d(d	p1d(d	PROPN
ejpam-5478	334	68	α	α	PROPN
ejpam-5478	334	69	s|tqi	s|tqi	PROPN
ejpam-5478	334	70	)	)	PUNCT
ejpam-5478	335	1	+	+	PROPN
ejpam-5478	335	2	dα	dα	PROPN
ejpam-5478	335	3	s|tqid(p1	s|tqid(p1	NOUN
ejpam-5478	335	4	)	)	PUNCT
ejpam-5478	336	1	+	+	CCONJ
ejpam-5478	336	2	p2d(d	p2d(d	PROPN
ejpam-5478	336	3	α	α	PROPN
ejpam-5478	336	4	s|td	s|td	PROPN
ejpam-5478	336	5	α	α	PROPN
ejpam-5478	336	6	s|tqi	s|tqi	PROPN
ejpam-5478	336	7	)	)	PUNCT
ejpam-5478	337	1	+	+	NOUN
ejpam-5478	337	2	d2α	d2α	NOUN
ejpam-5478	337	3	s|tqid(p2)−	s|tqid(p2)−	DET
ejpam-5478	338	1	∂l	∂l	VERB
ejpam-5478	338	2	∂qi	∂qi	PROPN
ejpam-5478	338	3	,	,	PUNCT
ejpam-5478	338	4	by	by	ADP
ejpam-5478	338	5	applying	apply	VERB
ejpam-5478	338	6	(	(	PUNCT
ejpam-5478	338	7	1	1	NUM
ejpam-5478	338	8	)	)	PUNCT
ejpam-5478	338	9	of	of	ADP
ejpam-5478	338	10	the	the	DET
ejpam-5478	338	11	euler	euler	NOUN
ejpam-5478	338	12	-	-	PUNCT
ejpam-5478	338	13	lagrange	lagrange	NOUN
ejpam-5478	338	14	equation	equation	NOUN
ejpam-5478	338	15	,	,	PUNCT
ejpam-5478	338	16	we	we	PRON
ejpam-5478	338	17	arrive	arrive	VERB
ejpam-5478	338	18	at	at	ADP
ejpam-5478	338	19	the	the	DET
ejpam-5478	338	20	following	follow	VERB
ejpam-5478	338	21	conclusion	conclusion	NOUN
ejpam-5478	338	22	:	:	PUNCT
ejpam-5478	338	23	dh	dh	NOUN
ejpam-5478	338	24	=	=	PROPN
ejpam-5478	338	25	p1d(d	p1d(d	PROPN
ejpam-5478	338	26	α	α	NOUN
ejpam-5478	338	27	s|tqi)+dα	s|tqi)+dα	VERB
ejpam-5478	338	28	s|tqid(p1)+p2d(d	s|tqid(p1)+p2d(d	ADJ
ejpam-5478	338	29	2α	2α	NUM
ejpam-5478	338	30	s|tqi)+d2α	s|tqi)+d2α	NOUN
ejpam-5478	338	31	s|tqid(p2)+	s|tqid(p2)+	PROPN
ejpam-5478	338	32	∂l	∂l	PROPN
ejpam-5478	339	1	∂t	∂t	PROPN
ejpam-5478	339	2	−(dα	−(dα	PROPN
ejpam-5478	339	3	s|tp1−d2α	s|tp1−d2α	NOUN
ejpam-5478	339	4	s|tp2)dqi	s|tp2)dqi	NOUN
ejpam-5478	339	5	,	,	PUNCT
ejpam-5478	339	6	(	(	PUNCT
ejpam-5478	339	7	a.3	a.3	X
ejpam-5478	339	8	)	)	PUNCT
ejpam-5478	339	9	this	this	PRON
ejpam-5478	339	10	indicates	indicate	VERB
ejpam-5478	339	11	that	that	SCONJ
ejpam-5478	339	12	the	the	DET
ejpam-5478	339	13	hamiltonian	hamiltonian	NOUN
ejpam-5478	339	14	can	can	AUX
ejpam-5478	339	15	be	be	AUX
ejpam-5478	339	16	represented	represent	VERB
ejpam-5478	339	17	in	in	ADP
ejpam-5478	339	18	the	the	DET
ejpam-5478	339	19	following	following	NOUN
ejpam-5478	339	20	as	as	SCONJ
ejpam-5478	339	21	follows	follow	VERB
ejpam-5478	339	22	:	:	PUNCT
ejpam-5478	339	23	h	h	NOUN
ejpam-5478	339	24	=	=	SYM
ejpam-5478	339	25	h(qi	h(qi	PROPN
ejpam-5478	339	26	,	,	PUNCT
ejpam-5478	339	27	p1	p1	NOUN
ejpam-5478	339	28	,	,	PUNCT
ejpam-5478	339	29	p2	p2	NOUN
ejpam-5478	339	30	,	,	PUNCT
ejpam-5478	339	31	t	t	PROPN
ejpam-5478	339	32	)	)	PUNCT
ejpam-5478	339	33	y.	y.	NOUN
ejpam-5478	339	34	m.	m.	NOUN
ejpam-5478	339	35	alawaideh	alawaideh	PROPN
ejpam-5478	339	36	et	et	PROPN
ejpam-5478	339	37	al	al	PROPN
ejpam-5478	339	38	.	.	PUNCT
ejpam-5478	339	39	/	/	SYM
ejpam-5478	339	40	eur	eur	PROPN
ejpam-5478	339	41	.	.	PUNCT
ejpam-5478	340	1	j.	j.	PROPN
ejpam-5478	340	2	pure	pure	PROPN
ejpam-5478	340	3	appl	appl	PROPN
ejpam-5478	340	4	.	.	PROPN
ejpam-5478	340	5	math	math	PROPN
ejpam-5478	340	6	,	,	PUNCT
ejpam-5478	340	7	18	18	NUM
ejpam-5478	340	8	(	(	PUNCT
ejpam-5478	340	9	1	1	NUM
ejpam-5478	340	10	)	)	PUNCT
ejpam-5478	340	11	(	(	PUNCT
ejpam-5478	340	12	2025	2025	NUM
ejpam-5478	340	13	)	)	PUNCT
ejpam-5478	340	14	,	,	PUNCT
ejpam-5478	340	15	5478	5478	NUM
ejpam-5478	340	16	14	14	NUM
ejpam-5478	340	17	of	of	ADP
ejpam-5478	340	18	14	14	NUM
ejpam-5478	340	19	the	the	DET
ejpam-5478	340	20	total	total	ADJ
ejpam-5478	340	21	differential	differential	NOUN
ejpam-5478	340	22	for	for	ADP
ejpam-5478	340	23	this	this	DET
ejpam-5478	340	24	function	function	NOUN
ejpam-5478	340	25	can	can	AUX
ejpam-5478	340	26	be	be	AUX
ejpam-5478	340	27	expressed	express	VERB
ejpam-5478	340	28	as	as	ADP
ejpam-5478	340	29	:	:	PUNCT
ejpam-5478	340	30	dh	dh	NOUN
ejpam-5478	341	1	=	=	SYM
ejpam-5478	341	2	∂h	∂h	PROPN
ejpam-5478	342	1	∂qi	∂qi	PROPN
ejpam-5478	342	2	dqi	dqi	NOUN
ejpam-5478	342	3	+	+	CCONJ
ejpam-5478	342	4	∂h	∂h	PROPN
ejpam-5478	342	5	∂p1	∂p1	NOUN
ejpam-5478	342	6	dp1	dp1	PROPN
ejpam-5478	342	7	+	+	PROPN
ejpam-5478	342	8	∂h	∂h	PROPN
ejpam-5478	342	9	∂p2	∂p2	PROPN
ejpam-5478	342	10	dp2	dp2	NOUN
ejpam-5478	343	1	+	+	CCONJ
ejpam-5478	344	1	∂h	∂h	PROPN
ejpam-5478	344	2	∂t	∂t	PROPN
ejpam-5478	344	3	dt	dt	X
ejpam-5478	344	4	(	(	PUNCT
ejpam-5478	344	5	a.4	a.4	X
ejpam-5478	344	6	)	)	PUNCT