id	sid	tid	token	lemma	pos
ejpam-5697	1	1	european	european	PROPN
ejpam-5697	1	2	journal	journal	PROPN
ejpam-5697	1	3	of	of	ADP
ejpam-5697	1	4	pure	pure	ADJ
ejpam-5697	1	5	and	and	CCONJ
ejpam-5697	1	6	applied	applied	ADJ
ejpam-5697	1	7	mathematics	mathematic	NOUN
ejpam-5697	1	8	2025	2025	NUM
ejpam-5697	1	9	,	,	PUNCT
ejpam-5697	1	10	vol	vol	NOUN
ejpam-5697	1	11	.	.	PROPN
ejpam-5697	1	12	18	18	NUM
ejpam-5697	1	13	,	,	PUNCT
ejpam-5697	1	14	issue	issue	NOUN
ejpam-5697	1	15	1	1	NUM
ejpam-5697	1	16	,	,	PUNCT
ejpam-5697	1	17	article	article	NOUN
ejpam-5697	1	18	number	number	NOUN
ejpam-5697	1	19	5697	5697	NUM
ejpam-5697	1	20	issn	issn	VERB
ejpam-5697	1	21	1307	1307	NUM
ejpam-5697	1	22	-	-	SYM
ejpam-5697	1	23	5543	5543	NUM
ejpam-5697	1	24	–	–	PUNCT
ejpam-5697	1	25	ejpam.com	ejpam.com	X
ejpam-5697	1	26	published	publish	VERB
ejpam-5697	1	27	by	by	ADP
ejpam-5697	1	28	new	new	PROPN
ejpam-5697	1	29	york	york	PROPN
ejpam-5697	1	30	business	business	PROPN
ejpam-5697	1	31	global	global	ADJ
ejpam-5697	1	32	new	new	ADJ
ejpam-5697	1	33	generalized	generalize	VERB
ejpam-5697	1	34	results	result	NOUN
ejpam-5697	1	35	for	for	ADP
ejpam-5697	1	36	modified	modified	ADJ
ejpam-5697	1	37	atangana	atangana	PROPN
ejpam-5697	1	38	-	-	PUNCT
ejpam-5697	1	39	baleanu	baleanu	ADJ
ejpam-5697	1	40	fractional	fractional	ADJ
ejpam-5697	1	41	derivatives	derivative	NOUN
ejpam-5697	1	42	and	and	CCONJ
ejpam-5697	1	43	integral	integral	ADJ
ejpam-5697	1	44	operators	operator	NOUN
ejpam-5697	1	45	gauhar	gauhar	PROPN
ejpam-5697	1	46	rahman1,∗	rahman1,∗	PROPN
ejpam-5697	1	47	,	,	PUNCT
ejpam-5697	1	48	muhammad	muhammad	PROPN
ejpam-5697	1	49	samraiz2	samraiz2	PROPN
ejpam-5697	1	50	,	,	PUNCT
ejpam-5697	1	51	çetin	çetin	PROPN
ejpam-5697	1	52	yıldız3	yıldız3	PROPN
ejpam-5697	1	53	,	,	PUNCT
ejpam-5697	1	54	thabet	thabet	ADJ
ejpam-5697	1	55	abdeljawad4,5,6,7,8,∗	abdeljawad4,5,6,7,8,∗	PROPN
ejpam-5697	1	56	,	,	PUNCT
ejpam-5697	1	57	manar	manar	PROPN
ejpam-5697	1	58	a.	a.	PROPN
ejpam-5697	1	59	alqudah9	alqudah9	PROPN
ejpam-5697	1	60	,	,	PUNCT
ejpam-5697	1	61	aiman	aiman	PROPN
ejpam-5697	1	62	mukheimer5	mukheimer5	PROPN
ejpam-5697	1	63	1	1	NUM
ejpam-5697	1	64	department	department	NOUN
ejpam-5697	1	65	of	of	ADP
ejpam-5697	1	66	mathematics	mathematic	NOUN
ejpam-5697	1	67	and	and	CCONJ
ejpam-5697	1	68	statistics	statistic	NOUN
ejpam-5697	1	69	,	,	PUNCT
ejpam-5697	1	70	hazara	hazara	PROPN
ejpam-5697	1	71	university	university	PROPN
ejpam-5697	1	72	,	,	PUNCT
ejpam-5697	1	73	mansehra	mansehra	PROPN
ejpam-5697	1	74	21300	21300	NUM
ejpam-5697	1	75	,	,	PUNCT
ejpam-5697	1	76	pakistan	pakistan	PROPN
ejpam-5697	1	77	2	2	NUM
ejpam-5697	1	78	department	department	NOUN
ejpam-5697	1	79	of	of	ADP
ejpam-5697	1	80	mathematics	mathematics	PROPN
ejpam-5697	1	81	,	,	PUNCT
ejpam-5697	1	82	university	university	PROPN
ejpam-5697	1	83	of	of	ADP
ejpam-5697	1	84	sargodha	sargodha	PROPN
ejpam-5697	1	85	p.o	p.o	PROPN
ejpam-5697	1	86	.	.	PROPN
ejpam-5697	1	87	box	box	PROPN
ejpam-5697	1	88	40100	40100	PROPN
ejpam-5697	1	89	,	,	PUNCT
ejpam-5697	1	90	sargodha	sargodha	PROPN
ejpam-5697	1	91	,	,	PUNCT
ejpam-5697	1	92	pakistan	pakistan	PROPN
ejpam-5697	1	93	3	3	NUM
ejpam-5697	1	94	deparment	deparment	NOUN
ejpam-5697	1	95	of	of	ADP
ejpam-5697	1	96	mathematics	mathematics	PROPN
ejpam-5697	1	97	,	,	PUNCT
ejpam-5697	1	98	k.k	k.k	PROPN
ejpam-5697	1	99	.	.	PROPN
ejpam-5697	1	100	education	education	PROPN
ejpam-5697	1	101	faculty	faculty	NOUN
ejpam-5697	1	102	,	,	PUNCT
ejpam-5697	1	103	atatürk	atatürk	PROPN
ejpam-5697	1	104	university	university	NOUN
ejpam-5697	1	105	,	,	PUNCT
ejpam-5697	1	106	25240	25240	NUM
ejpam-5697	1	107	erzurum	erzurum	PROPN
ejpam-5697	1	108	,	,	PUNCT
ejpam-5697	1	109	turkey	turkey	PROPN
ejpam-5697	1	110	4	4	NUM
ejpam-5697	1	111	department	department	NOUN
ejpam-5697	1	112	of	of	ADP
ejpam-5697	1	113	mathematics	mathematic	NOUN
ejpam-5697	1	114	,	,	PUNCT
ejpam-5697	1	115	saveetha	saveetha	PROPN
ejpam-5697	1	116	school	school	PROPN
ejpam-5697	1	117	of	of	ADP
ejpam-5697	1	118	engineering	engineering	PROPN
ejpam-5697	1	119	,	,	PUNCT
ejpam-5697	1	120	saveetha	saveetha	PROPN
ejpam-5697	1	121	institute	institute	PROPN
ejpam-5697	1	122	of	of	ADP
ejpam-5697	1	123	medical	medical	ADJ
ejpam-5697	1	124	and	and	CCONJ
ejpam-5697	1	125	technical	technical	ADJ
ejpam-5697	1	126	sciences	science	NOUN
ejpam-5697	1	127	,	,	PUNCT
ejpam-5697	1	128	saveetha	saveetha	PROPN
ejpam-5697	1	129	university	university	PROPN
ejpam-5697	1	130	,	,	PUNCT
ejpam-5697	1	131	chennai	chennai	NOUN
ejpam-5697	1	132	602105	602105	NUM
ejpam-5697	1	133	,	,	PUNCT
ejpam-5697	1	134	tamil	tamil	PROPN
ejpam-5697	1	135	nadu	nadu	PROPN
ejpam-5697	1	136	,	,	PUNCT
ejpam-5697	1	137	india	india	PROPN
ejpam-5697	1	138	5	5	NUM
ejpam-5697	1	139	department	department	NOUN
ejpam-5697	1	140	of	of	ADP
ejpam-5697	1	141	mathematics	mathematic	NOUN
ejpam-5697	1	142	and	and	CCONJ
ejpam-5697	1	143	sciences	science	NOUN
ejpam-5697	1	144	,	,	PUNCT
ejpam-5697	1	145	prince	prince	PROPN
ejpam-5697	1	146	sultan	sultan	PROPN
ejpam-5697	1	147	university	university	PROPN
ejpam-5697	1	148	,	,	PUNCT
ejpam-5697	1	149	riyadh	riyadh	NOUN
ejpam-5697	1	150	,	,	PUNCT
ejpam-5697	1	151	11586	11586	NUM
ejpam-5697	1	152	,	,	PUNCT
ejpam-5697	1	153	saudi	saudi	PROPN
ejpam-5697	1	154	arabia	arabia	PROPN
ejpam-5697	1	155	6	6	NUM
ejpam-5697	1	156	department	department	NOUN
ejpam-5697	1	157	of	of	ADP
ejpam-5697	1	158	medical	medical	ADJ
ejpam-5697	1	159	research	research	NOUN
ejpam-5697	1	160	,	,	PUNCT
ejpam-5697	1	161	china	china	PROPN
ejpam-5697	1	162	medical	medical	PROPN
ejpam-5697	1	163	university	university	PROPN
ejpam-5697	1	164	,	,	PUNCT
ejpam-5697	1	165	taichung	taichung	PROPN
ejpam-5697	1	166	,	,	PUNCT
ejpam-5697	1	167	40402	40402	NUM
ejpam-5697	1	168	,	,	PUNCT
ejpam-5697	1	169	taiwan	taiwan	PROPN
ejpam-5697	1	170	7	7	NUM
ejpam-5697	1	171	center	center	NOUN
ejpam-5697	1	172	for	for	ADP
ejpam-5697	1	173	applied	applied	ADJ
ejpam-5697	1	174	mathematics	mathematic	NOUN
ejpam-5697	1	175	and	and	CCONJ
ejpam-5697	1	176	bioinformatics	bioinformatics	NOUN
ejpam-5697	1	177	(	(	PUNCT
ejpam-5697	1	178	camb	camb	PROPN
ejpam-5697	1	179	)	)	PUNCT
ejpam-5697	1	180	,	,	PUNCT
ejpam-5697	1	181	gulf	gulf	PROPN
ejpam-5697	1	182	university	university	PROPN
ejpam-5697	1	183	for	for	ADP
ejpam-5697	1	184	science	science	NOUN
ejpam-5697	1	185	and	and	CCONJ
ejpam-5697	1	186	technology	technology	NOUN
ejpam-5697	1	187	,	,	PUNCT
ejpam-5697	1	188	hawally	hawally	ADV
ejpam-5697	1	189	,	,	PUNCT
ejpam-5697	1	190	32093	32093	NUM
ejpam-5697	1	191	,	,	PUNCT
ejpam-5697	1	192	kuwait	kuwait	PROPN
ejpam-5697	1	193	8	8	NUM
ejpam-5697	1	194	department	department	NOUN
ejpam-5697	1	195	of	of	ADP
ejpam-5697	1	196	mathematics	mathematic	NOUN
ejpam-5697	1	197	and	and	CCONJ
ejpam-5697	1	198	applied	apply	VERB
ejpam-5697	1	199	mathematics	mathematic	NOUN
ejpam-5697	1	200	,	,	PUNCT
ejpam-5697	1	201	sefako	sefako	VERB
ejpam-5697	1	202	makgatho	makgatho	PROPN
ejpam-5697	1	203	health	health	PROPN
ejpam-5697	1	204	sciences	sciences	PROPN
ejpam-5697	1	205	university	university	PROPN
ejpam-5697	1	206	,	,	PUNCT
ejpam-5697	1	207	garankuwa	garankuwa	NOUN
ejpam-5697	1	208	,	,	PUNCT
ejpam-5697	1	209	medusa	medusa	NOUN
ejpam-5697	1	210	,	,	PUNCT
ejpam-5697	1	211	0204	0204	NUM
ejpam-5697	1	212	,	,	PUNCT
ejpam-5697	1	213	south	south	PROPN
ejpam-5697	1	214	africa	africa	PROPN
ejpam-5697	1	215	9	9	NUM
ejpam-5697	1	216	department	department	PROPN
ejpam-5697	1	217	of	of	ADP
ejpam-5697	1	218	mathematical	mathematical	ADJ
ejpam-5697	1	219	science	science	NOUN
ejpam-5697	1	220	,	,	PUNCT
ejpam-5697	1	221	college	college	NOUN
ejpam-5697	1	222	of	of	ADP
ejpam-5697	1	223	science	science	NOUN
ejpam-5697	1	224	,	,	PUNCT
ejpam-5697	1	225	princess	princess	PROPN
ejpam-5697	1	226	nourah	nourah	PROPN
ejpam-5697	1	227	bint	bint	PROPN
ejpam-5697	1	228	abdulrahman	abdulrahman	PROPN
ejpam-5697	1	229	university	university	PROPN
ejpam-5697	1	230	,	,	PUNCT
ejpam-5697	1	231	p.o	p.o	PROPN
ejpam-5697	1	232	.	.	PROPN
ejpam-5697	1	233	box	box	PROPN
ejpam-5697	1	234	84428	84428	NUM
ejpam-5697	1	235	,	,	PUNCT
ejpam-5697	1	236	riyadh	riyadh	PROPN
ejpam-5697	1	237	11671	11671	NUM
ejpam-5697	1	238	,	,	PUNCT
ejpam-5697	1	239	saudi	saudi	PROPN
ejpam-5697	1	240	arabia	arabia	PROPN
ejpam-5697	1	241	abstract	abstract	NOUN
ejpam-5697	1	242	.	.	PUNCT
ejpam-5697	2	1	in	in	ADP
ejpam-5697	2	2	this	this	DET
ejpam-5697	2	3	current	current	ADJ
ejpam-5697	2	4	study	study	NOUN
ejpam-5697	2	5	,	,	PUNCT
ejpam-5697	2	6	first	first	ADV
ejpam-5697	2	7	we	we	PRON
ejpam-5697	2	8	establish	establish	VERB
ejpam-5697	2	9	the	the	DET
ejpam-5697	2	10	modified	modify	VERB
ejpam-5697	2	11	power	power	NOUN
ejpam-5697	2	12	atangana	atangana	PROPN
ejpam-5697	2	13	-	-	PUNCT
ejpam-5697	2	14	baleanu	baleanu	ADJ
ejpam-5697	2	15	fractional	fractional	ADJ
ejpam-5697	2	16	derivative	derivative	ADJ
ejpam-5697	2	17	operators	operator	NOUN
ejpam-5697	2	18	(	(	PUNCT
ejpam-5697	2	19	mpc	mpc	NOUN
ejpam-5697	2	20	)	)	PUNCT
ejpam-5697	2	21	in	in	ADP
ejpam-5697	2	22	both	both	CCONJ
ejpam-5697	2	23	the	the	DET
ejpam-5697	2	24	caputo	caputo	PROPN
ejpam-5697	2	25	and	and	CCONJ
ejpam-5697	2	26	riemann	riemann	PROPN
ejpam-5697	2	27	-	-	PUNCT
ejpam-5697	2	28	liouville	liouville	PROPN
ejpam-5697	2	29	(	(	PUNCT
ejpam-5697	2	30	mprl	mprl	NOUN
ejpam-5697	2	31	)	)	PUNCT
ejpam-5697	2	32	senses	sense	NOUN
ejpam-5697	2	33	.	.	PUNCT
ejpam-5697	3	1	using	use	VERB
ejpam-5697	3	2	the	the	DET
ejpam-5697	3	3	convolution	convolution	NOUN
ejpam-5697	3	4	approach	approach	NOUN
ejpam-5697	3	5	and	and	CCONJ
ejpam-5697	3	6	laplace	laplace	NOUN
ejpam-5697	3	7	transformation	transformation	NOUN
ejpam-5697	3	8	,	,	PUNCT
ejpam-5697	3	9	the	the	DET
ejpam-5697	3	10	so	so	ADV
ejpam-5697	3	11	-	-	PUNCT
ejpam-5697	3	12	called	call	VERB
ejpam-5697	3	13	modified	modify	VERB
ejpam-5697	3	14	power	power	NOUN
ejpam-5697	3	15	fractional	fractional	PROPN
ejpam-5697	3	16	caputo	caputo	PROPN
ejpam-5697	3	17	and	and	CCONJ
ejpam-5697	3	18	r	r	PROPN
ejpam-5697	3	19	-	-	PUNCT
ejpam-5697	3	20	l	l	NOUN
ejpam-5697	3	21	derivative	derivative	ADJ
ejpam-5697	3	22	operators	operator	NOUN
ejpam-5697	3	23	with	with	ADP
ejpam-5697	3	24	non	non	ADJ
ejpam-5697	3	25	-	-	ADJ
ejpam-5697	3	26	singular	singular	ADJ
ejpam-5697	3	27	kernels	kernel	NOUN
ejpam-5697	3	28	are	be	AUX
ejpam-5697	3	29	introduced	introduce	VERB
ejpam-5697	3	30	.	.	PUNCT
ejpam-5697	4	1	we	we	PRON
ejpam-5697	4	2	establish	establish	VERB
ejpam-5697	4	3	the	the	DET
ejpam-5697	4	4	boundedness	boundedness	NOUN
ejpam-5697	4	5	of	of	ADP
ejpam-5697	4	6	the	the	DET
ejpam-5697	4	7	modified	modified	PROPN
ejpam-5697	4	8	caputo	caputo	PROPN
ejpam-5697	4	9	fractional	fractional	ADJ
ejpam-5697	4	10	derivative	derivative	ADJ
ejpam-5697	4	11	operator	operator	NOUN
ejpam-5697	4	12	in	in	ADP
ejpam-5697	4	13	this	this	DET
ejpam-5697	4	14	study	study	NOUN
ejpam-5697	4	15	.	.	PUNCT
ejpam-5697	5	1	the	the	DET
ejpam-5697	5	2	fractional	fractional	ADJ
ejpam-5697	5	3	differential	differential	ADJ
ejpam-5697	5	4	equations	equation	NOUN
ejpam-5697	5	5	are	be	AUX
ejpam-5697	5	6	solved	solve	VERB
ejpam-5697	5	7	with	with	ADP
ejpam-5697	5	8	the	the	DET
ejpam-5697	5	9	generalised	generalise	VERB
ejpam-5697	5	10	laplace	laplace	NOUN
ejpam-5697	5	11	transform	transform	NOUN
ejpam-5697	5	12	(	(	PUNCT
ejpam-5697	5	13	glt	glt	PROPN
ejpam-5697	5	14	)	)	PUNCT
ejpam-5697	5	15	.	.	PUNCT
ejpam-5697	6	1	in	in	ADP
ejpam-5697	6	2	addition	addition	NOUN
ejpam-5697	6	3	,	,	PUNCT
ejpam-5697	6	4	the	the	DET
ejpam-5697	6	5	corresponding	corresponding	ADJ
ejpam-5697	6	6	form	form	NOUN
ejpam-5697	6	7	of	of	ADP
ejpam-5697	6	8	the	the	DET
ejpam-5697	6	9	fractional	fractional	ADJ
ejpam-5697	6	10	integral	integral	ADJ
ejpam-5697	6	11	operator	operator	NOUN
ejpam-5697	6	12	is	be	AUX
ejpam-5697	6	13	defined	define	VERB
ejpam-5697	6	14	.	.	PUNCT
ejpam-5697	7	1	also	also	ADV
ejpam-5697	7	2	,	,	PUNCT
ejpam-5697	7	3	we	we	PRON
ejpam-5697	7	4	prove	prove	VERB
ejpam-5697	7	5	the	the	DET
ejpam-5697	7	6	boundedness	boundedness	NOUN
ejpam-5697	7	7	and	and	CCONJ
ejpam-5697	7	8	laplace	laplace	NOUN
ejpam-5697	7	9	transform	transform	NOUN
ejpam-5697	7	10	of	of	ADP
ejpam-5697	7	11	the	the	DET
ejpam-5697	7	12	fractional	fractional	ADJ
ejpam-5697	7	13	integral	integral	ADJ
ejpam-5697	7	14	operator	operator	NOUN
ejpam-5697	7	15	.	.	PUNCT
ejpam-5697	8	1	the	the	DET
ejpam-5697	8	2	composition	composition	NOUN
ejpam-5697	8	3	of	of	ADP
ejpam-5697	8	4	power	power	NOUN
ejpam-5697	8	5	fractional	fractional	ADJ
ejpam-5697	8	6	derivative	derivative	ADJ
ejpam-5697	8	7	and	and	CCONJ
ejpam-5697	8	8	integral	integral	ADJ
ejpam-5697	8	9	operators	operator	NOUN
ejpam-5697	8	10	is	be	AUX
ejpam-5697	8	11	given	give	VERB
ejpam-5697	8	12	in	in	ADP
ejpam-5697	8	13	the	the	DET
ejpam-5697	8	14	study	study	NOUN
ejpam-5697	8	15	.	.	PUNCT
ejpam-5697	9	1	additionally	additionally	ADV
ejpam-5697	9	2	,	,	PUNCT
ejpam-5697	9	3	several	several	ADJ
ejpam-5697	9	4	examples	example	NOUN
ejpam-5697	9	5	related	relate	VERB
ejpam-5697	9	6	to	to	ADP
ejpam-5697	9	7	our	our	PRON
ejpam-5697	9	8	findings	finding	NOUN
ejpam-5697	9	9	along	along	ADP
ejpam-5697	9	10	with	with	ADP
ejpam-5697	9	11	their	their	PRON
ejpam-5697	9	12	graphical	graphical	ADJ
ejpam-5697	9	13	representation	representation	NOUN
ejpam-5697	9	14	are	be	AUX
ejpam-5697	9	15	presented	present	VERB
ejpam-5697	9	16	.	.	PUNCT
ejpam-5697	10	1	2020	2020	NUM
ejpam-5697	10	2	mathematics	mathematics	PROPN
ejpam-5697	10	3	subject	subject	NOUN
ejpam-5697	10	4	classifications	classification	NOUN
ejpam-5697	10	5	:	:	PUNCT
ejpam-5697	10	6	26a51	26a51	NUM
ejpam-5697	10	7	,	,	PUNCT
ejpam-5697	10	8	26a33	26a33	NUM
ejpam-5697	10	9	,	,	PUNCT
ejpam-5697	10	10	26d07	26d07	NUM
ejpam-5697	10	11	,	,	PUNCT
ejpam-5697	10	12	26d10	26d10	NUM
ejpam-5697	10	13	,	,	PUNCT
ejpam-5697	10	14	26d15	26d15	NUM
ejpam-5697	10	15	key	key	ADJ
ejpam-5697	10	16	words	word	NOUN
ejpam-5697	10	17	and	and	CCONJ
ejpam-5697	10	18	phrases	phrase	NOUN
ejpam-5697	10	19	:	:	PUNCT
ejpam-5697	10	20	mittag	mittag	ADJ
ejpam-5697	10	21	-	-	PUNCT
ejpam-5697	10	22	leffler	leffler	NOUN
ejpam-5697	10	23	function	function	NOUN
ejpam-5697	10	24	,	,	PUNCT
ejpam-5697	10	25	power	power	NOUN
ejpam-5697	10	26	mittag	mittag	ADJ
ejpam-5697	10	27	-	-	PUNCT
ejpam-5697	10	28	leffler	leffler	NOUN
ejpam-5697	10	29	function	function	NOUN
ejpam-5697	10	30	,	,	PUNCT
ejpam-5697	10	31	power	power	NOUN
ejpam-5697	10	32	fractional	fractional	ADJ
ejpam-5697	10	33	derivative	derivative	ADJ
ejpam-5697	10	34	,	,	PUNCT
ejpam-5697	10	35	fractional	fractional	ADJ
ejpam-5697	10	36	differential	differential	NOUN
ejpam-5697	10	37	equation	equation	NOUN
ejpam-5697	10	38	,	,	PUNCT
ejpam-5697	10	39	generalized	generalize	VERB
ejpam-5697	10	40	laplace	laplace	NOUN
ejpam-5697	10	41	transform	transform	NOUN
ejpam-5697	10	42	∗corresponding	∗corresponde	VERB
ejpam-5697	10	43	author	author	NOUN
ejpam-5697	10	44	.	.	PUNCT
ejpam-5697	11	1	∗corresponding	∗corresponde	VERB
ejpam-5697	11	2	author	author	NOUN
ejpam-5697	11	3	.	.	PUNCT
ejpam-5697	12	1	doi	doi	NOUN
ejpam-5697	12	2	:	:	PUNCT
ejpam-5697	12	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5697	https://doi.org/10.29020/nybg.ejpam.v18i1.5697	PUNCT
ejpam-5697	12	4	email	email	NOUN
ejpam-5697	12	5	addresses	address	NOUN
ejpam-5697	12	6	:	:	PUNCT
ejpam-5697	12	7	gauhar55uom@gmail.com	gauhar55uom@gmail.com	X
ejpam-5697	12	8	,	,	PUNCT
ejpam-5697	12	9	drgauhar.rahman@hu.edu.pk	drgauhar.rahman@hu.edu.pk	INTJ
ejpam-5697	12	10	(	(	PUNCT
ejpam-5697	12	11	g.	g.	PROPN
ejpam-5697	12	12	rahman	rahman	PROPN
ejpam-5697	12	13	)	)	PUNCT
ejpam-5697	12	14	,	,	PUNCT
ejpam-5697	12	15	muhammad.samraiz@uos.edu.pk	muhammad.samraiz@uos.edu.pk	PROPN
ejpam-5697	12	16	,	,	PUNCT
ejpam-5697	12	17	msamraizuos@gmail.com	msamraizuos@gmail.com	PROPN
ejpam-5697	12	18	(	(	PUNCT
ejpam-5697	12	19	m.	m.	NOUN
ejpam-5697	12	20	samraiz	samraiz	PROPN
ejpam-5697	12	21	)	)	PUNCT
ejpam-5697	12	22	,	,	PUNCT
ejpam-5697	12	23	cetin@atauni.edu.tr	cetin@atauni.edu.tr	NOUN
ejpam-5697	12	24	(	(	PUNCT
ejpam-5697	12	25	ç.	ç.	ADP
ejpam-5697	12	26	yıldız	yıldız	PROPN
ejpam-5697	12	27	)	)	PUNCT
ejpam-5697	12	28	,	,	PUNCT
ejpam-5697	12	29	tabdeljawad@psu.edu.sa	tabdeljawad@psu.edu.sa	PROPN
ejpam-5697	12	30	(	(	PUNCT
ejpam-5697	12	31	t.	t.	NOUN
ejpam-5697	12	32	abdeljawad	abdeljawad	PROPN
ejpam-5697	12	33	)	)	PUNCT
ejpam-5697	12	34	,	,	PUNCT
ejpam-5697	12	35	maalqudah@pnu.edu.sa	maalqudah@pnu.edu.sa	PROPN
ejpam-5697	12	36	(	(	PUNCT
ejpam-5697	12	37	m.	m.	NOUN
ejpam-5697	12	38	a.	a.	PROPN
ejpam-5697	12	39	alqudah	alqudah	PROPN
ejpam-5697	12	40	)	)	PUNCT
ejpam-5697	12	41	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5697	13	1	1	1	NUM
ejpam-5697	13	2	copyright	copyright	NOUN
ejpam-5697	13	3	:	:	PUNCT
ejpam-5697	13	4	©	©	PROPN
ejpam-5697	13	5	2025	2025	NUM
ejpam-5697	13	6	the	the	DET
ejpam-5697	13	7	author(s	author(s	NOUN
ejpam-5697	13	8	)	)	PUNCT
ejpam-5697	13	9	.	.	PUNCT
ejpam-5697	14	1	(	(	PUNCT
ejpam-5697	14	2	cc	cc	NOUN
ejpam-5697	14	3	by	by	ADP
ejpam-5697	14	4	-	-	PUNCT
ejpam-5697	14	5	nc	nc	PROPN
ejpam-5697	14	6	4.0	4.0	NUM
ejpam-5697	14	7	)	)	PUNCT
ejpam-5697	14	8	gauhar	gauhar	PROPN
ejpam-5697	15	1	rahman	rahman	PROPN
ejpam-5697	15	2	et	et	PROPN
ejpam-5697	15	3	al	al	PROPN
ejpam-5697	15	4	.	.	PUNCT
ejpam-5697	15	5	/	/	SYM
ejpam-5697	15	6	eur	eur	PROPN
ejpam-5697	15	7	.	.	PUNCT
ejpam-5697	16	1	j.	j.	PROPN
ejpam-5697	16	2	pure	pure	PROPN
ejpam-5697	16	3	appl	appl	PROPN
ejpam-5697	16	4	.	.	PROPN
ejpam-5697	16	5	math	math	PROPN
ejpam-5697	16	6	,	,	PUNCT
ejpam-5697	16	7	18	18	NUM
ejpam-5697	16	8	(	(	PUNCT
ejpam-5697	16	9	1	1	NUM
ejpam-5697	16	10	)	)	PUNCT
ejpam-5697	16	11	(	(	PUNCT
ejpam-5697	16	12	2025	2025	NUM
ejpam-5697	16	13	)	)	PUNCT
ejpam-5697	16	14	,	,	PUNCT
ejpam-5697	16	15	5697	5697	NUM
ejpam-5697	16	16	2	2	NUM
ejpam-5697	16	17	of	of	ADP
ejpam-5697	16	18	26	26	NUM
ejpam-5697	16	19	1	1	NUM
ejpam-5697	16	20	.	.	PUNCT
ejpam-5697	17	1	introduction	introduction	NOUN
ejpam-5697	17	2	fractional	fractional	ADJ
ejpam-5697	17	3	calculus	calculus	NOUN
ejpam-5697	17	4	has	have	VERB
ejpam-5697	17	5	a	a	DET
ejpam-5697	17	6	remarkable	remarkable	ADJ
ejpam-5697	17	7	325	325	NUM
ejpam-5697	17	8	years	year	NOUN
ejpam-5697	17	9	history	history	NOUN
ejpam-5697	17	10	,	,	PUNCT
ejpam-5697	17	11	but	but	CCONJ
ejpam-5697	17	12	there	there	PRON
ejpam-5697	17	13	are	be	VERB
ejpam-5697	17	14	still	still	ADV
ejpam-5697	17	15	many	many	ADJ
ejpam-5697	17	16	unanswered	unanswered	ADJ
ejpam-5697	17	17	theoretical	theoretical	ADJ
ejpam-5697	17	18	and	and	CCONJ
ejpam-5697	17	19	practical	practical	ADJ
ejpam-5697	17	20	questions	question	NOUN
ejpam-5697	17	21	.	.	PUNCT
ejpam-5697	18	1	fractional	fractional	ADJ
ejpam-5697	18	2	calculus	calculus	NOUN
ejpam-5697	18	3	is	be	AUX
ejpam-5697	18	4	used	use	VERB
ejpam-5697	18	5	by	by	ADP
ejpam-5697	18	6	abel	abel	PROPN
ejpam-5697	19	1	[	[	X
ejpam-5697	19	2	1	1	X
ejpam-5697	19	3	]	]	PUNCT
ejpam-5697	19	4	to	to	PART
ejpam-5697	19	5	solve	solve	VERB
ejpam-5697	19	6	the	the	DET
ejpam-5697	19	7	tautrocrone	tautrocrone	NOUN
ejpam-5697	19	8	problem	problem	NOUN
ejpam-5697	19	9	.	.	PUNCT
ejpam-5697	20	1	the	the	DET
ejpam-5697	20	2	use	use	NOUN
ejpam-5697	20	3	of	of	ADP
ejpam-5697	20	4	fractional	fractional	ADJ
ejpam-5697	20	5	calculus	calculus	NOUN
ejpam-5697	20	6	in	in	ADP
ejpam-5697	20	7	differential	differential	ADJ
ejpam-5697	20	8	and	and	CCONJ
ejpam-5697	20	9	integral	integral	ADJ
ejpam-5697	20	10	equations	equation	NOUN
ejpam-5697	20	11	is	be	AUX
ejpam-5697	20	12	highlighted	highlight	VERB
ejpam-5697	20	13	in	in	ADP
ejpam-5697	20	14	this	this	DET
ejpam-5697	20	15	work	work	NOUN
ejpam-5697	20	16	[	[	X
ejpam-5697	20	17	9	9	NUM
ejpam-5697	20	18	]	]	PUNCT
ejpam-5697	20	19	.	.	PUNCT
ejpam-5697	21	1	numerous	numerous	ADJ
ejpam-5697	21	2	more	more	ADJ
ejpam-5697	21	3	articles	article	NOUN
ejpam-5697	21	4	written	write	VERB
ejpam-5697	21	5	by	by	ADP
ejpam-5697	21	6	other	other	ADJ
ejpam-5697	21	7	scholars	scholar	NOUN
ejpam-5697	21	8	in	in	ADP
ejpam-5697	21	9	[	[	X
ejpam-5697	21	10	13	13	NUM
ejpam-5697	21	11	,	,	PUNCT
ejpam-5697	21	12	16	16	NUM
ejpam-5697	21	13	,	,	PUNCT
ejpam-5697	21	14	21	21	NUM
ejpam-5697	21	15	,	,	PUNCT
ejpam-5697	21	16	24	24	NUM
ejpam-5697	21	17	]	]	PUNCT
ejpam-5697	21	18	provide	provide	VERB
ejpam-5697	21	19	a	a	DET
ejpam-5697	21	20	variety	variety	NOUN
ejpam-5697	21	21	of	of	ADP
ejpam-5697	21	22	concepts	concept	NOUN
ejpam-5697	21	23	and	and	CCONJ
ejpam-5697	21	24	applications	application	NOUN
ejpam-5697	21	25	related	relate	VERB
ejpam-5697	21	26	to	to	ADP
ejpam-5697	21	27	fractional	fractional	ADJ
ejpam-5697	21	28	operators	operator	NOUN
ejpam-5697	21	29	.	.	PUNCT
ejpam-5697	22	1	many	many	ADJ
ejpam-5697	22	2	researchers	researcher	NOUN
ejpam-5697	22	3	argue	argue	VERB
ejpam-5697	22	4	that	that	SCONJ
ejpam-5697	22	5	a	a	DET
ejpam-5697	22	6	single	single	ADJ
ejpam-5697	22	7	fractional	fractional	ADJ
ejpam-5697	22	8	operator	operator	NOUN
ejpam-5697	22	9	can	can	AUX
ejpam-5697	22	10	not	not	PART
ejpam-5697	22	11	correctly	correctly	ADV
ejpam-5697	22	12	represent	represent	VERB
ejpam-5697	22	13	the	the	DET
ejpam-5697	22	14	complexity	complexity	NOUN
ejpam-5697	22	15	of	of	ADP
ejpam-5697	22	16	various	various	ADJ
ejpam-5697	22	17	complex	complex	ADJ
ejpam-5697	22	18	scientific	scientific	ADJ
ejpam-5697	22	19	and	and	CCONJ
ejpam-5697	22	20	engineering	engineering	NOUN
ejpam-5697	22	21	processes	process	NOUN
ejpam-5697	22	22	,	,	PUNCT
ejpam-5697	22	23	such	such	ADJ
ejpam-5697	22	24	as	as	ADP
ejpam-5697	22	25	the	the	DET
ejpam-5697	22	26	caputo	caputo	PROPN
ejpam-5697	22	27	ones	one	NOUN
ejpam-5697	22	28	.	.	PUNCT
ejpam-5697	23	1	considering	consider	VERB
ejpam-5697	23	2	that	that	SCONJ
ejpam-5697	23	3	additional	additional	ADJ
ejpam-5697	23	4	experimental	experimental	ADJ
ejpam-5697	23	5	proof	proof	NOUN
ejpam-5697	23	6	is	be	AUX
ejpam-5697	23	7	needed	need	VERB
ejpam-5697	23	8	to	to	PART
ejpam-5697	23	9	verify	verify	VERB
ejpam-5697	23	10	the	the	DET
ejpam-5697	23	11	fractional	fractional	ADJ
ejpam-5697	23	12	models	model	NOUN
ejpam-5697	23	13	’	'	PUNCT
ejpam-5697	23	14	accuracy	accuracy	NOUN
ejpam-5697	24	1	[	[	X
ejpam-5697	24	2	3	3	NUM
ejpam-5697	24	3	,	,	PUNCT
ejpam-5697	24	4	12	12	NUM
ejpam-5697	24	5	]	]	PUNCT
ejpam-5697	24	6	.	.	PUNCT
ejpam-5697	25	1	an	an	DET
ejpam-5697	25	2	increasing	increase	VERB
ejpam-5697	25	3	number	number	NOUN
ejpam-5697	25	4	of	of	ADP
ejpam-5697	25	5	mathematicians	mathematician	NOUN
ejpam-5697	25	6	and	and	CCONJ
ejpam-5697	25	7	experts	expert	NOUN
ejpam-5697	25	8	have	have	AUX
ejpam-5697	25	9	focused	focus	VERB
ejpam-5697	25	10	on	on	ADP
ejpam-5697	25	11	fractional	fractional	ADJ
ejpam-5697	25	12	differential	differential	ADJ
ejpam-5697	25	13	and	and	CCONJ
ejpam-5697	25	14	integral	integral	ADJ
ejpam-5697	25	15	equations	equation	NOUN
ejpam-5697	25	16	in	in	ADP
ejpam-5697	25	17	recent	recent	ADJ
ejpam-5697	25	18	years	year	NOUN
ejpam-5697	26	1	[	[	X
ejpam-5697	26	2	2	2	NUM
ejpam-5697	26	3	,	,	PUNCT
ejpam-5697	26	4	22	22	NUM
ejpam-5697	26	5	]	]	PUNCT
ejpam-5697	26	6	.	.	PUNCT
ejpam-5697	27	1	many	many	ADJ
ejpam-5697	27	2	phenomena	phenomenon	NOUN
ejpam-5697	27	3	in	in	ADP
ejpam-5697	27	4	a	a	DET
ejpam-5697	27	5	variety	variety	NOUN
ejpam-5697	27	6	of	of	ADP
ejpam-5697	27	7	disciplines	discipline	NOUN
ejpam-5697	27	8	,	,	PUNCT
ejpam-5697	27	9	such	such	ADJ
ejpam-5697	27	10	as	as	ADP
ejpam-5697	27	11	dynamics	dynamic	NOUN
ejpam-5697	27	12	,	,	PUNCT
ejpam-5697	27	13	physics	physics	NOUN
ejpam-5697	27	14	,	,	PUNCT
ejpam-5697	27	15	biology	biology	NOUN
ejpam-5697	27	16	,	,	PUNCT
ejpam-5697	27	17	and	and	CCONJ
ejpam-5697	27	18	mechanics	mechanic	NOUN
ejpam-5697	27	19	,	,	PUNCT
ejpam-5697	27	20	have	have	VERB
ejpam-5697	27	21	scientific	scientific	ADJ
ejpam-5697	27	22	interpretations	interpretation	NOUN
ejpam-5697	27	23	that	that	PRON
ejpam-5697	27	24	align	align	VERB
ejpam-5697	27	25	with	with	ADP
ejpam-5697	27	26	the	the	DET
ejpam-5697	27	27	fractional	fractional	ADJ
ejpam-5697	27	28	order	order	NOUN
ejpam-5697	27	29	derivatives	derivative	NOUN
ejpam-5697	27	30	.	.	PUNCT
ejpam-5697	28	1	the	the	DET
ejpam-5697	28	2	existence	existence	NOUN
ejpam-5697	28	3	theory	theory	NOUN
ejpam-5697	28	4	of	of	ADP
ejpam-5697	28	5	solutions	solution	NOUN
ejpam-5697	28	6	is	be	AUX
ejpam-5697	28	7	one	one	NUM
ejpam-5697	28	8	of	of	ADP
ejpam-5697	28	9	the	the	DET
ejpam-5697	28	10	primary	primary	ADJ
ejpam-5697	28	11	study	study	NOUN
ejpam-5697	28	12	topics	topic	NOUN
ejpam-5697	28	13	for	for	ADP
ejpam-5697	28	14	fractional	fractional	ADJ
ejpam-5697	28	15	order	order	NOUN
ejpam-5697	28	16	differential	differential	NOUN
ejpam-5697	28	17	equations	equation	NOUN
ejpam-5697	28	18	,	,	PUNCT
ejpam-5697	28	19	and	and	CCONJ
ejpam-5697	28	20	analysts	analyst	NOUN
ejpam-5697	28	21	are	be	AUX
ejpam-5697	28	22	closely	closely	ADV
ejpam-5697	28	23	monitoring	monitor	VERB
ejpam-5697	28	24	.	.	PUNCT
ejpam-5697	29	1	an	an	DET
ejpam-5697	29	2	exact	exact	ADJ
ejpam-5697	29	3	solution	solution	NOUN
ejpam-5697	29	4	to	to	ADP
ejpam-5697	29	5	a	a	DET
ejpam-5697	29	6	fractional	fractional	ADJ
ejpam-5697	29	7	order	order	NOUN
ejpam-5697	29	8	differential	differential	NOUN
ejpam-5697	29	9	equation	equation	NOUN
ejpam-5697	29	10	may	may	AUX
ejpam-5697	29	11	be	be	AUX
ejpam-5697	29	12	difficult	difficult	ADJ
ejpam-5697	29	13	to	to	PART
ejpam-5697	29	14	find	find	VERB
ejpam-5697	29	15	.	.	PUNCT
ejpam-5697	30	1	it	it	PRON
ejpam-5697	30	2	can	can	AUX
ejpam-5697	30	3	be	be	AUX
ejpam-5697	30	4	difficult	difficult	ADJ
ejpam-5697	30	5	to	to	PART
ejpam-5697	30	6	work	work	VERB
ejpam-5697	30	7	with	with	ADP
ejpam-5697	30	8	fractional	fractional	ADJ
ejpam-5697	30	9	calculus	calculus	NOUN
ejpam-5697	30	10	’s	’s	PART
ejpam-5697	30	11	non	non	ADJ
ejpam-5697	30	12	-	-	ADJ
ejpam-5697	30	13	singular	singular	ADJ
ejpam-5697	30	14	kernel	kernel	NOUN
ejpam-5697	30	15	.	.	PUNCT
ejpam-5697	31	1	by	by	ADP
ejpam-5697	31	2	expanding	expand	VERB
ejpam-5697	31	3	their	their	PRON
ejpam-5697	31	4	kernels	kernel	NOUN
ejpam-5697	31	5	,	,	PUNCT
ejpam-5697	31	6	the	the	DET
ejpam-5697	31	7	authors	author	NOUN
ejpam-5697	31	8	[	[	X
ejpam-5697	31	9	8	8	NUM
ejpam-5697	31	10	,	,	PUNCT
ejpam-5697	31	11	15	15	NUM
ejpam-5697	31	12	,	,	PUNCT
ejpam-5697	31	13	27	27	NUM
ejpam-5697	31	14	]	]	PUNCT
ejpam-5697	31	15	has	have	AUX
ejpam-5697	31	16	recently	recently	ADV
ejpam-5697	31	17	defined	define	VERB
ejpam-5697	31	18	the	the	DET
ejpam-5697	31	19	generalization	generalization	NOUN
ejpam-5697	31	20	of	of	ADP
ejpam-5697	31	21	fractional	fractional	ADJ
ejpam-5697	31	22	operators	operator	NOUN
ejpam-5697	31	23	.	.	PUNCT
ejpam-5697	32	1	samraiz	samraiz	PROPN
ejpam-5697	32	2	et	et	PROPN
ejpam-5697	32	3	al	al	PROPN
ejpam-5697	32	4	.	.	PROPN
ejpam-5697	32	5	described	describe	VERB
ejpam-5697	32	6	the	the	DET
ejpam-5697	32	7	(	(	PUNCT
ejpam-5697	32	8	k	k	X
ejpam-5697	32	9	,	,	PUNCT
ejpam-5697	32	10	s	s	NOUN
ejpam-5697	32	11	)	)	PUNCT
ejpam-5697	32	12	form	form	NOUN
ejpam-5697	32	13	of	of	ADP
ejpam-5697	32	14	fractional	fractional	ADJ
ejpam-5697	32	15	operators	operator	NOUN
ejpam-5697	32	16	with	with	ADP
ejpam-5697	32	17	a	a	DET
ejpam-5697	32	18	non	non	ADJ
ejpam-5697	32	19	-	-	ADJ
ejpam-5697	32	20	singular	singular	ADJ
ejpam-5697	32	21	kernel	kernel	NOUN
ejpam-5697	32	22	and	and	CCONJ
ejpam-5697	32	23	their	their	PRON
ejpam-5697	32	24	physics	physics	NOUN
ejpam-5697	32	25	applications	application	NOUN
ejpam-5697	32	26	in	in	ADP
ejpam-5697	32	27	[	[	X
ejpam-5697	32	28	27	27	NUM
ejpam-5697	32	29	]	]	PUNCT
ejpam-5697	32	30	.	.	PUNCT
ejpam-5697	33	1	they	they	PRON
ejpam-5697	33	2	used	use	VERB
ejpam-5697	33	3	the	the	DET
ejpam-5697	33	4	(	(	PUNCT
ejpam-5697	33	5	k	k	X
ejpam-5697	33	6	,	,	PUNCT
ejpam-5697	33	7	s	s	NOUN
ejpam-5697	33	8	)	)	PUNCT
ejpam-5697	33	9	form	form	NOUN
ejpam-5697	33	10	of	of	ADP
ejpam-5697	33	11	fractional	fractional	ADJ
ejpam-5697	33	12	operators	operator	NOUN
ejpam-5697	33	13	to	to	PART
ejpam-5697	33	14	solve	solve	VERB
ejpam-5697	33	15	the	the	DET
ejpam-5697	33	16	cauchy	cauchy	ADJ
ejpam-5697	33	17	problems	problem	NOUN
ejpam-5697	33	18	after	after	ADP
ejpam-5697	33	19	proving	prove	VERB
ejpam-5697	33	20	them	they	PRON
ejpam-5697	33	21	.	.	PUNCT
ejpam-5697	34	1	the	the	DET
ejpam-5697	34	2	hilfer	hilfer	NOUN
ejpam-5697	34	3	-	-	PUNCT
ejpam-5697	34	4	prabhakar	prabhakar	NOUN
ejpam-5697	34	5	fractional	fractional	ADJ
ejpam-5697	34	6	derivative	derivative	NOUN
ejpam-5697	34	7	(	(	PUNCT
ejpam-5697	34	8	k	k	X
ejpam-5697	34	9	,	,	PUNCT
ejpam-5697	34	10	s	s	PART
ejpam-5697	34	11	)	)	PUNCT
ejpam-5697	34	12	was	be	AUX
ejpam-5697	34	13	introduced	introduce	VERB
ejpam-5697	34	14	by	by	ADP
ejpam-5697	34	15	samraiz	samraiz	PROPN
ejpam-5697	34	16	et	et	PROPN
ejpam-5697	34	17	al	al	PROPN
ejpam-5697	34	18	.	.	PUNCT
ejpam-5697	35	1	[	[	X
ejpam-5697	35	2	28	28	NUM
ejpam-5697	35	3	]	]	PUNCT
ejpam-5697	35	4	.	.	PUNCT
ejpam-5697	36	1	the	the	DET
ejpam-5697	36	2	weighted	weight	VERB
ejpam-5697	36	3	generalized	generalized	ADJ
ejpam-5697	36	4	form	form	NOUN
ejpam-5697	36	5	of	of	ADP
ejpam-5697	36	6	fractional	fractional	ADJ
ejpam-5697	36	7	operators	operator	NOUN
ejpam-5697	36	8	with	with	ADP
ejpam-5697	36	9	a	a	DET
ejpam-5697	36	10	non	non	ADJ
ejpam-5697	36	11	-	-	ADJ
ejpam-5697	36	12	singular	singular	ADJ
ejpam-5697	36	13	kernel	kernel	NOUN
ejpam-5697	36	14	associated	associate	VERB
ejpam-5697	36	15	with	with	ADP
ejpam-5697	36	16	mittag	mittag	ADJ
ejpam-5697	36	17	-	-	PUNCT
ejpam-5697	36	18	leffler	leffler	NOUN
ejpam-5697	36	19	(	(	PUNCT
ejpam-5697	36	20	m	m	NOUN
ejpam-5697	36	21	-	-	PUNCT
ejpam-5697	36	22	l	l	NOUN
ejpam-5697	36	23	)	)	PUNCT
ejpam-5697	36	24	function	function	NOUN
ejpam-5697	36	25	are	be	AUX
ejpam-5697	36	26	presented	present	VERB
ejpam-5697	36	27	by	by	ADP
ejpam-5697	36	28	[	[	X
ejpam-5697	36	29	25	25	NUM
ejpam-5697	36	30	,	,	PUNCT
ejpam-5697	36	31	29	29	NUM
ejpam-5697	36	32	]	]	PUNCT
ejpam-5697	36	33	.	.	PUNCT
ejpam-5697	37	1	these	these	DET
ejpam-5697	37	2	operators	operator	NOUN
ejpam-5697	37	3	are	be	AUX
ejpam-5697	37	4	used	use	VERB
ejpam-5697	37	5	to	to	PART
ejpam-5697	37	6	identify	identify	VERB
ejpam-5697	37	7	cauchy	cauchy	NOUN
ejpam-5697	37	8	problems	problem	NOUN
ejpam-5697	37	9	in	in	ADP
ejpam-5697	37	10	continuous	continuous	ADJ
ejpam-5697	37	11	time	time	NOUN
ejpam-5697	37	12	random	random	ADJ
ejpam-5697	37	13	walk	walk	NOUN
ejpam-5697	37	14	theory.by	theory.by	X
ejpam-5697	37	15	using	use	VERB
ejpam-5697	37	16	the	the	DET
ejpam-5697	37	17	multivariate	multivariate	NOUN
ejpam-5697	37	18	m	m	NOUN
ejpam-5697	37	19	-	-	ADJ
ejpam-5697	37	20	l	l	NOUN
ejpam-5697	37	21	function	function	NOUN
ejpam-5697	37	22	as	as	ADP
ejpam-5697	37	23	a	a	DET
ejpam-5697	37	24	non	non	ADJ
ejpam-5697	37	25	-	-	ADJ
ejpam-5697	37	26	singular	singular	ADJ
ejpam-5697	37	27	kernel	kernel	NOUN
ejpam-5697	37	28	,	,	PUNCT
ejpam-5697	37	29	the	the	DET
ejpam-5697	37	30	authors	author	NOUN
ejpam-5697	37	31	in	in	ADP
ejpam-5697	37	32	[	[	X
ejpam-5697	37	33	26	26	NUM
ejpam-5697	37	34	]	]	PUNCT
ejpam-5697	37	35	developed	develop	VERB
ejpam-5697	37	36	the	the	DET
ejpam-5697	37	37	generalized	generalized	ADJ
ejpam-5697	37	38	(	(	PUNCT
ejpam-5697	37	39	k	k	X
ejpam-5697	37	40	,	,	PUNCT
ejpam-5697	37	41	s	s	NOUN
ejpam-5697	37	42	)	)	PUNCT
ejpam-5697	37	43	fractional	fractional	ADJ
ejpam-5697	37	44	operators	operator	NOUN
ejpam-5697	37	45	.	.	PUNCT
ejpam-5697	38	1	to	to	PART
ejpam-5697	38	2	learn	learn	VERB
ejpam-5697	38	3	more	more	ADJ
ejpam-5697	38	4	about	about	ADP
ejpam-5697	38	5	the	the	DET
ejpam-5697	38	6	applications	application	NOUN
ejpam-5697	38	7	of	of	ADP
ejpam-5697	38	8	fractional	fractional	ADJ
ejpam-5697	38	9	operators	operator	NOUN
ejpam-5697	38	10	with	with	ADP
ejpam-5697	38	11	non	non	ADJ
ejpam-5697	38	12	-	-	ADJ
ejpam-5697	38	13	singular	singular	ADJ
ejpam-5697	38	14	kernels	kernel	NOUN
ejpam-5697	38	15	,	,	PUNCT
ejpam-5697	38	16	we	we	PRON
ejpam-5697	38	17	refer	refer	VERB
ejpam-5697	38	18	the	the	DET
ejpam-5697	38	19	interested	interested	ADJ
ejpam-5697	38	20	reader	reader	NOUN
ejpam-5697	38	21	to	to	ADP
ejpam-5697	38	22	[	[	X
ejpam-5697	38	23	4	4	NUM
ejpam-5697	38	24	,	,	PUNCT
ejpam-5697	38	25	5	5	NUM
ejpam-5697	38	26	,	,	PUNCT
ejpam-5697	38	27	10	10	NUM
ejpam-5697	38	28	,	,	PUNCT
ejpam-5697	38	29	14	14	NUM
ejpam-5697	38	30	,	,	PUNCT
ejpam-5697	38	31	23	23	NUM
ejpam-5697	38	32	,	,	PUNCT
ejpam-5697	38	33	30	30	NUM
ejpam-5697	38	34	,	,	PUNCT
ejpam-5697	38	35	31	31	NUM
ejpam-5697	38	36	]	]	PUNCT
ejpam-5697	38	37	.	.	PUNCT
ejpam-5697	39	1	2	2	X
ejpam-5697	39	2	.	.	X
ejpam-5697	39	3	preliminaries	preliminary	NOUN
ejpam-5697	39	4	let	let	VERB
ejpam-5697	39	5	’s	’s	NOUN
ejpam-5697	39	6	recall	recall	VERB
ejpam-5697	39	7	the	the	DET
ejpam-5697	39	8	following	follow	VERB
ejpam-5697	39	9	essential	essential	ADJ
ejpam-5697	39	10	definitions	definition	NOUN
ejpam-5697	39	11	.	.	PUNCT
ejpam-5697	40	1	the	the	DET
ejpam-5697	40	2	following	follow	VERB
ejpam-5697	40	3	are	be	AUX
ejpam-5697	40	4	the	the	DET
ejpam-5697	40	5	definitions	definition	NOUN
ejpam-5697	40	6	of	of	ADP
ejpam-5697	40	7	beta	beta	NOUN
ejpam-5697	40	8	and	and	CCONJ
ejpam-5697	40	9	gamma	gamma	NOUN
ejpam-5697	40	10	functions	function	NOUN
ejpam-5697	40	11	found	find	VERB
ejpam-5697	40	12	in	in	ADP
ejpam-5697	40	13	[	[	X
ejpam-5697	40	14	32	32	NUM
ejpam-5697	40	15	]	]	PUNCT
ejpam-5697	40	16	.	.	PUNCT
ejpam-5697	41	1	definition	definition	NOUN
ejpam-5697	41	2	1	1	NUM
ejpam-5697	41	3	.	.	PUNCT
ejpam-5697	42	1	we	we	PRON
ejpam-5697	42	2	begin	begin	VERB
ejpam-5697	42	3	with	with	ADP
ejpam-5697	42	4	the	the	DET
ejpam-5697	42	5	well	well	ADV
ejpam-5697	42	6	-	-	PUNCT
ejpam-5697	42	7	known	know	VERB
ejpam-5697	42	8	gamma	gamma	NOUN
ejpam-5697	42	9	function	function	NOUN
ejpam-5697	42	10	which	which	PRON
ejpam-5697	42	11	is	be	AUX
ejpam-5697	42	12	defined	define	VERB
ejpam-5697	42	13	by	by	ADP
ejpam-5697	42	14	γ(κ1	γ(κ1	NOUN
ejpam-5697	42	15	)	)	PUNCT
ejpam-5697	43	1	=	=	SYM
ejpam-5697	43	2	∞∫	∞∫	PROPN
ejpam-5697	43	3	0	0	PUNCT
ejpam-5697	43	4	uκ1−1e−udu	uκ1−1e−udu	ADJ
ejpam-5697	43	5	,	,	PUNCT
ejpam-5697	43	6	re(κ1	re(κ1	NOUN
ejpam-5697	43	7	)	)	PUNCT
ejpam-5697	43	8	>	>	X
ejpam-5697	43	9	0	0	X
ejpam-5697	43	10	.	.	PUNCT
ejpam-5697	43	11	definition	definition	NOUN
ejpam-5697	43	12	2	2	NUM
ejpam-5697	43	13	.	.	PUNCT
ejpam-5697	44	1	the	the	DET
ejpam-5697	44	2	well	well	ADV
ejpam-5697	44	3	-	-	PUNCT
ejpam-5697	44	4	known	know	VERB
ejpam-5697	44	5	beta	beta	NOUN
ejpam-5697	44	6	function	function	NOUN
ejpam-5697	44	7	b(κ1	b(κ1	NOUN
ejpam-5697	44	8	,	,	PUNCT
ejpam-5697	44	9	ζ1	ζ1	NOUN
ejpam-5697	44	10	)	)	PUNCT
ejpam-5697	44	11	can	can	AUX
ejpam-5697	44	12	be	be	AUX
ejpam-5697	44	13	defined	define	VERB
ejpam-5697	44	14	by	by	ADP
ejpam-5697	44	15	b(κ1	b(κ1	NOUN
ejpam-5697	44	16	,	,	PUNCT
ejpam-5697	44	17	ζ1	ζ1	NOUN
ejpam-5697	44	18	)	)	PUNCT
ejpam-5697	44	19	=	=	PUNCT
ejpam-5697	45	1	1∫	1∫	NUM
ejpam-5697	45	2	0	0	NUM
ejpam-5697	45	3	τκ1−1(1−	τκ1−1(1−	NOUN
ejpam-5697	45	4	τ)ζ1−1dτ	τ)ζ1−1dτ	NUM
ejpam-5697	45	5	,	,	PUNCT
ejpam-5697	45	6	r(κ1	r(κ1	NOUN
ejpam-5697	45	7	)	)	PUNCT
ejpam-5697	45	8	>	>	X
ejpam-5697	45	9	0	0	NUM
ejpam-5697	45	10	,	,	PUNCT
ejpam-5697	45	11	r(ζ1	r(ζ1	NOUN
ejpam-5697	45	12	)	)	PUNCT
ejpam-5697	45	13	>	>	SYM
ejpam-5697	45	14	0	0	NUM
ejpam-5697	45	15	gauhar	gauhar	PROPN
ejpam-5697	45	16	rahman	rahman	PROPN
ejpam-5697	45	17	et	et	PROPN
ejpam-5697	45	18	al	al	PROPN
ejpam-5697	45	19	.	.	PUNCT
ejpam-5697	45	20	/	/	SYM
ejpam-5697	45	21	eur	eur	PROPN
ejpam-5697	45	22	.	.	PUNCT
ejpam-5697	46	1	j.	j.	PROPN
ejpam-5697	46	2	pure	pure	PROPN
ejpam-5697	46	3	appl	appl	PROPN
ejpam-5697	46	4	.	.	PROPN
ejpam-5697	46	5	math	math	PROPN
ejpam-5697	46	6	,	,	PUNCT
ejpam-5697	46	7	18	18	NUM
ejpam-5697	46	8	(	(	PUNCT
ejpam-5697	46	9	1	1	NUM
ejpam-5697	46	10	)	)	PUNCT
ejpam-5697	46	11	(	(	PUNCT
ejpam-5697	46	12	2025	2025	NUM
ejpam-5697	46	13	)	)	PUNCT
ejpam-5697	46	14	,	,	PUNCT
ejpam-5697	46	15	5697	5697	NUM
ejpam-5697	46	16	3	3	NUM
ejpam-5697	46	17	of	of	ADP
ejpam-5697	46	18	26	26	NUM
ejpam-5697	46	19	and	and	CCONJ
ejpam-5697	46	20	its	its	PRON
ejpam-5697	46	21	relation	relation	NOUN
ejpam-5697	46	22	with	with	ADP
ejpam-5697	46	23	γ	γ	NOUN
ejpam-5697	46	24	function	function	NOUN
ejpam-5697	46	25	is	be	AUX
ejpam-5697	46	26	given	give	VERB
ejpam-5697	46	27	by	by	ADP
ejpam-5697	46	28	b(κ1	b(κ1	NOUN
ejpam-5697	46	29	,	,	PUNCT
ejpam-5697	46	30	ζ1	ζ1	NOUN
ejpam-5697	46	31	)	)	PUNCT
ejpam-5697	46	32	=	=	SYM
ejpam-5697	46	33	γ(κ1)γ(ζ1	γ(κ1)γ(ζ1	PROPN
ejpam-5697	46	34	)	)	PUNCT
ejpam-5697	46	35	γ(κ1	γ(κ1	NOUN
ejpam-5697	46	36	+	+	CCONJ
ejpam-5697	46	37	ζ1	ζ1	NOUN
ejpam-5697	46	38	)	)	PUNCT
ejpam-5697	46	39	.	.	PUNCT
ejpam-5697	47	1	definition	definition	NOUN
ejpam-5697	47	2	3	3	NUM
ejpam-5697	47	3	.	.	PUNCT
ejpam-5697	48	1	the	the	DET
ejpam-5697	48	2	power	power	NOUN
ejpam-5697	48	3	m	m	PROPN
ejpam-5697	48	4	-	-	ADJ
ejpam-5697	48	5	l	l	NOUN
ejpam-5697	48	6	function	function	NOUN
ejpam-5697	48	7	is	be	AUX
ejpam-5697	48	8	recently	recently	ADV
ejpam-5697	48	9	introduced	introduce	VERB
ejpam-5697	48	10	by	by	ADP
ejpam-5697	48	11	lotfi	lotfi	PROPN
ejpam-5697	48	12	et	et	PROPN
ejpam-5697	48	13	al	al	PROPN
ejpam-5697	48	14	.	.	PUNCT
ejpam-5697	49	1	[	[	X
ejpam-5697	49	2	11	11	NUM
ejpam-5697	49	3	]	]	PUNCT
ejpam-5697	49	4	as	as	SCONJ
ejpam-5697	49	5	follows	follow	VERB
ejpam-5697	49	6	:	:	PUNCT
ejpam-5697	49	7	peϱ1,κ1(ϱ	peϱ1,κ1(ϱ	X
ejpam-5697	49	8	)	)	PUNCT
ejpam-5697	50	1	=	=	PUNCT
ejpam-5697	51	1	∞∑	∞∑	NUM
ejpam-5697	51	2	n=0	n=0	NUM
ejpam-5697	51	3	(	(	PUNCT
ejpam-5697	51	4	ϱ	ϱ	PROPN
ejpam-5697	51	5	ln	ln	ADJ
ejpam-5697	51	6	p)n	p)n	NOUN
ejpam-5697	51	7	γ(ϱ1n+	γ(ϱ1n+	PROPN
ejpam-5697	51	8	κ1	κ1	NOUN
ejpam-5697	51	9	)	)	PUNCT
ejpam-5697	51	10	,	,	PUNCT
ejpam-5697	51	11	(	(	PUNCT
ejpam-5697	51	12	1	1	X
ejpam-5697	51	13	)	)	PUNCT
ejpam-5697	51	14	where	where	SCONJ
ejpam-5697	51	15	ϱ	ϱ	ADP
ejpam-5697	51	16	∈	∈	PROPN
ejpam-5697	51	17	c	c	X
ejpam-5697	51	18	,	,	PUNCT
ejpam-5697	51	19	p	p	X
ejpam-5697	51	20	>	>	X
ejpam-5697	51	21	1	1	NUM
ejpam-5697	51	22	,	,	PUNCT
ejpam-5697	51	23	ℜ(κ	ℜ(κ	NOUN
ejpam-5697	51	24	)	)	PUNCT
ejpam-5697	51	25	>	>	X
ejpam-5697	51	26	0	0	PUNCT
ejpam-5697	51	27	and	and	CCONJ
ejpam-5697	51	28	ℜ(ϱ	ℜ(ϱ	NOUN
ejpam-5697	51	29	)	)	PUNCT
ejpam-5697	51	30	>	>	X
ejpam-5697	51	31	0	0	X
ejpam-5697	51	32	.	.	PUNCT
ejpam-5697	51	33	remark	remark	PROPN
ejpam-5697	51	34	1	1	NUM
ejpam-5697	51	35	.	.	PUNCT
ejpam-5697	52	1	the	the	DET
ejpam-5697	52	2	following	follow	VERB
ejpam-5697	52	3	are	be	AUX
ejpam-5697	52	4	the	the	DET
ejpam-5697	52	5	special	special	ADJ
ejpam-5697	52	6	cases	case	NOUN
ejpam-5697	52	7	of	of	ADP
ejpam-5697	52	8	power	power	NOUN
ejpam-5697	52	9	m	m	PROPN
ejpam-5697	52	10	-	-	ADJ
ejpam-5697	52	11	l	l	NOUN
ejpam-5697	52	12	function	function	NOUN
ejpam-5697	52	13	:	:	PUNCT
ejpam-5697	52	14	i.	i.	NOUN
ejpam-5697	52	15	if	if	SCONJ
ejpam-5697	52	16	we	we	PRON
ejpam-5697	52	17	take	take	VERB
ejpam-5697	52	18	ϱ	ϱ	NOUN
ejpam-5697	52	19	=	=	SYM
ejpam-5697	52	20	κ	κ	NOUN
ejpam-5697	52	21	=	=	SYM
ejpam-5697	52	22	1	1	NUM
ejpam-5697	52	23	and	and	CCONJ
ejpam-5697	52	24	p	p	X
ejpam-5697	52	25	=	=	SYM
ejpam-5697	52	26	e	e	NOUN
ejpam-5697	52	27	,	,	PUNCT
ejpam-5697	52	28	we	we	PRON
ejpam-5697	52	29	get	get	VERB
ejpam-5697	52	30	ee1,1(ϱ	ee1,1(ϱ	PRON
ejpam-5697	52	31	)	)	PUNCT
ejpam-5697	52	32	=	=	PUNCT
ejpam-5697	53	1	∞∑	∞∑	ADJ
ejpam-5697	53	2	n=0	n=0	NUM
ejpam-5697	53	3	ϱn	ϱn	ADP
ejpam-5697	53	4	γ(n+	γ(n+	NUM
ejpam-5697	53	5	1	1	NUM
ejpam-5697	53	6	)	)	PUNCT
ejpam-5697	53	7	=	=	NOUN
ejpam-5697	54	1	∞∑	∞∑	NUM
ejpam-5697	54	2	n=0	n=0	NUM
ejpam-5697	54	3	ϱn	ϱn	NOUN
ejpam-5697	54	4	n	n	NOUN
ejpam-5697	54	5	!	!	PUNCT
ejpam-5697	55	1	=	=	PUNCT
ejpam-5697	55	2	eϱ.	eϱ.	PRON
ejpam-5697	55	3	ii	ii	NOUN
ejpam-5697	55	4	.	.	PUNCT
ejpam-5697	56	1	if	if	SCONJ
ejpam-5697	56	2	we	we	PRON
ejpam-5697	56	3	take	take	VERB
ejpam-5697	56	4	κ	κ	NOUN
ejpam-5697	56	5	=	=	SYM
ejpam-5697	56	6	1	1	NUM
ejpam-5697	56	7	and	and	CCONJ
ejpam-5697	56	8	p	p	X
ejpam-5697	56	9	=	=	SYM
ejpam-5697	56	10	e	e	NOUN
ejpam-5697	56	11	,	,	PUNCT
ejpam-5697	56	12	we	we	PRON
ejpam-5697	56	13	get	get	VERB
ejpam-5697	56	14	eeϱ1,1(ϱ	eeϱ1,1(ϱ	PUNCT
ejpam-5697	56	15	)	)	PUNCT
ejpam-5697	57	1	=	=	PUNCT
ejpam-5697	58	1	∞∑	∞∑	NUM
ejpam-5697	58	2	n=0	n=0	NUM
ejpam-5697	58	3	ϱn	ϱn	ADP
ejpam-5697	58	4	γ(ϱ1n+	γ(ϱ1n+	PROPN
ejpam-5697	58	5	1	1	NUM
ejpam-5697	58	6	)	)	PUNCT
ejpam-5697	58	7	.	.	PUNCT
ejpam-5697	59	1	iii	iii	X
ejpam-5697	59	2	.	.	PUNCT
ejpam-5697	60	1	if	if	SCONJ
ejpam-5697	60	2	we	we	PRON
ejpam-5697	60	3	take	take	VERB
ejpam-5697	60	4	p	p	NOUN
ejpam-5697	60	5	=	=	SYM
ejpam-5697	60	6	e	e	NOUN
ejpam-5697	60	7	,	,	PUNCT
ejpam-5697	60	8	we	we	PRON
ejpam-5697	60	9	get	get	VERB
ejpam-5697	60	10	eeϱ1,κ1(ϱ	eeϱ1,κ1(ϱ	ADV
ejpam-5697	60	11	)	)	PUNCT
ejpam-5697	61	1	=	=	PUNCT
ejpam-5697	62	1	∞∑	∞∑	NUM
ejpam-5697	62	2	n=0	n=0	NUM
ejpam-5697	62	3	ϱn	ϱn	ADP
ejpam-5697	62	4	γ(ϱ1n+	γ(ϱ1n+	PROPN
ejpam-5697	62	5	κ1	κ1	NOUN
ejpam-5697	62	6	)	)	PUNCT
ejpam-5697	62	7	.	.	PUNCT
ejpam-5697	63	1	hölder	hölder	PROPN
ejpam-5697	63	2	’s	’s	PART
ejpam-5697	63	3	inequality	inequality	NOUN
ejpam-5697	63	4	was	be	AUX
ejpam-5697	63	5	first	first	ADV
ejpam-5697	63	6	derived	derive	VERB
ejpam-5697	63	7	by	by	ADP
ejpam-5697	63	8	leonard	leonard	PROPN
ejpam-5697	63	9	james	james	PROPN
ejpam-5697	63	10	rogers	rogers	PROPN
ejpam-5697	63	11	in	in	ADP
ejpam-5697	63	12	1888	1888	NUM
ejpam-5697	63	13	,	,	PUNCT
ejpam-5697	63	14	then	then	ADV
ejpam-5697	63	15	ludwig	ludwig	PROPN
ejpam-5697	63	16	otto	otto	PROPN
ejpam-5697	63	17	hölder	hölder	PROPN
ejpam-5697	63	18	presented	present	VERB
ejpam-5697	63	19	it	it	PRON
ejpam-5697	63	20	in	in	ADP
ejpam-5697	63	21	a	a	DET
ejpam-5697	63	22	different	different	ADJ
ejpam-5697	63	23	way	way	NOUN
ejpam-5697	63	24	in	in	ADP
ejpam-5697	63	25	1889	1889	NUM
ejpam-5697	63	26	.	.	PUNCT
ejpam-5697	64	1	the	the	DET
ejpam-5697	64	2	following	follow	VERB
ejpam-5697	64	3	definition	definition	NOUN
ejpam-5697	64	4	provides	provide	VERB
ejpam-5697	64	5	an	an	DET
ejpam-5697	64	6	explanation	explanation	NOUN
ejpam-5697	64	7	of	of	ADP
ejpam-5697	64	8	hölder	hölder	NOUN
ejpam-5697	64	9	inequality	inequality	NOUN
ejpam-5697	64	10	.	.	PUNCT
ejpam-5697	65	1	definition	definition	NOUN
ejpam-5697	65	2	4	4	NUM
ejpam-5697	65	3	.	.	PUNCT
ejpam-5697	66	1	[	[	X
ejpam-5697	66	2	6	6	NUM
ejpam-5697	66	3	]	]	PUNCT
ejpam-5697	66	4	for	for	ADP
ejpam-5697	66	5	a	a	DET
ejpam-5697	66	6	given	give	VERB
ejpam-5697	66	7	two	two	NUM
ejpam-5697	66	8	real	real	ADJ
ejpam-5697	66	9	numbers	number	NOUN
ejpam-5697	66	10	,	,	PUNCT
ejpam-5697	66	11	r1	r1	NOUN
ejpam-5697	66	12	and	and	CCONJ
ejpam-5697	66	13	s1	s1	NOUN
ejpam-5697	66	14	,	,	PUNCT
ejpam-5697	66	15	such	such	ADJ
ejpam-5697	66	16	that	that	SCONJ
ejpam-5697	66	17	r1	r1	NOUN
ejpam-5697	66	18	,	,	PUNCT
ejpam-5697	66	19	s1	s1	PROPN
ejpam-5697	66	20	>	>	X
ejpam-5697	66	21	1	1	NUM
ejpam-5697	66	22	and	and	CCONJ
ejpam-5697	66	23	1	1	NUM
ejpam-5697	66	24	r1	r1	NOUN
ejpam-5697	66	25	+	+	CCONJ
ejpam-5697	66	26	1	1	NUM
ejpam-5697	66	27	s1	s1	NOUN
ejpam-5697	66	28	=	=	SYM
ejpam-5697	66	29	1	1	NUM
ejpam-5697	66	30	,	,	PUNCT
ejpam-5697	66	31	the	the	DET
ejpam-5697	66	32	hölder	hölder	NOUN
ejpam-5697	66	33	integral	integral	ADJ
ejpam-5697	66	34	inequality	inequality	NOUN
ejpam-5697	66	35	is	be	AUX
ejpam-5697	66	36	stated	state	VERB
ejpam-5697	66	37	by	by	ADP
ejpam-5697	66	38	u∫	u∫	NOUN
ejpam-5697	66	39	v	v	ADP
ejpam-5697	66	40	|f1(ϱ)g1(ϱ)|dϱ	|f1(ϱ)g1(ϱ)|dϱ	PROPN
ejpam-5697	66	41	≤	≤	NOUN
ejpam-5697	66	42			PROPN
ejpam-5697	66	43	u∫	u∫	NOUN
ejpam-5697	66	44	v	v	NOUN
ejpam-5697	66	45	|f1(ϱ)|r1dϱ	|f1(ϱ)|r1dϱ	PUNCT
ejpam-5697	66	46			PROPN
ejpam-5697	66	47	1	1	NUM
ejpam-5697	66	48	r1	r1	NOUN
ejpam-5697	66	49			PROPN
ejpam-5697	66	50	u∫	u∫	NOUN
ejpam-5697	66	51	v	v	NOUN
ejpam-5697	66	52	|g1(ϱ)|s1dϱ	|g1(ϱ)|s1dϱ	PUNCT
ejpam-5697	66	53			PROPN
ejpam-5697	66	54	1	1	NUM
ejpam-5697	66	55	s1	s1	NOUN
ejpam-5697	66	56	,	,	PUNCT
ejpam-5697	66	57	where	where	SCONJ
ejpam-5697	66	58	f1	f1	NOUN
ejpam-5697	66	59	,	,	PUNCT
ejpam-5697	66	60	g1	g1	PROPN
ejpam-5697	66	61	∈	∈	PROPN
ejpam-5697	66	62	c1[u	c1[u	PROPN
ejpam-5697	66	63	,	,	PUNCT
ejpam-5697	66	64	v	v	NOUN
ejpam-5697	66	65	]	]	PUNCT
ejpam-5697	66	66	.	.	PUNCT
ejpam-5697	67	1	the	the	DET
ejpam-5697	67	2	lebesgue	lebesgue	ADJ
ejpam-5697	67	3	measurable	measurable	ADJ
ejpam-5697	67	4	functions	function	NOUN
ejpam-5697	67	5	with	with	ADP
ejpam-5697	67	6	norm	norm	NOUN
ejpam-5697	67	7	are	be	AUX
ejpam-5697	67	8	defined	define	VERB
ejpam-5697	67	9	as	as	SCONJ
ejpam-5697	67	10	follows	follow	VERB
ejpam-5697	67	11	by	by	ADP
ejpam-5697	67	12	kilbas	kilbas	PROPN
ejpam-5697	67	13	et	et	PROPN
ejpam-5697	67	14	al	al	PROPN
ejpam-5697	67	15	.	.	PUNCT
ejpam-5697	68	1	in	in	ADP
ejpam-5697	68	2	[	[	X
ejpam-5697	68	3	9	9	NUM
ejpam-5697	68	4	]	]	PUNCT
ejpam-5697	68	5	.	.	PUNCT
ejpam-5697	69	1	definition	definition	NOUN
ejpam-5697	69	2	5	5	NUM
ejpam-5697	69	3	.	.	PUNCT
ejpam-5697	69	4	consider	consider	VERB
ejpam-5697	69	5	a	a	DET
ejpam-5697	69	6	function	function	NOUN
ejpam-5697	69	7	g	g	NOUN
ejpam-5697	69	8	that	that	PRON
ejpam-5697	69	9	is	be	AUX
ejpam-5697	69	10	defined	define	VERB
ejpam-5697	69	11	on	on	ADP
ejpam-5697	69	12	[	[	X
ejpam-5697	69	13	c	c	X
ejpam-5697	69	14	,	,	PUNCT
ejpam-5697	69	15	d	d	NOUN
ejpam-5697	69	16	]	]	X
ejpam-5697	69	17	.	.	PUNCT
ejpam-5697	70	1	the	the	DET
ejpam-5697	70	2	lebesgue	lebesgue	ADJ
ejpam-5697	70	3	measurable	measurable	ADJ
ejpam-5697	70	4	functions	function	NOUN
ejpam-5697	70	5	space	space	NOUN
ejpam-5697	70	6	χq(c	χq(c	ADJ
ejpam-5697	70	7	,	,	PUNCT
ejpam-5697	70	8	d	d	NOUN
ejpam-5697	70	9	)	)	PUNCT
ejpam-5697	70	10	,	,	PUNCT
ejpam-5697	70	11	1	1	NUM
ejpam-5697	70	12	≤	≤	NUM
ejpam-5697	70	13	q	q	ADJ
ejpam-5697	70	14	≤	≤	NUM
ejpam-5697	70	15	∞	∞	PROPN
ejpam-5697	70	16	,	,	PUNCT
ejpam-5697	70	17	for	for	ADP
ejpam-5697	70	18	which	which	PRON
ejpam-5697	70	19	∥	∥	NUM
ejpam-5697	70	20	ψ	ψ	X
ejpam-5697	70	21	∥χq<∞	∥χq<∞	PROPN
ejpam-5697	70	22	,	,	PUNCT
ejpam-5697	70	23	i.e.	i.e.	X
ejpam-5697	70	24	,	,	PUNCT
ejpam-5697	70	25	∥	∥	PROPN
ejpam-5697	70	26	ψ	ψ	SYM
ejpam-5697	70	27	∥χq=	∥χq=	X
ejpam-5697	71	1	[	[	X
ejpam-5697	71	2	∫	∫	X
ejpam-5697	71	3	s	s	PART
ejpam-5697	71	4	r	r	NOUN
ejpam-5697	71	5	|	|	ADV
ejpam-5697	71	6	ψ(ζ	ψ(ζ	NOUN
ejpam-5697	71	7	)	)	PUNCT
ejpam-5697	71	8	|q	|q	NOUN
ejpam-5697	71	9	dζ	dζ	PROPN
ejpam-5697	71	10	]	]	PUNCT
ejpam-5697	71	11	1	1	NUM
ejpam-5697	71	12	q	q	NOUN
ejpam-5697	71	13	,	,	PUNCT
ejpam-5697	71	14	1	1	NUM
ejpam-5697	71	15	≤	≤	NUM
ejpam-5697	71	16	q	q	NOUN
ejpam-5697	71	17	<	<	X
ejpam-5697	71	18	∞	∞	PROPN
ejpam-5697	71	19	,	,	PUNCT
ejpam-5697	71	20	∥	∥	X
ejpam-5697	71	21	ψ	ψ	X
ejpam-5697	71	22	∥χ∞=	∥χ∞=	PUNCT
ejpam-5697	71	23	ess	ess	NOUN
ejpam-5697	71	24	supc≤t≤d	supc≤t≤d	VERB
ejpam-5697	71	25	|	|	ADV
ejpam-5697	71	26	ψ(ζ	ψ(ζ	NOUN
ejpam-5697	71	27	)	)	PUNCT
ejpam-5697	72	1	|<∞.	|<∞.	PROPN
ejpam-5697	72	2	gauhar	gauhar	NOUN
ejpam-5697	72	3	rahman	rahman	PROPN
ejpam-5697	72	4	et	et	PROPN
ejpam-5697	72	5	al	al	PROPN
ejpam-5697	72	6	.	.	PUNCT
ejpam-5697	72	7	/	/	SYM
ejpam-5697	72	8	eur	eur	PROPN
ejpam-5697	72	9	.	.	PUNCT
ejpam-5697	73	1	j.	j.	PROPN
ejpam-5697	73	2	pure	pure	PROPN
ejpam-5697	73	3	appl	appl	PROPN
ejpam-5697	73	4	.	.	PROPN
ejpam-5697	73	5	math	math	PROPN
ejpam-5697	73	6	,	,	PUNCT
ejpam-5697	73	7	18	18	NUM
ejpam-5697	73	8	(	(	PUNCT
ejpam-5697	73	9	1	1	NUM
ejpam-5697	73	10	)	)	PUNCT
ejpam-5697	73	11	(	(	PUNCT
ejpam-5697	73	12	2025	2025	NUM
ejpam-5697	73	13	)	)	PUNCT
ejpam-5697	73	14	,	,	PUNCT
ejpam-5697	73	15	5697	5697	NUM
ejpam-5697	73	16	4	4	NUM
ejpam-5697	73	17	of	of	ADP
ejpam-5697	73	18	26	26	NUM
ejpam-5697	73	19	fractional	fractional	ADJ
ejpam-5697	73	20	calculus	calculus	NOUN
ejpam-5697	73	21	theory	theory	NOUN
ejpam-5697	73	22	still	still	ADV
ejpam-5697	73	23	has	have	VERB
ejpam-5697	73	24	many	many	ADJ
ejpam-5697	73	25	remaining	remain	VERB
ejpam-5697	73	26	challenges	challenge	NOUN
ejpam-5697	73	27	since	since	SCONJ
ejpam-5697	73	28	the	the	DET
ejpam-5697	73	29	riemann	riemann	PROPN
ejpam-5697	73	30	and	and	CCONJ
ejpam-5697	73	31	caputo	caputo	PROPN
ejpam-5697	73	32	fractional	fractional	PROPN
ejpam-5697	73	33	operators	operator	NOUN
ejpam-5697	73	34	are	be	AUX
ejpam-5697	73	35	not	not	PART
ejpam-5697	73	36	enough	enough	ADJ
ejpam-5697	73	37	to	to	PART
ejpam-5697	73	38	solve	solve	VERB
ejpam-5697	73	39	theoretical	theoretical	ADJ
ejpam-5697	73	40	and	and	CCONJ
ejpam-5697	73	41	physical	physical	ADJ
ejpam-5697	73	42	problems	problem	NOUN
ejpam-5697	73	43	.	.	PUNCT
ejpam-5697	74	1	the	the	DET
ejpam-5697	74	2	theory	theory	NOUN
ejpam-5697	74	3	still	still	ADV
ejpam-5697	74	4	has	have	VERB
ejpam-5697	74	5	a	a	DET
ejpam-5697	74	6	lot	lot	NOUN
ejpam-5697	74	7	of	of	ADP
ejpam-5697	74	8	challenges	challenge	NOUN
ejpam-5697	74	9	,	,	PUNCT
ejpam-5697	74	10	even	even	ADV
ejpam-5697	74	11	though	though	SCONJ
ejpam-5697	74	12	researchers	researcher	NOUN
ejpam-5697	74	13	have	have	AUX
ejpam-5697	74	14	defined	define	VERB
ejpam-5697	74	15	their	their	PRON
ejpam-5697	74	16	own	own	ADJ
ejpam-5697	74	17	operators	operator	NOUN
ejpam-5697	74	18	to	to	PART
ejpam-5697	74	19	fill	fill	VERB
ejpam-5697	74	20	in	in	ADP
ejpam-5697	74	21	these	these	DET
ejpam-5697	74	22	gaps	gap	NOUN
ejpam-5697	74	23	.	.	PUNCT
ejpam-5697	75	1	atangana	atangana	PROPN
ejpam-5697	75	2	-	-	PUNCT
ejpam-5697	75	3	baleanu	baleanu	PROPN
ejpam-5697	75	4	developed	develop	VERB
ejpam-5697	75	5	the	the	DET
ejpam-5697	75	6	fractional	fractional	ADJ
ejpam-5697	75	7	operators	operator	NOUN
ejpam-5697	75	8	to	to	PART
ejpam-5697	75	9	fill	fill	VERB
ejpam-5697	75	10	in	in	ADP
ejpam-5697	75	11	these	these	DET
ejpam-5697	75	12	gaps	gap	NOUN
ejpam-5697	75	13	.	.	PUNCT
ejpam-5697	76	1	these	these	DET
ejpam-5697	76	2	operators	operator	NOUN
ejpam-5697	76	3	are	be	AUX
ejpam-5697	76	4	useful	useful	ADJ
ejpam-5697	76	5	in	in	ADP
ejpam-5697	76	6	many	many	ADJ
ejpam-5697	76	7	theoretical	theoretical	ADJ
ejpam-5697	76	8	and	and	CCONJ
ejpam-5697	76	9	physical	physical	ADJ
ejpam-5697	76	10	applications	application	NOUN
ejpam-5697	76	11	,	,	PUNCT
ejpam-5697	76	12	both	both	CCONJ
ejpam-5697	76	13	in	in	ADP
ejpam-5697	76	14	the	the	DET
ejpam-5697	76	15	riemann	riemann	PROPN
ejpam-5697	76	16	and	and	CCONJ
ejpam-5697	76	17	caputo	caputo	PROPN
ejpam-5697	76	18	senses	sense	NOUN
ejpam-5697	76	19	.	.	PUNCT
ejpam-5697	77	1	for	for	ADP
ejpam-5697	77	2	example	example	NOUN
ejpam-5697	77	3	,	,	PUNCT
ejpam-5697	77	4	panda	panda	NOUN
ejpam-5697	77	5	et	et	PROPN
ejpam-5697	77	6	al	al	PROPN
ejpam-5697	77	7	.	.	PUNCT
ejpam-5697	78	1	[	[	X
ejpam-5697	78	2	20	20	NUM
ejpam-5697	78	3	]	]	PUNCT
ejpam-5697	78	4	investigated	investigate	VERB
ejpam-5697	78	5	the	the	DET
ejpam-5697	78	6	willis	willis	PROPN
ejpam-5697	78	7	aneurysm	aneurysm	NOUN
ejpam-5697	78	8	system	system	NOUN
ejpam-5697	78	9	and	and	CCONJ
ejpam-5697	78	10	solved	solve	VERB
ejpam-5697	78	11	a	a	DET
ejpam-5697	78	12	nonlinear	nonlinear	ADJ
ejpam-5697	78	13	singularity	singularity	NOUN
ejpam-5697	78	14	perturbed	perturb	VERB
ejpam-5697	78	15	boundary	boundary	ADJ
ejpam-5697	78	16	value	value	NOUN
ejpam-5697	78	17	problem	problem	NOUN
ejpam-5697	78	18	using	use	VERB
ejpam-5697	78	19	the	the	DET
ejpam-5697	78	20	atangana	atangana	PROPN
ejpam-5697	78	21	-	-	PUNCT
ejpam-5697	78	22	baleanu	baleanu	NOUN
ejpam-5697	78	23	operator	operator	NOUN
ejpam-5697	78	24	.	.	PUNCT
ejpam-5697	79	1	the	the	DET
ejpam-5697	79	2	investigation	investigation	NOUN
ejpam-5697	79	3	of	of	ADP
ejpam-5697	79	4	covid-19	covid-19	PROPN
ejpam-5697	79	5	prevalence	prevalence	NOUN
ejpam-5697	79	6	in	in	ADP
ejpam-5697	79	7	france	france	PROPN
ejpam-5697	79	8	,	,	PUNCT
ejpam-5697	79	9	italy	italy	PROPN
ejpam-5697	79	10	,	,	PUNCT
ejpam-5697	79	11	and	and	CCONJ
ejpam-5697	79	12	the	the	DET
ejpam-5697	79	13	us	us	PROPN
ejpam-5697	79	14	by	by	ADP
ejpam-5697	79	15	panda	panda	NOUN
ejpam-5697	79	16	et	et	PROPN
ejpam-5697	79	17	al	al	PROPN
ejpam-5697	79	18	.	.	PUNCT
ejpam-5697	80	1	in	in	ADP
ejpam-5697	80	2	[	[	X
ejpam-5697	80	3	17	17	NUM
ejpam-5697	80	4	]	]	PUNCT
ejpam-5697	80	5	is	be	AUX
ejpam-5697	80	6	one	one	NUM
ejpam-5697	80	7	of	of	ADP
ejpam-5697	80	8	the	the	DET
ejpam-5697	80	9	other	other	ADJ
ejpam-5697	80	10	uses	use	NOUN
ejpam-5697	80	11	of	of	ADP
ejpam-5697	80	12	the	the	DET
ejpam-5697	80	13	atanganabaleanu	atanganabaleanu	NOUN
ejpam-5697	80	14	operators	operator	NOUN
ejpam-5697	80	15	.	.	PUNCT
ejpam-5697	81	1	he	he	PRON
ejpam-5697	81	2	introduced	introduce	VERB
ejpam-5697	81	3	new	new	ADJ
ejpam-5697	81	4	results	result	NOUN
ejpam-5697	81	5	on	on	ADP
ejpam-5697	81	6	the	the	DET
ejpam-5697	81	7	existence	existence	NOUN
ejpam-5697	81	8	and	and	CCONJ
ejpam-5697	81	9	uniqueness	uniqueness	NOUN
ejpam-5697	81	10	of	of	ADP
ejpam-5697	81	11	the	the	DET
ejpam-5697	81	12	2019ncov	2019ncov	NUM
ejpam-5697	81	13	models	model	NOUN
ejpam-5697	81	14	with	with	ADP
ejpam-5697	81	15	respect	respect	NOUN
ejpam-5697	81	16	to	to	ADP
ejpam-5697	81	17	fractional	fractional	ADJ
ejpam-5697	81	18	and	and	CCONJ
ejpam-5697	81	19	fractal	fractal	ADJ
ejpam-5697	81	20	-	-	PUNCT
ejpam-5697	81	21	fractional	fractional	ADJ
ejpam-5697	81	22	operator	operator	NOUN
ejpam-5697	81	23	-	-	PUNCT
ejpam-5697	81	24	based	base	VERB
ejpam-5697	81	25	solutions	solution	NOUN
ejpam-5697	81	26	.	.	PUNCT
ejpam-5697	82	1	moreover	moreover	ADV
ejpam-5697	82	2	,	,	PUNCT
ejpam-5697	82	3	the	the	DET
ejpam-5697	82	4	solutions	solution	NOUN
ejpam-5697	82	5	to	to	ADP
ejpam-5697	82	6	the	the	DET
ejpam-5697	82	7	atangana	atangana	PROPN
ejpam-5697	82	8	-	-	PUNCT
ejpam-5697	82	9	baleanu	baleanu	ADJ
ejpam-5697	82	10	fractional	fractional	ADJ
ejpam-5697	82	11	equations	equation	NOUN
ejpam-5697	82	12	,	,	PUNCT
ejpam-5697	82	13	the	the	DET
ejpam-5697	82	14	complex	complex	NOUN
ejpam-5697	82	15	valued	value	VERB
ejpam-5697	82	16	atangana	atangana	PROPN
ejpam-5697	82	17	-	-	PUNCT
ejpam-5697	82	18	baleanu	baleanu	NOUN
ejpam-5697	82	19	operator	operator	NOUN
ejpam-5697	82	20	,	,	PUNCT
ejpam-5697	82	21	and	and	CCONJ
ejpam-5697	82	22	the	the	DET
ejpam-5697	82	23	lp	lp	ADJ
ejpam-5697	82	24	-	-	PUNCT
ejpam-5697	82	25	fredholm	fredholm	ADJ
ejpam-5697	82	26	integral	integral	ADJ
ejpam-5697	82	27	equations	equation	NOUN
ejpam-5697	82	28	are	be	AUX
ejpam-5697	82	29	examined	examine	VERB
ejpam-5697	82	30	in	in	ADP
ejpam-5697	82	31	[	[	X
ejpam-5697	82	32	18	18	NUM
ejpam-5697	82	33	]	]	PUNCT
ejpam-5697	82	34	and	and	CCONJ
ejpam-5697	82	35	[	[	X
ejpam-5697	82	36	19	19	NUM
ejpam-5697	82	37	]	]	PUNCT
ejpam-5697	82	38	.	.	PUNCT
ejpam-5697	83	1	using	use	VERB
ejpam-5697	83	2	this	this	DET
ejpam-5697	83	3	method	method	NOUN
ejpam-5697	83	4	,	,	PUNCT
ejpam-5697	83	5	fractional	fractional	ADJ
ejpam-5697	83	6	operators	operator	NOUN
ejpam-5697	83	7	in	in	ADP
ejpam-5697	83	8	the	the	DET
ejpam-5697	83	9	caputo	caputo	PROPN
ejpam-5697	83	10	sense	sense	NOUN
ejpam-5697	83	11	take	take	VERB
ejpam-5697	83	12	on	on	ADP
ejpam-5697	83	13	a	a	DET
ejpam-5697	83	14	new	new	ADJ
ejpam-5697	83	15	shape	shape	NOUN
ejpam-5697	83	16	.	.	PUNCT
ejpam-5697	84	1	definition	definition	NOUN
ejpam-5697	84	2	6	6	NUM
ejpam-5697	84	3	.	.	PUNCT
ejpam-5697	85	1	[	[	X
ejpam-5697	85	2	2	2	X
ejpam-5697	85	3	]	]	PUNCT
ejpam-5697	85	4	if	if	SCONJ
ejpam-5697	85	5	g′	g′	PROPN
ejpam-5697	85	6	∈	∈	PROPN
ejpam-5697	85	7	h1(0	h1(0	PROPN
ejpam-5697	85	8	,	,	PUNCT
ejpam-5697	85	9	t	t	PROPN
ejpam-5697	85	10	)	)	PUNCT
ejpam-5697	85	11	,	,	PUNCT
ejpam-5697	85	12	then	then	ADV
ejpam-5697	85	13	the	the	DET
ejpam-5697	85	14	atangana	atangana	PROPN
ejpam-5697	85	15	-	-	PUNCT
ejpam-5697	85	16	baleanu	baleanu	ADJ
ejpam-5697	85	17	fractional	fractional	ADJ
ejpam-5697	85	18	operator	operator	NOUN
ejpam-5697	85	19	in	in	ADP
ejpam-5697	85	20	caputo	caputo	PROPN
ejpam-5697	85	21	sense	sense	NOUN
ejpam-5697	85	22	of	of	ADP
ejpam-5697	85	23	order	order	NOUN
ejpam-5697	85	24	0	0	PUNCT
ejpam-5697	85	25	<	<	X
ejpam-5697	85	26	δ	δ	X
ejpam-5697	85	27	<	<	X
ejpam-5697	85	28	1	1	NUM
ejpam-5697	85	29	is	be	AUX
ejpam-5697	85	30	defined	define	VERB
ejpam-5697	85	31	as	as	SCONJ
ejpam-5697	85	32	follows	follow	VERB
ejpam-5697	85	33	:	:	PUNCT
ejpam-5697	85	34	abcd	abcd	PROPN
ejpam-5697	85	35	δ	δ	PROPN
ejpam-5697	85	36	0g(ξ	0g(ξ	PROPN
ejpam-5697	85	37	)	)	PUNCT
ejpam-5697	86	1	=	=	SYM
ejpam-5697	86	2	r(δ	r(δ	PROPN
ejpam-5697	86	3	)	)	PUNCT
ejpam-5697	86	4	1−	1−	NUM
ejpam-5697	87	1	δ	δ	NOUN
ejpam-5697	87	2	∫	∫	PROPN
ejpam-5697	88	1	ξ	ξ	X
ejpam-5697	88	2	0	0	NUM
ejpam-5697	88	3	eδ	eδ	NOUN
ejpam-5697	88	4	(	(	PUNCT
ejpam-5697	88	5	−	−	PROPN
ejpam-5697	88	6	ωδ	ωδ	X
ejpam-5697	88	7	(	(	PUNCT
ejpam-5697	88	8	ξ	ξ	PROPN
ejpam-5697	88	9	−	−	PROPN
ejpam-5697	88	10	ζ	ζ	NOUN
ejpam-5697	88	11	)	)	PUNCT
ejpam-5697	88	12	δ	δ	PROPN
ejpam-5697	88	13	)	)	PUNCT
ejpam-5697	88	14	g′(ζ)dζ	g′(ζ)dζ	PROPN
ejpam-5697	88	15	,	,	PUNCT
ejpam-5697	89	1	ζ	ζ	X
ejpam-5697	89	2	≥	≥	NOUN
ejpam-5697	89	3	0	0	NUM
ejpam-5697	89	4	and	and	CCONJ
ejpam-5697	89	5	its	its	PRON
ejpam-5697	89	6	associated	associated	ADJ
ejpam-5697	89	7	integral	integral	ADJ
ejpam-5697	89	8	operator	operator	NOUN
ejpam-5697	89	9	is	be	AUX
ejpam-5697	89	10	provided	provide	VERB
ejpam-5697	89	11	by	by	ADP
ejpam-5697	89	12	abci	abci	PROPN
ejpam-5697	89	13	δ	δ	PROPN
ejpam-5697	89	14	0g(ξ	0g(ξ	PROPN
ejpam-5697	89	15	)	)	PUNCT
ejpam-5697	90	1	=	=	SYM
ejpam-5697	90	2	1−	1−	NUM
ejpam-5697	90	3	δ	δ	PROPN
ejpam-5697	90	4	r(δ	r(δ	PROPN
ejpam-5697	90	5	)	)	PUNCT
ejpam-5697	90	6	g(ξ	g(ξ	PROPN
ejpam-5697	90	7	)	)	PUNCT
ejpam-5697	90	8	+	+	CCONJ
ejpam-5697	90	9	r(δ	r(δ	NOUN
ejpam-5697	90	10	)	)	PUNCT
ejpam-5697	91	1	1−	1−	NUM
ejpam-5697	91	2	δ	δ	NOUN
ejpam-5697	91	3	∫	∫	PROPN
ejpam-5697	91	4	ξ	ξ	X
ejpam-5697	91	5	0	0	PUNCT
ejpam-5697	91	6	(	(	PUNCT
ejpam-5697	91	7	ξ	ξ	PROPN
ejpam-5697	91	8	−	−	PROPN
ejpam-5697	91	9	ζ	ζ	NOUN
ejpam-5697	91	10	)	)	PUNCT
ejpam-5697	91	11	δ	δ	PROPN
ejpam-5697	91	12	g(ζ)dζ	g(ζ)dζ	PROPN
ejpam-5697	91	13	,	,	PUNCT
ejpam-5697	91	14	ζ	ζ	NOUN
ejpam-5697	91	15	≥	≥	NOUN
ejpam-5697	91	16	0	0	NUM
ejpam-5697	91	17	.	.	PUNCT
ejpam-5697	92	1	(	(	PUNCT
ejpam-5697	92	2	2	2	X
ejpam-5697	92	3	)	)	PUNCT
ejpam-5697	92	4	numerous	numerous	ADJ
ejpam-5697	92	5	theoretical	theoretical	ADJ
ejpam-5697	92	6	results	result	NOUN
ejpam-5697	92	7	can	can	AUX
ejpam-5697	92	8	be	be	AUX
ejpam-5697	92	9	solved	solve	VERB
ejpam-5697	92	10	using	use	VERB
ejpam-5697	92	11	the	the	DET
ejpam-5697	92	12	aforementioned	aforementioned	ADJ
ejpam-5697	92	13	operators	operator	NOUN
ejpam-5697	92	14	.	.	PUNCT
ejpam-5697	93	1	alrefai	alrefai	PROPN
ejpam-5697	93	2	et	et	PROPN
ejpam-5697	93	3	al	al	PROPN
ejpam-5697	93	4	.	.	PUNCT
ejpam-5697	94	1	in	in	ADP
ejpam-5697	94	2	[	[	X
ejpam-5697	94	3	23	23	NUM
ejpam-5697	94	4	]	]	PUNCT
ejpam-5697	94	5	explains	explain	VERB
ejpam-5697	94	6	how	how	SCONJ
ejpam-5697	94	7	spaces	space	NOUN
ejpam-5697	94	8	are	be	AUX
ejpam-5697	94	9	utilised	utilise	VERB
ejpam-5697	94	10	extensively	extensively	ADV
ejpam-5697	94	11	in	in	ADP
ejpam-5697	94	12	operator	operator	NOUN
ejpam-5697	94	13	applications	application	NOUN
ejpam-5697	94	14	.	.	PUNCT
ejpam-5697	95	1	consider	consider	VERB
ejpam-5697	95	2	the	the	DET
ejpam-5697	95	3	differential	differential	ADJ
ejpam-5697	95	4	equation	equation	NOUN
ejpam-5697	95	5	abcd	abcd	PROPN
ejpam-5697	95	6	δ	δ	PROPN
ejpam-5697	95	7	0g(ξ	0g(ξ	PROPN
ejpam-5697	95	8	)	)	PUNCT
ejpam-5697	96	1	=	=	PUNCT
ejpam-5697	96	2	λg(ξ	λg(ξ	ADP
ejpam-5697	96	3	)	)	PUNCT
ejpam-5697	96	4	,	,	PUNCT
ejpam-5697	96	5	where	where	SCONJ
ejpam-5697	96	6	g(ξ	g(ξ	PROPN
ejpam-5697	96	7	)	)	PUNCT
ejpam-5697	96	8	∈	∈	PROPN
ejpam-5697	96	9	c1(0	c1(0	PROPN
ejpam-5697	96	10	,	,	PUNCT
ejpam-5697	96	11	t	t	PROPN
ejpam-5697	96	12	)	)	PUNCT
ejpam-5697	96	13	.	.	PUNCT
ejpam-5697	97	1	the	the	DET
ejpam-5697	97	2	trivial	trivial	ADJ
ejpam-5697	97	3	solution	solution	NOUN
ejpam-5697	97	4	,	,	PUNCT
ejpam-5697	97	5	abcd	abcd	PROPN
ejpam-5697	97	6	δ	δ	PROPN
ejpam-5697	97	7	0g(0	0g(0	NOUN
ejpam-5697	97	8	)	)	PUNCT
ejpam-5697	98	1	=	=	SYM
ejpam-5697	98	2	0	0	NUM
ejpam-5697	98	3	,	,	PUNCT
ejpam-5697	98	4	is	be	AUX
ejpam-5697	98	5	given	give	VERB
ejpam-5697	98	6	by	by	ADP
ejpam-5697	98	7	the	the	DET
ejpam-5697	98	8	solution	solution	NOUN
ejpam-5697	98	9	λg(0	λg(0	NOUN
ejpam-5697	98	10	)	)	PUNCT
ejpam-5697	98	11	+	+	X
ejpam-5697	99	1	h(0	h(0	PROPN
ejpam-5697	99	2	)	)	PUNCT
ejpam-5697	99	3	=	=	SYM
ejpam-5697	99	4	0	0	NUM
ejpam-5697	99	5	to	to	ADP
ejpam-5697	99	6	the	the	DET
ejpam-5697	99	7	fractional	fractional	ADJ
ejpam-5697	99	8	equation	equation	NOUN
ejpam-5697	99	9	abcd	abcd	PROPN
ejpam-5697	99	10	δ	δ	PROPN
ejpam-5697	99	11	0g(ξ	0g(ξ	PROPN
ejpam-5697	99	12	)	)	PUNCT
ejpam-5697	100	1	=	=	PUNCT
ejpam-5697	100	2	−λg(ξ	−λg(ξ	PROPN
ejpam-5697	100	3	)	)	PUNCT
ejpam-5697	100	4	+	+	CCONJ
ejpam-5697	100	5	h(ξ	h(ξ	NOUN
ejpam-5697	100	6	)	)	PUNCT
ejpam-5697	100	7	.	.	PUNCT
ejpam-5697	101	1	however	however	ADV
ejpam-5697	101	2	,	,	PUNCT
ejpam-5697	101	3	the	the	DET
ejpam-5697	101	4	caputo	caputo	PROPN
ejpam-5697	101	5	derivative	derivative	NOUN
ejpam-5697	101	6	is	be	AUX
ejpam-5697	101	7	constrained	constrain	VERB
ejpam-5697	101	8	by	by	ADP
ejpam-5697	101	9	this	this	DET
ejpam-5697	101	10	area	area	NOUN
ejpam-5697	101	11	.	.	PUNCT
ejpam-5697	102	1	we	we	PRON
ejpam-5697	102	2	will	will	AUX
ejpam-5697	102	3	consider	consider	VERB
ejpam-5697	102	4	χ(g	χ(g	PROPN
ejpam-5697	102	5	)	)	PUNCT
ejpam-5697	103	1	=	=	PRON
ejpam-5697	103	2	{	{	PUNCT
ejpam-5697	103	3	g	g	NOUN
ejpam-5697	103	4	:	:	PUNCT
ejpam-5697	103	5	g′	g′	NOUN
ejpam-5697	103	6	∈	∈	PROPN
ejpam-5697	104	1	l1[0	l1[0	PROPN
ejpam-5697	104	2	,	,	PUNCT
ejpam-5697	104	3	1	1	NUM
ejpam-5697	104	4	]	]	PUNCT
ejpam-5697	104	5	}	}	PUNCT
ejpam-5697	104	6	is	be	AUX
ejpam-5697	104	7	the	the	DET
ejpam-5697	104	8	space	space	NOUN
ejpam-5697	104	9	for	for	ADP
ejpam-5697	104	10	the	the	DET
ejpam-5697	104	11	following	follow	VERB
ejpam-5697	104	12	initial	initial	ADJ
ejpam-5697	104	13	value	value	NOUN
ejpam-5697	104	14	problem	problem	NOUN
ejpam-5697	104	15	abcd	abcd	PROPN
ejpam-5697	104	16	δ	δ	PROPN
ejpam-5697	104	17	0g(ξ	0g(ξ	PROPN
ejpam-5697	104	18	)	)	PUNCT
ejpam-5697	105	1	=	=	PRON
ejpam-5697	105	2	{	{	PUNCT
ejpam-5697	105	3	−λg(ξ	−λg(ξ	PROPN
ejpam-5697	105	4	)	)	PUNCT
ejpam-5697	105	5	+	+	CCONJ
ejpam-5697	105	6	h(ξ	h(ξ	NOUN
ejpam-5697	105	7	)	)	PUNCT
ejpam-5697	105	8	,	,	PUNCT
ejpam-5697	105	9	ξ	ξ	PROPN
ejpam-5697	105	10	∈	∈	PROPN
ejpam-5697	105	11	(	(	PUNCT
ejpam-5697	105	12	0	0	NUM
ejpam-5697	105	13	,	,	PUNCT
ejpam-5697	105	14	t	t	PROPN
ejpam-5697	105	15	)	)	PUNCT
ejpam-5697	105	16	;	;	PUNCT
ejpam-5697	105	17	g0	g0	PROPN
ejpam-5697	105	18	,	,	PUNCT
ejpam-5697	105	19	ξ	ξ	X
ejpam-5697	105	20	=	=	SYM
ejpam-5697	105	21	0	0	NUM
ejpam-5697	105	22	,	,	PUNCT
ejpam-5697	105	23	we	we	PRON
ejpam-5697	105	24	obtain	obtain	VERB
ejpam-5697	105	25	the	the	DET
ejpam-5697	105	26	following	following	ADJ
ejpam-5697	105	27	solution	solution	NOUN
ejpam-5697	105	28	for	for	ADP
ejpam-5697	105	29	0	0	NUM
ejpam-5697	105	30	<	<	X
ejpam-5697	105	31	δ	δ	X
ejpam-5697	105	32	<	<	X
ejpam-5697	105	33	1	1	NUM
ejpam-5697	105	34	,	,	PUNCT
ejpam-5697	105	35	g(ξ	g(ξ	PROPN
ejpam-5697	105	36	)	)	PUNCT
ejpam-5697	105	37	=	=	SYM
ejpam-5697	105	38	g0eδ,1(−λθδ	g0eδ,1(−λθδ	NOUN
ejpam-5697	105	39	)	)	PUNCT
ejpam-5697	106	1	+	+	CCONJ
ejpam-5697	106	2	∫	∫	PROPN
ejpam-5697	106	3	θ	θ	NOUN
ejpam-5697	106	4	0	0	PUNCT
ejpam-5697	106	5	(	(	PUNCT
ejpam-5697	106	6	θ	θ	X
ejpam-5697	106	7	−	−	PROPN
ejpam-5697	106	8	ζ)δ−1eδ	ζ)δ−1eδ	PROPN
ejpam-5697	106	9	,	,	PUNCT
ejpam-5697	106	10	δ(−λ(θ	δ(−λ(θ	VERB
ejpam-5697	106	11	−	−	NOUN
ejpam-5697	106	12	ζ)δ)h(ζ)dζ	ζ)δ)h(ζ)dζ	NOUN
ejpam-5697	106	13	.	.	PUNCT
ejpam-5697	107	1	the	the	DET
ejpam-5697	107	2	related	relate	VERB
ejpam-5697	107	3	homogeneous	homogeneous	ADJ
ejpam-5697	107	4	equation	equation	NOUN
ejpam-5697	107	5	g(ξ	g(ξ	PROPN
ejpam-5697	107	6	)	)	PUNCT
ejpam-5697	107	7	=	=	PUNCT
ejpam-5697	107	8	g0eδ,1(−λθδ	g0eδ,1(−λθδ	NOUN
ejpam-5697	107	9	)	)	PUNCT
ejpam-5697	107	10	likewise	likewise	ADV
ejpam-5697	107	11	yields	yield	VERB
ejpam-5697	107	12	a	a	DET
ejpam-5697	107	13	nontrivial	nontrivial	ADJ
ejpam-5697	107	14	solution	solution	NOUN
ejpam-5697	107	15	.	.	PUNCT
ejpam-5697	108	1	the	the	DET
ejpam-5697	108	2	definition	definition	NOUN
ejpam-5697	108	3	and	and	CCONJ
ejpam-5697	108	4	discussion	discussion	NOUN
ejpam-5697	108	5	of	of	ADP
ejpam-5697	108	6	the	the	DET
ejpam-5697	108	7	weighted	weight	VERB
ejpam-5697	108	8	form	form	NOUN
ejpam-5697	108	9	of	of	ADP
ejpam-5697	108	10	atangana	atangana	PROPN
ejpam-5697	108	11	-	-	PUNCT
ejpam-5697	108	12	baeanu	baeanu	VERB
ejpam-5697	108	13	operators	operator	NOUN
ejpam-5697	108	14	in	in	ADP
ejpam-5697	108	15	differential	differential	ADJ
ejpam-5697	108	16	equations	equation	NOUN
ejpam-5697	108	17	is	be	AUX
ejpam-5697	108	18	found	find	VERB
ejpam-5697	108	19	in	in	ADP
ejpam-5697	108	20	[	[	X
ejpam-5697	108	21	22	22	NUM
ejpam-5697	108	22	]	]	PUNCT
ejpam-5697	108	23	.	.	PUNCT
ejpam-5697	109	1	gauhar	gauhar	PROPN
ejpam-5697	109	2	rahman	rahman	PROPN
ejpam-5697	109	3	et	et	PROPN
ejpam-5697	109	4	al	al	PROPN
ejpam-5697	109	5	.	.	PUNCT
ejpam-5697	109	6	/	/	SYM
ejpam-5697	109	7	eur	eur	PROPN
ejpam-5697	109	8	.	.	PUNCT
ejpam-5697	110	1	j.	j.	PROPN
ejpam-5697	110	2	pure	pure	PROPN
ejpam-5697	110	3	appl	appl	PROPN
ejpam-5697	110	4	.	.	PROPN
ejpam-5697	110	5	math	math	PROPN
ejpam-5697	110	6	,	,	PUNCT
ejpam-5697	110	7	18	18	NUM
ejpam-5697	110	8	(	(	PUNCT
ejpam-5697	110	9	1	1	NUM
ejpam-5697	110	10	)	)	PUNCT
ejpam-5697	110	11	(	(	PUNCT
ejpam-5697	110	12	2025	2025	NUM
ejpam-5697	110	13	)	)	PUNCT
ejpam-5697	110	14	,	,	PUNCT
ejpam-5697	110	15	5697	5697	NUM
ejpam-5697	110	16	5	5	NUM
ejpam-5697	110	17	of	of	ADP
ejpam-5697	110	18	26	26	NUM
ejpam-5697	110	19	definition	definition	NOUN
ejpam-5697	110	20	7	7	NUM
ejpam-5697	110	21	.	.	PUNCT
ejpam-5697	111	1	[	[	X
ejpam-5697	111	2	22	22	NUM
ejpam-5697	111	3	]	]	PUNCT
ejpam-5697	111	4	the	the	DET
ejpam-5697	111	5	weighted	weight	VERB
ejpam-5697	111	6	atangana	atangana	PROPN
ejpam-5697	111	7	-	-	PUNCT
ejpam-5697	111	8	baleanu	baleanu	ADJ
ejpam-5697	111	9	fractional	fractional	ADJ
ejpam-5697	111	10	operator	operator	NOUN
ejpam-5697	111	11	of	of	ADP
ejpam-5697	111	12	order	order	NOUN
ejpam-5697	111	13	0	0	PUNCT
ejpam-5697	111	14	<	<	X
ejpam-5697	111	15	δ	δ	X
ejpam-5697	111	16	<	<	X
ejpam-5697	111	17	1	1	NUM
ejpam-5697	111	18	for	for	ADP
ejpam-5697	111	19	a	a	DET
ejpam-5697	111	20	given	give	VERB
ejpam-5697	111	21	g′	g′	NOUN
ejpam-5697	111	22	∈	∈	PROPN
ejpam-5697	111	23	l1(0	l1(0	PROPN
ejpam-5697	111	24	,	,	PUNCT
ejpam-5697	111	25	t	t	PROPN
ejpam-5697	111	26	)	)	PUNCT
ejpam-5697	111	27	,	,	PUNCT
ejpam-5697	111	28	is	be	AUX
ejpam-5697	111	29	defined	define	VERB
ejpam-5697	111	30	by	by	ADP
ejpam-5697	111	31	abcd	abcd	PROPN
ejpam-5697	111	32	δ	δ	PROPN
ejpam-5697	111	33	0g(ξ	0g(ξ	PROPN
ejpam-5697	111	34	)	)	PUNCT
ejpam-5697	112	1	=	=	SYM
ejpam-5697	112	2	r(δ)w−1(ζ	r(δ)w−1(ζ	NOUN
ejpam-5697	112	3	)	)	PUNCT
ejpam-5697	112	4	1−	1−	NUM
ejpam-5697	113	1	δ	δ	NOUN
ejpam-5697	113	2	∫	∫	PROPN
ejpam-5697	114	1	ξ	ξ	X
ejpam-5697	114	2	0	0	NUM
ejpam-5697	114	3	eδ	eδ	NOUN
ejpam-5697	114	4	(	(	PUNCT
ejpam-5697	114	5	−	−	PROPN
ejpam-5697	114	6	ωδ	ωδ	X
ejpam-5697	114	7	(	(	PUNCT
ejpam-5697	114	8	ξ	ξ	PROPN
ejpam-5697	114	9	−	−	PROPN
ejpam-5697	114	10	ζ	ζ	NOUN
ejpam-5697	114	11	)	)	PUNCT
ejpam-5697	114	12	δ	δ	PROPN
ejpam-5697	114	13	)	)	PUNCT
ejpam-5697	114	14	(	(	PUNCT
ejpam-5697	114	15	w(ζ)g(ζ))′dζ	w(ζ)g(ζ))′dζ	NOUN
ejpam-5697	114	16	,	,	PUNCT
ejpam-5697	114	17	ζ	ζ	NOUN
ejpam-5697	114	18	≥	≥	NOUN
ejpam-5697	114	19	0	0	NUM
ejpam-5697	114	20	,	,	PUNCT
ejpam-5697	114	21	and	and	CCONJ
ejpam-5697	114	22	its	its	PRON
ejpam-5697	114	23	associated	associated	ADJ
ejpam-5697	114	24	integral	integral	ADJ
ejpam-5697	114	25	operator	operator	NOUN
ejpam-5697	114	26	is	be	AUX
ejpam-5697	114	27	given	give	VERB
ejpam-5697	114	28	by	by	ADP
ejpam-5697	114	29	abci	abci	PROPN
ejpam-5697	114	30	δ	δ	PROPN
ejpam-5697	114	31	0g(ξ	0g(ξ	PROPN
ejpam-5697	114	32	)	)	PUNCT
ejpam-5697	115	1	=	=	SYM
ejpam-5697	115	2	1−	1−	NUM
ejpam-5697	115	3	δ	δ	PROPN
ejpam-5697	115	4	r(δ	r(δ	PROPN
ejpam-5697	115	5	)	)	PUNCT
ejpam-5697	115	6	g(ξ	g(ξ	PROPN
ejpam-5697	115	7	)	)	PUNCT
ejpam-5697	116	1	+	+	CCONJ
ejpam-5697	116	2	r(δ	r(δ	NOUN
ejpam-5697	116	3	)	)	PUNCT
ejpam-5697	116	4	1−	1−	NUM
ejpam-5697	116	5	δ	δ	PROPN
ejpam-5697	116	6	w−1(ζ	w−1(ζ	PROPN
ejpam-5697	116	7	)	)	PUNCT
ejpam-5697	116	8	∫	∫	PROPN
ejpam-5697	117	1	ξ	ξ	X
ejpam-5697	117	2	0	0	PUNCT
ejpam-5697	117	3	(	(	PUNCT
ejpam-5697	117	4	ξ	ξ	PROPN
ejpam-5697	117	5	−	−	PROPN
ejpam-5697	117	6	ζ	ζ	NOUN
ejpam-5697	117	7	)	)	PUNCT
ejpam-5697	117	8	δ	δ	PROPN
ejpam-5697	117	9	w(ζ)g(ζ)dζ	w(ζ)g(ζ)dζ	NOUN
ejpam-5697	117	10	,	,	PUNCT
ejpam-5697	117	11	ζ	ζ	X
ejpam-5697	117	12	≥	≥	NOUN
ejpam-5697	117	13	0	0	NUM
ejpam-5697	117	14	,	,	PUNCT
ejpam-5697	117	15	where	where	SCONJ
ejpam-5697	117	16	the	the	DET
ejpam-5697	117	17	normalised	normalise	VERB
ejpam-5697	117	18	function	function	NOUN
ejpam-5697	117	19	r(δ	r(δ	PROPN
ejpam-5697	117	20	)	)	PUNCT
ejpam-5697	117	21	,	,	PUNCT
ejpam-5697	117	22	has	have	VERB
ejpam-5697	117	23	the	the	DET
ejpam-5697	117	24	property	property	NOUN
ejpam-5697	117	25	r(0	r(0	PROPN
ejpam-5697	117	26	)	)	PUNCT
ejpam-5697	117	27	=	=	SYM
ejpam-5697	117	28	r(1	r(1	PROPN
ejpam-5697	117	29	)	)	PUNCT
ejpam-5697	117	30	=	=	PUNCT
ejpam-5697	118	1	1	1	X
ejpam-5697	118	2	.	.	PUNCT
ejpam-5697	119	1	our	our	PRON
ejpam-5697	119	2	main	main	ADJ
ejpam-5697	119	3	objective	objective	NOUN
ejpam-5697	119	4	is	be	AUX
ejpam-5697	119	5	to	to	PART
ejpam-5697	119	6	define	define	VERB
ejpam-5697	119	7	the	the	DET
ejpam-5697	119	8	modified	modify	VERB
ejpam-5697	119	9	power	power	NOUN
ejpam-5697	119	10	fractional	fractional	ADJ
ejpam-5697	119	11	operators	operator	NOUN
ejpam-5697	119	12	and	and	CCONJ
ejpam-5697	119	13	power	power	NOUN
ejpam-5697	119	14	fractional	fractional	ADJ
ejpam-5697	119	15	differential	differential	NOUN
ejpam-5697	119	16	equations	equation	NOUN
ejpam-5697	119	17	and	and	CCONJ
ejpam-5697	119	18	to	to	PART
ejpam-5697	119	19	determine	determine	VERB
ejpam-5697	119	20	their	their	PRON
ejpam-5697	119	21	exact	exact	ADJ
ejpam-5697	119	22	solutions	solution	NOUN
ejpam-5697	119	23	using	use	VERB
ejpam-5697	119	24	a	a	DET
ejpam-5697	119	25	variety	variety	NOUN
ejpam-5697	119	26	of	of	ADP
ejpam-5697	119	27	methods	method	NOUN
ejpam-5697	119	28	.	.	PUNCT
ejpam-5697	120	1	we	we	PRON
ejpam-5697	120	2	offer	offer	VERB
ejpam-5697	120	3	the	the	DET
ejpam-5697	120	4	modified	modify	VERB
ejpam-5697	120	5	power	power	NOUN
ejpam-5697	120	6	fractional	fractional	ADJ
ejpam-5697	120	7	operators	operator	NOUN
ejpam-5697	120	8	as	as	ADP
ejpam-5697	120	9	a	a	DET
ejpam-5697	120	10	tool	tool	NOUN
ejpam-5697	120	11	to	to	PART
ejpam-5697	120	12	characterise	characterise	VERB
ejpam-5697	120	13	numerous	numerous	ADJ
ejpam-5697	120	14	power	power	NOUN
ejpam-5697	120	15	differential	differential	NOUN
ejpam-5697	120	16	equations	equation	NOUN
ejpam-5697	120	17	.	.	PUNCT
ejpam-5697	121	1	the	the	DET
ejpam-5697	121	2	work	work	NOUN
ejpam-5697	121	3	presented	present	VERB
ejpam-5697	121	4	in	in	ADP
ejpam-5697	121	5	this	this	DET
ejpam-5697	121	6	paper	paper	NOUN
ejpam-5697	121	7	are	be	AUX
ejpam-5697	121	8	the	the	DET
ejpam-5697	121	9	generalization	generalization	NOUN
ejpam-5697	121	10	of	of	ADP
ejpam-5697	121	11	the	the	DET
ejpam-5697	121	12	work	work	NOUN
ejpam-5697	121	13	done	do	VERB
ejpam-5697	121	14	by	by	ADP
ejpam-5697	121	15	[	[	X
ejpam-5697	121	16	2	2	NUM
ejpam-5697	121	17	,	,	PUNCT
ejpam-5697	121	18	7	7	NUM
ejpam-5697	121	19	,	,	PUNCT
ejpam-5697	121	20	11	11	NUM
ejpam-5697	121	21	]	]	PUNCT
ejpam-5697	121	22	.	.	PUNCT
ejpam-5697	122	1	3	3	X
ejpam-5697	122	2	.	.	X
ejpam-5697	122	3	the	the	DET
ejpam-5697	122	4	modified	modify	VERB
ejpam-5697	122	5	power	power	NOUN
ejpam-5697	122	6	fractional	fractional	ADJ
ejpam-5697	122	7	derivative	derivative	NOUN
ejpam-5697	122	8	in	in	ADP
ejpam-5697	122	9	caputo	caputo	PROPN
ejpam-5697	122	10	sense	sense	NOUN
ejpam-5697	122	11	we	we	PRON
ejpam-5697	122	12	introduce	introduce	VERB
ejpam-5697	122	13	the	the	DET
ejpam-5697	122	14	modified	modify	VERB
ejpam-5697	122	15	power	power	NOUN
ejpam-5697	122	16	fractional	fractional	ADJ
ejpam-5697	122	17	derivative	derivative	ADJ
ejpam-5697	122	18	operators	operator	NOUN
ejpam-5697	122	19	in	in	ADP
ejpam-5697	122	20	this	this	DET
ejpam-5697	122	21	section	section	NOUN
ejpam-5697	122	22	.	.	PUNCT
ejpam-5697	123	1	we	we	PRON
ejpam-5697	123	2	introduce	introduce	VERB
ejpam-5697	123	3	its	its	PRON
ejpam-5697	123	4	laplace	laplace	NOUN
ejpam-5697	123	5	transformation	transformation	NOUN
ejpam-5697	123	6	and	and	CCONJ
ejpam-5697	123	7	boundedeness	boundedeness	NOUN
ejpam-5697	123	8	.	.	PUNCT
ejpam-5697	124	1	moreover	moreover	ADV
ejpam-5697	124	2	,	,	PUNCT
ejpam-5697	124	3	a	a	DET
ejpam-5697	124	4	few	few	ADJ
ejpam-5697	124	5	relevant	relevant	ADJ
ejpam-5697	124	6	examples	example	NOUN
ejpam-5697	124	7	are	be	AUX
ejpam-5697	124	8	shown	show	VERB
ejpam-5697	124	9	.	.	PUNCT
ejpam-5697	125	1	definition	definition	NOUN
ejpam-5697	125	2	8	8	NUM
ejpam-5697	125	3	.	.	PUNCT
ejpam-5697	126	1	the	the	DET
ejpam-5697	126	2	generalised	generalise	VERB
ejpam-5697	126	3	form	form	NOUN
ejpam-5697	126	4	of	of	ADP
ejpam-5697	126	5	the	the	DET
ejpam-5697	126	6	modified	modify	VERB
ejpam-5697	126	7	fractional	fractional	NOUN
ejpam-5697	126	8	(	(	PUNCT
ejpam-5697	126	9	mpc	mpc	NOUN
ejpam-5697	126	10	)	)	PUNCT
ejpam-5697	126	11	derivative	derivative	ADJ
ejpam-5697	126	12	operator	operator	NOUN
ejpam-5697	126	13	of	of	ADP
ejpam-5697	126	14	order	order	NOUN
ejpam-5697	126	15	0	0	PUNCT
ejpam-5697	126	16	<	<	X
ejpam-5697	126	17	δ	δ	X
ejpam-5697	126	18	<	<	X
ejpam-5697	126	19	1	1	NUM
ejpam-5697	126	20	and	and	CCONJ
ejpam-5697	126	21	p	p	X
ejpam-5697	126	22	>	>	X
ejpam-5697	126	23	1	1	NUM
ejpam-5697	126	24	with	with	ADP
ejpam-5697	126	25	regard	regard	NOUN
ejpam-5697	126	26	to	to	ADP
ejpam-5697	126	27	another	another	DET
ejpam-5697	126	28	function	function	NOUN
ejpam-5697	126	29	ℏ	ℏ	PROPN
ejpam-5697	126	30	,	,	PUNCT
ejpam-5697	126	31	given	give	VERB
ejpam-5697	126	32	g	g	PROPN
ejpam-5697	126	33	as	as	ADP
ejpam-5697	126	34	a	a	DET
ejpam-5697	126	35	continuous	continuous	ADJ
ejpam-5697	126	36	function	function	NOUN
ejpam-5697	126	37	and	and	CCONJ
ejpam-5697	126	38	g′	g′	NOUN
ejpam-5697	126	39	∈	∈	PROPN
ejpam-5697	126	40	l1(0	l1(0	PROPN
ejpam-5697	126	41	,	,	PUNCT
ejpam-5697	126	42	t	t	PROPN
ejpam-5697	126	43	)	)	PUNCT
ejpam-5697	126	44	,	,	PUNCT
ejpam-5697	126	45	is	be	AUX
ejpam-5697	126	46	defined	define	VERB
ejpam-5697	126	47	as	as	SCONJ
ejpam-5697	126	48	follows	follow	VERB
ejpam-5697	126	49	:	:	PUNCT
ejpam-5697	126	50	mpc	mpc	NOUN
ejpam-5697	126	51	ℏ	ℏ	NOUN
ejpam-5697	126	52	dδ;κ;p	dδ;κ;p	X
ejpam-5697	126	53	a+	a+	PUNCT
ejpam-5697	126	54	g(ξ	g(ξ	PROPN
ejpam-5697	126	55	)	)	PUNCT
ejpam-5697	126	56	=	=	SYM
ejpam-5697	126	57	r(δ	r(δ	PROPN
ejpam-5697	126	58	)	)	PUNCT
ejpam-5697	126	59	1−	1−	NUM
ejpam-5697	127	1	δ	δ	NOUN
ejpam-5697	127	2	∫	∫	PROPN
ejpam-5697	127	3	ξ	ξ	PROPN
ejpam-5697	127	4	a	a	DET
ejpam-5697	127	5	peκ,1	peκ,1	NOUN
ejpam-5697	127	6	(	(	PUNCT
ejpam-5697	127	7	−	−	PROPN
ejpam-5697	127	8	ωδ	ωδ	X
ejpam-5697	127	9	(	(	PUNCT
ejpam-5697	127	10	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	127	11	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	127	12	)	)	PUNCT
ejpam-5697	127	13	)	)	PUNCT
ejpam-5697	127	14	κ	κ	X
ejpam-5697	127	15	)	)	PUNCT
ejpam-5697	127	16	g′(ζ)dζ	g′(ζ)dζ	PROPN
ejpam-5697	127	17	,	,	PUNCT
ejpam-5697	127	18	ζ	ζ	X
ejpam-5697	127	19	≥	≥	NOUN
ejpam-5697	127	20	0	0	NUM
ejpam-5697	127	21	.	.	PUNCT
ejpam-5697	128	1	(	(	PUNCT
ejpam-5697	128	2	3	3	X
ejpam-5697	128	3	)	)	PUNCT
ejpam-5697	128	4	integrating	integrating	NOUN
ejpam-5697	128	5	by	by	ADP
ejpam-5697	128	6	parts	part	NOUN
ejpam-5697	128	7	leads	lead	VERB
ejpam-5697	128	8	to	to	ADP
ejpam-5697	128	9	mpc	mpc	NOUN
ejpam-5697	128	10	ℏ	ℏ	NOUN
ejpam-5697	128	11	dδ;κ;p	dδ;κ;p	X
ejpam-5697	128	12	a+	a+	PUNCT
ejpam-5697	128	13	g(ξ	g(ξ	PROPN
ejpam-5697	128	14	)	)	PUNCT
ejpam-5697	128	15	=	=	SYM
ejpam-5697	128	16	r(δ	r(δ	PROPN
ejpam-5697	128	17	)	)	PUNCT
ejpam-5697	128	18	1−	1−	NUM
ejpam-5697	128	19	δ	δ	PROPN
ejpam-5697	128	20	[	[	PUNCT
ejpam-5697	128	21	g(ξ)−	g(ξ)−	NOUN
ejpam-5697	128	22	peκ,1	peκ,1	NOUN
ejpam-5697	128	23	(	(	PUNCT
ejpam-5697	128	24	−	−	PROPN
ejpam-5697	128	25	ωδ	ωδ	X
ejpam-5697	128	26	(	(	PUNCT
ejpam-5697	128	27	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	128	28	ℏ(a	ℏ(a	NOUN
ejpam-5697	128	29	)	)	PUNCT
ejpam-5697	128	30	)	)	PUNCT
ejpam-5697	128	31	κ	κ	X
ejpam-5697	128	32	)	)	PUNCT
ejpam-5697	128	33	g(a	g(a	PROPN
ejpam-5697	128	34	)	)	PUNCT
ejpam-5697	128	35	−	−	ADP
ejpam-5697	128	36	ωδ(ln	ωδ(ln	PROPN
ejpam-5697	128	37	p	p	NOUN
ejpam-5697	128	38	)	)	PUNCT
ejpam-5697	128	39	∫	∫	PROPN
ejpam-5697	129	1	ξ	ξ	PROPN
ejpam-5697	129	2	a	a	PRON
ejpam-5697	129	3	(	(	PUNCT
ejpam-5697	129	4	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	129	5	ℏ(ζ))κ−1	ℏ(ζ))κ−1	X
ejpam-5697	129	6	peκ	peκ	NOUN
ejpam-5697	129	7	,	,	PUNCT
ejpam-5697	129	8	κ	κ	X
ejpam-5697	129	9	(	(	PUNCT
ejpam-5697	129	10	−	−	PROPN
ejpam-5697	129	11	ωδ	ωδ	X
ejpam-5697	129	12	(	(	PUNCT
ejpam-5697	129	13	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	129	14	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	129	15	)	)	PUNCT
ejpam-5697	129	16	)	)	PUNCT
ejpam-5697	129	17	κ)ℏ′(ζ)g(ζ)dζ	κ)ℏ′(ζ)g(ζ)dζ	NOUN
ejpam-5697	129	18	]	]	PUNCT
ejpam-5697	129	19	.	.	PUNCT
ejpam-5697	130	1	the	the	DET
ejpam-5697	130	2	functions	function	NOUN
ejpam-5697	130	3	ωδ	ωδ	ADP
ejpam-5697	130	4	=	=	SYM
ejpam-5697	130	5	δ	δ	PROPN
ejpam-5697	130	6	1−δ	1−δ	NUM
ejpam-5697	130	7	,	,	PUNCT
ejpam-5697	130	8	ℏ	ℏ	PROPN
ejpam-5697	130	9	,	,	PUNCT
ejpam-5697	130	10	a	a	DET
ejpam-5697	130	11	strictly	strictly	ADV
ejpam-5697	130	12	increasing	increase	VERB
ejpam-5697	130	13	function	function	NOUN
ejpam-5697	130	14	,	,	PUNCT
ejpam-5697	130	15	and	and	CCONJ
ejpam-5697	130	16	r(δ	r(δ	PROPN
ejpam-5697	130	17	)	)	PUNCT
ejpam-5697	130	18	,	,	PUNCT
ejpam-5697	130	19	a	a	DET
ejpam-5697	130	20	normalized	normalize	VERB
ejpam-5697	130	21	function	function	NOUN
ejpam-5697	130	22	with	with	ADP
ejpam-5697	130	23	the	the	DET
ejpam-5697	130	24	condition	condition	NOUN
ejpam-5697	130	25	r(0	r(0	PROPN
ejpam-5697	130	26	)	)	PUNCT
ejpam-5697	131	1	=	=	SYM
ejpam-5697	131	2	r(1	r(1	PROPN
ejpam-5697	131	3	)	)	PUNCT
ejpam-5697	132	1	=	=	SYM
ejpam-5697	132	2	1	1	NUM
ejpam-5697	132	3	are	be	AUX
ejpam-5697	132	4	among	among	ADP
ejpam-5697	132	5	them	they	PRON
ejpam-5697	132	6	.	.	PUNCT
ejpam-5697	133	1	remark	remark	PROPN
ejpam-5697	133	2	2	2	NUM
ejpam-5697	133	3	.	.	PUNCT
ejpam-5697	134	1	i.	i.	PROPN
ejpam-5697	134	2	letting	let	VERB
ejpam-5697	134	3	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	134	4	)	)	PUNCT
ejpam-5697	135	1	=	=	SYM
ejpam-5697	135	2	ξ	ξ	PROPN
ejpam-5697	135	3	,	,	PUNCT
ejpam-5697	135	4	κ	κ	X
ejpam-5697	135	5	=	=	SYM
ejpam-5697	135	6	δ	δ	PROPN
ejpam-5697	135	7	and	and	CCONJ
ejpam-5697	135	8	p	p	NOUN
ejpam-5697	135	9	=	=	PUNCT
ejpam-5697	135	10	e	e	X
ejpam-5697	135	11	in	in	ADP
ejpam-5697	135	12	(	(	PUNCT
ejpam-5697	135	13	3	3	NUM
ejpam-5697	135	14	)	)	PUNCT
ejpam-5697	135	15	then	then	ADV
ejpam-5697	135	16	we	we	PRON
ejpam-5697	135	17	get	get	VERB
ejpam-5697	135	18	definition	definition	NOUN
ejpam-5697	135	19	7	7	NUM
ejpam-5697	135	20	.	.	PUNCT
ejpam-5697	135	21	ii	ii	PROPN
ejpam-5697	135	22	.	.	PUNCT
ejpam-5697	136	1	letting	let	VERB
ejpam-5697	136	2	we	we	PRON
ejpam-5697	136	3	substitute	substitute	VERB
ejpam-5697	136	4	κ	κ	PROPN
ejpam-5697	136	5	=	=	PROPN
ejpam-5697	136	6	δ	δ	PROPN
ejpam-5697	136	7	and	and	CCONJ
ejpam-5697	136	8	p	p	NOUN
ejpam-5697	136	9	=	=	PUNCT
ejpam-5697	136	10	e	e	X
ejpam-5697	136	11	in	in	ADP
ejpam-5697	136	12	(	(	PUNCT
ejpam-5697	136	13	3	3	NUM
ejpam-5697	136	14	)	)	PUNCT
ejpam-5697	136	15	then	then	ADV
ejpam-5697	136	16	we	we	PRON
ejpam-5697	136	17	get	get	VERB
ejpam-5697	136	18	the	the	DET
ejpam-5697	136	19	operator	operator	NOUN
ejpam-5697	136	20	defined	define	VERB
ejpam-5697	136	21	by	by	ADP
ejpam-5697	136	22	[	[	X
ejpam-5697	136	23	7	7	NUM
ejpam-5697	136	24	]	]	PUNCT
ejpam-5697	136	25	.	.	PUNCT
ejpam-5697	137	1	iii	iii	X
ejpam-5697	137	2	.	.	PUNCT
ejpam-5697	138	1	letting	let	VERB
ejpam-5697	138	2	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	138	3	)	)	PUNCT
ejpam-5697	138	4	=	=	SYM
ejpam-5697	139	1	ξ	ξ	X
ejpam-5697	139	2	in	in	ADP
ejpam-5697	139	3	(	(	PUNCT
ejpam-5697	139	4	3	3	NUM
ejpam-5697	139	5	)	)	PUNCT
ejpam-5697	139	6	then	then	ADV
ejpam-5697	139	7	we	we	PRON
ejpam-5697	139	8	get	get	VERB
ejpam-5697	139	9	definition	definition	NOUN
ejpam-5697	139	10	of	of	ADP
ejpam-5697	139	11	power	power	NOUN
ejpam-5697	139	12	fractional	fractional	ADJ
ejpam-5697	139	13	derivative	derivative	NOUN
ejpam-5697	139	14	defined	define	VERB
ejpam-5697	139	15	by	by	ADP
ejpam-5697	139	16	[	[	PUNCT
ejpam-5697	139	17	11	11	NUM
ejpam-5697	139	18	]	]	PUNCT
ejpam-5697	139	19	.	.	PUNCT
ejpam-5697	140	1	gauhar	gauhar	PROPN
ejpam-5697	140	2	rahman	rahman	PROPN
ejpam-5697	140	3	et	et	PROPN
ejpam-5697	140	4	al	al	PROPN
ejpam-5697	140	5	.	.	PUNCT
ejpam-5697	140	6	/	/	SYM
ejpam-5697	140	7	eur	eur	PROPN
ejpam-5697	140	8	.	.	PUNCT
ejpam-5697	141	1	j.	j.	PROPN
ejpam-5697	141	2	pure	pure	PROPN
ejpam-5697	141	3	appl	appl	PROPN
ejpam-5697	141	4	.	.	PROPN
ejpam-5697	141	5	math	math	PROPN
ejpam-5697	141	6	,	,	PUNCT
ejpam-5697	141	7	18	18	NUM
ejpam-5697	141	8	(	(	PUNCT
ejpam-5697	141	9	1	1	NUM
ejpam-5697	141	10	)	)	PUNCT
ejpam-5697	141	11	(	(	PUNCT
ejpam-5697	141	12	2025	2025	NUM
ejpam-5697	141	13	)	)	PUNCT
ejpam-5697	141	14	,	,	PUNCT
ejpam-5697	141	15	5697	5697	NUM
ejpam-5697	141	16	6	6	NUM
ejpam-5697	141	17	of	of	ADP
ejpam-5697	141	18	26	26	NUM
ejpam-5697	141	19	we	we	PRON
ejpam-5697	141	20	demonstrate	demonstrate	VERB
ejpam-5697	141	21	the	the	DET
ejpam-5697	141	22	boundedness	boundedness	NOUN
ejpam-5697	141	23	of	of	ADP
ejpam-5697	141	24	the	the	DET
ejpam-5697	141	25	operator	operator	NOUN
ejpam-5697	141	26	given	give	VERB
ejpam-5697	141	27	by	by	ADP
ejpam-5697	141	28	definition	definition	NOUN
ejpam-5697	141	29	8	8	NUM
ejpam-5697	141	30	in	in	ADP
ejpam-5697	141	31	the	the	DET
ejpam-5697	141	32	first	first	ADJ
ejpam-5697	141	33	result	result	NOUN
ejpam-5697	141	34	of	of	ADP
ejpam-5697	141	35	this	this	DET
ejpam-5697	141	36	section	section	NOUN
ejpam-5697	141	37	.	.	PUNCT
ejpam-5697	142	1	theorem	theorem	NOUN
ejpam-5697	142	2	1	1	NUM
ejpam-5697	142	3	.	.	PUNCT
ejpam-5697	142	4	considering	consider	VERB
ejpam-5697	142	5	g	g	PROPN
ejpam-5697	142	6	∈	∈	PROPN
ejpam-5697	142	7	xp(0	xp(0	PROPN
ejpam-5697	142	8	,	,	PUNCT
ejpam-5697	142	9	t	t	PROPN
ejpam-5697	142	10	)	)	PUNCT
ejpam-5697	142	11	,	,	PUNCT
ejpam-5697	142	12	and	and	CCONJ
ejpam-5697	142	13	ℏ	ℏ	PROPN
ejpam-5697	142	14	,	,	PUNCT
ejpam-5697	142	15	δ	δ	PROPN
ejpam-5697	142	16	1−δ	1−δ	NUM
ejpam-5697	143	1	=	=	SYM
ejpam-5697	143	2	ωδ	ωδ	NOUN
ejpam-5697	143	3	and	and	CCONJ
ejpam-5697	143	4	r(δ	r(δ	PROPN
ejpam-5697	143	5	)	)	PUNCT
ejpam-5697	143	6	,	,	PUNCT
ejpam-5697	143	7	permit	permit	VERB
ejpam-5697	143	8	the	the	DET
ejpam-5697	143	9	same	same	ADJ
ejpam-5697	143	10	characteristics	characteristic	NOUN
ejpam-5697	143	11	as	as	SCONJ
ejpam-5697	143	12	stated	state	VERB
ejpam-5697	143	13	in	in	ADP
ejpam-5697	143	14	8	8	NUM
ejpam-5697	143	15	;	;	PUNCT
ejpam-5697	143	16	hence	hence	ADV
ejpam-5697	143	17	,	,	PUNCT
ejpam-5697	143	18	the	the	DET
ejpam-5697	143	19	inequality∥∥∥mpc	inequality∥∥∥mpc	NOUN
ejpam-5697	143	20	ℏ	ℏ	NOUN
ejpam-5697	143	21	dδ;κ;p	dδ;κ;p	X
ejpam-5697	143	22	a+	a+	PUNCT
ejpam-5697	143	23	g(ξ	g(ξ	PROPN
ejpam-5697	143	24	)	)	PUNCT
ejpam-5697	143	25	∥∥∥	∥∥∥	PROPN
ejpam-5697	143	26	xp	xp	CCONJ
ejpam-5697	143	27	≤	≤	VERB
ejpam-5697	143	28	r(δ	r(δ	NOUN
ejpam-5697	143	29	)	)	PUNCT
ejpam-5697	144	1	1−	1−	NUM
ejpam-5697	144	2	δ	δ	PROPN
ejpam-5697	144	3	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	144	4	+	+	CCONJ
ejpam-5697	144	5	r(δ	r(δ	PROPN
ejpam-5697	144	6	)	)	PUNCT
ejpam-5697	144	7	1−	1−	NUM
ejpam-5697	144	8	δ	δ	PROPN
ejpam-5697	144	9	∥∥∥	∥∥∥	PROPN
ejpam-5697	144	10	peκ,1	peκ,1	NOUN
ejpam-5697	144	11	(	(	PUNCT
ejpam-5697	144	12	−	−	PROPN
ejpam-5697	144	13	ωδ	ωδ	X
ejpam-5697	144	14	(	(	PUNCT
ejpam-5697	144	15	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	144	16	ℏ(a	ℏ(a	NOUN
ejpam-5697	144	17	)	)	PUNCT
ejpam-5697	144	18	)	)	PUNCT
ejpam-5697	144	19	κ	κ	X
ejpam-5697	144	20	)	)	PUNCT
ejpam-5697	144	21	g(a	g(a	PROPN
ejpam-5697	144	22	)	)	PUNCT
ejpam-5697	144	23	∥∥∥	∥∥∥	PROPN
ejpam-5697	144	24	xp	xp	NOUN
ejpam-5697	144	25	+	+	CCONJ
ejpam-5697	144	26	r(δ	r(δ	PROPN
ejpam-5697	144	27	)	)	PUNCT
ejpam-5697	144	28	1−	1−	NUM
ejpam-5697	145	1	δ	δ	PROPN
ejpam-5697	145	2	∞∑	∞∑	ADJ
ejpam-5697	145	3	n=0	n=0	NUM
ejpam-5697	145	4	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	145	5	p)|n	p)|n	NOUN
ejpam-5697	145	6	|γ(κn+	|γ(κn+	VERB
ejpam-5697	145	7	κ)|	κ)|	PROPN
ejpam-5697	145	8	|	|	ADV
ejpam-5697	145	9	(	(	PUNCT
ejpam-5697	145	10	ℏ(θ)−	ℏ(θ)−	ADJ
ejpam-5697	145	11	ℏ(a	ℏ(a	NOUN
ejpam-5697	145	12	)	)	PUNCT
ejpam-5697	145	13	)	)	PUNCT
ejpam-5697	145	14	|(κn+κ−1	|(κn+κ−1	PROPN
ejpam-5697	145	15	)	)	PUNCT
ejpam-5697	145	16	(	(	PUNCT
ejpam-5697	145	17	κn+	κn+	PROPN
ejpam-5697	145	18	κ−	κ−	PROPN
ejpam-5697	145	19	1	1	NUM
ejpam-5697	145	20	)	)	PUNCT
ejpam-5697	145	21	||f	||f	PROPN
ejpam-5697	145	22	||xp	||xp	NOUN
ejpam-5697	145	23	,	,	PUNCT
ejpam-5697	145	24	(	(	PUNCT
ejpam-5697	145	25	4	4	X
ejpam-5697	145	26	)	)	PUNCT
ejpam-5697	145	27	holds	hold	VERB
ejpam-5697	145	28	for	for	ADP
ejpam-5697	145	29	1	1	NUM
ejpam-5697	145	30	≤	≤	NOUN
ejpam-5697	145	31	r1	r1	PROPN
ejpam-5697	145	32	<	<	X
ejpam-5697	145	33	∞.	∞.	PROPN
ejpam-5697	145	34	proof	proof	NOUN
ejpam-5697	145	35	.	.	PUNCT
ejpam-5697	146	1	through	through	ADP
ejpam-5697	146	2	application	application	NOUN
ejpam-5697	146	3	of	of	ADP
ejpam-5697	146	4	definition	definition	NOUN
ejpam-5697	146	5	8	8	NUM
ejpam-5697	146	6	,	,	PUNCT
ejpam-5697	146	7	we	we	PRON
ejpam-5697	146	8	have∥∥∥mpc	have∥∥∥mpc	VERB
ejpam-5697	146	9	ℏ	ℏ	NOUN
ejpam-5697	146	10	dδ;κ;p	dδ;κ;p	X
ejpam-5697	146	11	a+	a+	PUNCT
ejpam-5697	146	12	g(ξ	g(ξ	PROPN
ejpam-5697	146	13	)	)	PUNCT
ejpam-5697	146	14	∥∥∥	∥∥∥	PROPN
ejpam-5697	146	15	xp	xp	CCONJ
ejpam-5697	146	16	≤	≤	VERB
ejpam-5697	146	17	r(δ	r(δ	NOUN
ejpam-5697	146	18	)	)	PUNCT
ejpam-5697	147	1	1−	1−	NUM
ejpam-5697	147	2	δ	δ	PROPN
ejpam-5697	147	3	∥∥∥g(ξ)−	∥∥∥g(ξ)−	PROPN
ejpam-5697	147	4	eκ,1	eκ,1	PROPN
ejpam-5697	147	5	(	(	PUNCT
ejpam-5697	147	6	−	−	PROPN
ejpam-5697	147	7	ωδ	ωδ	X
ejpam-5697	147	8	(	(	PUNCT
ejpam-5697	147	9	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	147	10	ℏ(a	ℏ(a	NOUN
ejpam-5697	147	11	)	)	PUNCT
ejpam-5697	147	12	)	)	PUNCT
ejpam-5697	147	13	κ	κ	X
ejpam-5697	147	14	)	)	PUNCT
ejpam-5697	147	15	g(a	g(a	PROPN
ejpam-5697	147	16	)	)	PUNCT
ejpam-5697	147	17	∥∥∥	∥∥∥	PROPN
ejpam-5697	147	18	xp	xp	NOUN
ejpam-5697	147	19	+	+	CCONJ
ejpam-5697	147	20	r(δ	r(δ	PROPN
ejpam-5697	147	21	)	)	PUNCT
ejpam-5697	147	22	1−	1−	NUM
ejpam-5697	147	23	δ	δ	PROPN
ejpam-5697	147	24	∥∥∥∥ωδ(ln	∥∥∥∥ωδ(ln	NOUN
ejpam-5697	147	25	p	p	NOUN
ejpam-5697	147	26	)	)	PUNCT
ejpam-5697	147	27	∫	∫	PROPN
ejpam-5697	148	1	ξ	ξ	PROPN
ejpam-5697	148	2	a	a	DET
ejpam-5697	148	3	(	(	PUNCT
ejpam-5697	148	4	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	148	5	ℏ(ζ))κ−1	ℏ(ζ))κ−1	X
ejpam-5697	148	6	peκ	peκ	NOUN
ejpam-5697	148	7	,	,	PUNCT
ejpam-5697	148	8	κ	κ	X
ejpam-5697	148	9	(	(	PUNCT
ejpam-5697	148	10	−	−	PROPN
ejpam-5697	148	11	ωδ	ωδ	X
ejpam-5697	148	12	(	(	PUNCT
ejpam-5697	148	13	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	148	14	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	148	15	)	)	PUNCT
ejpam-5697	148	16	)	)	PUNCT
ejpam-5697	149	1	κ)ℏ′(ζ)g(ζ)dζ∥∥∥∥	κ)ℏ′(ζ)g(ζ)dζ∥∥∥∥	PROPN
ejpam-5697	149	2	xp	xp	CCONJ
ejpam-5697	149	3	≤	≤	VERB
ejpam-5697	149	4	r(δ	r(δ	NOUN
ejpam-5697	149	5	)	)	PUNCT
ejpam-5697	149	6	1−	1−	NUM
ejpam-5697	149	7	δ	δ	PROPN
ejpam-5697	149	8	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	149	9	+	+	CCONJ
ejpam-5697	149	10	r(δ	r(δ	PROPN
ejpam-5697	149	11	)	)	PUNCT
ejpam-5697	149	12	1−	1−	NUM
ejpam-5697	149	13	δ	δ	PROPN
ejpam-5697	149	14	∥∥∥eκ	∥∥∥eκ	PROPN
ejpam-5697	149	15	,	,	PUNCT
ejpam-5697	149	16	κ	κ	X
ejpam-5697	149	17	(	(	PUNCT
ejpam-5697	149	18	−	−	PROPN
ejpam-5697	149	19	ωδ	ωδ	X
ejpam-5697	149	20	(	(	PUNCT
ejpam-5697	149	21	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	149	22	ℏ(a	ℏ(a	NOUN
ejpam-5697	149	23	)	)	PUNCT
ejpam-5697	149	24	)	)	PUNCT
ejpam-5697	149	25	κ	κ	X
ejpam-5697	149	26	)	)	PUNCT
ejpam-5697	149	27	g(a	g(a	PROPN
ejpam-5697	149	28	)	)	PUNCT
ejpam-5697	149	29	∥∥∥	∥∥∥	PROPN
ejpam-5697	149	30	xp	xp	NOUN
ejpam-5697	149	31	+	+	CCONJ
ejpam-5697	149	32	r(δ	r(δ	PROPN
ejpam-5697	149	33	)	)	PUNCT
ejpam-5697	149	34	1−	1−	NUM
ejpam-5697	149	35	δ	δ	PROPN
ejpam-5697	149	36	∥∥∥∥ωδ(ln	∥∥∥∥ωδ(ln	NOUN
ejpam-5697	149	37	p	p	NOUN
ejpam-5697	149	38	)	)	PUNCT
ejpam-5697	149	39	∫	∫	PROPN
ejpam-5697	150	1	ξ	ξ	PROPN
ejpam-5697	150	2	a	a	PRON
ejpam-5697	150	3	(	(	PUNCT
ejpam-5697	150	4	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	150	5	ℏ(ζ))κ−1eκ	ℏ(ζ))κ−1eκ	PROPN
ejpam-5697	150	6	,	,	PUNCT
ejpam-5697	150	7	κ	κ	X
ejpam-5697	150	8	(	(	PUNCT
ejpam-5697	150	9	−	−	PROPN
ejpam-5697	150	10	ωδ	ωδ	X
ejpam-5697	150	11	(	(	PUNCT
ejpam-5697	150	12	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	150	13	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	150	14	)	)	PUNCT
ejpam-5697	150	15	)	)	PUNCT
ejpam-5697	151	1	κ)ℏ′(ζ)g(ζ)dζ∥∥∥∥	κ)ℏ′(ζ)g(ζ)dζ∥∥∥∥	PROPN
ejpam-5697	151	2	xp	xp	INTJ
ejpam-5697	151	3	.	.	PUNCT
ejpam-5697	152	1	(	(	PUNCT
ejpam-5697	152	2	5	5	X
ejpam-5697	152	3	)	)	PUNCT
ejpam-5697	152	4	consider∥∥∥∥∫	consider∥∥∥∥∫	PROPN
ejpam-5697	152	5	ξ	ξ	SYM
ejpam-5697	152	6	0	0	PUNCT
ejpam-5697	152	7	(	(	PUNCT
ejpam-5697	152	8	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	152	9	ℏ(ζ))δ−1	ℏ(ζ))δ−1	X
ejpam-5697	152	10	peκ	peκ	NOUN
ejpam-5697	152	11	,	,	PUNCT
ejpam-5697	152	12	κ	κ	X
ejpam-5697	152	13	(	(	PUNCT
ejpam-5697	152	14	−	−	PROPN
ejpam-5697	152	15	ωδ	ωδ	X
ejpam-5697	152	16	(	(	PUNCT
ejpam-5697	152	17	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	152	18	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	152	19	)	)	PUNCT
ejpam-5697	152	20	)	)	PUNCT
ejpam-5697	153	1	κ)ℏ′(ζ)g(ζ)dζ∥∥∥∥	κ)ℏ′(ζ)g(ζ)dζ∥∥∥∥	PROPN
ejpam-5697	153	2	xp	xp	NOUN
ejpam-5697	153	3	=	=	PUNCT
ejpam-5697	154	1	∞∑	∞∑	PRON
ejpam-5697	154	2	n=0	n=0	NUM
ejpam-5697	154	3	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	154	4	p)|n	p)|n	NOUN
ejpam-5697	154	5	|γ(κn+	|γ(κn+	VERB
ejpam-5697	154	6	κ)|	κ)|	PROPN
ejpam-5697	154	7	∥∥∥∥∫	∥∥∥∥∫	VERB
ejpam-5697	154	8	ξ	ξ	PROPN
ejpam-5697	154	9	0	0	NUM
ejpam-5697	154	10	(	(	PUNCT
ejpam-5697	154	11	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	154	12	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	154	13	)	)	PUNCT
ejpam-5697	154	14	)	)	PUNCT
ejpam-5697	155	1	κn+κ−1ℏ′(ζ)g(ζ)dζ	κn+κ−1ℏ′(ζ)g(ζ)dζ	NUM
ejpam-5697	155	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-5697	155	3	xp	xp	NOUN
ejpam-5697	155	4	=	=	PUNCT
ejpam-5697	156	1	∞∑	∞∑	PRON
ejpam-5697	156	2	n=0	n=0	NUM
ejpam-5697	156	3	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	156	4	p)|n	p)|n	NOUN
ejpam-5697	156	5	|γ(κn+	|γ(κn+	VERB
ejpam-5697	156	6	κ)|	κ)|	PROPN
ejpam-5697	156	7	(	(	PUNCT
ejpam-5697	156	8	∫	∫	PROPN
ejpam-5697	156	9	θ	θ	PROPN
ejpam-5697	156	10	a	a	PRON
ejpam-5697	156	11	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5697	156	12	∫	∫	PROPN
ejpam-5697	156	13	ξ	ξ	PROPN
ejpam-5697	156	14	a	a	DET
ejpam-5697	156	15	(	(	PUNCT
ejpam-5697	156	16	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	156	17	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	156	18	)	)	PUNCT
ejpam-5697	156	19	)	)	PUNCT
ejpam-5697	157	1	κn+κ−1ℏ′(ζ)g(ζ)dζ	κn+κ−1ℏ′(ζ)g(ζ)dζ	NUM
ejpam-5697	157	2	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-5697	157	3	r1	r1	NOUN
ejpam-5697	157	4	ℏ′(ξ)du	ℏ′(ξ)du	PROPN
ejpam-5697	157	5	)	)	PUNCT
ejpam-5697	157	6	1	1	NUM
ejpam-5697	157	7	r1	r1	NOUN
ejpam-5697	157	8	.	.	PUNCT
ejpam-5697	158	1	substituting	substitute	VERB
ejpam-5697	158	2	λ	λ	PROPN
ejpam-5697	158	3	=	=	SYM
ejpam-5697	158	4	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	158	5	)	)	PUNCT
ejpam-5697	158	6	and	and	CCONJ
ejpam-5697	158	7	ρ	ρ	NOUN
ejpam-5697	158	8	=	=	SYM
ejpam-5697	158	9	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	158	10	)	)	PUNCT
ejpam-5697	158	11	,	,	PUNCT
ejpam-5697	158	12	we	we	PRON
ejpam-5697	158	13	obtain	obtain	VERB
ejpam-5697	158	14	=	=	PUNCT
ejpam-5697	158	15	∞∑	∞∑	NUM
ejpam-5697	158	16	n=0	n=0	NUM
ejpam-5697	158	17	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	158	18	p)|n	p)|n	NOUN
ejpam-5697	158	19	|γ(κn+	|γ(κn+	VERB
ejpam-5697	158	20	κ)|	κ)|	PROPN
ejpam-5697	158	21	(	(	PUNCT
ejpam-5697	158	22	∫	∫	PROPN
ejpam-5697	158	23	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	158	24	)	)	PUNCT
ejpam-5697	158	25	ℏ(a	ℏ(a	NOUN
ejpam-5697	158	26	)	)	PUNCT
ejpam-5697	159	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5697	159	2	∫	∫	PROPN
ejpam-5697	159	3	ℏ(ξ	ℏ(ξ	NOUN
ejpam-5697	159	4	)	)	PUNCT
ejpam-5697	159	5	ℏ(a	ℏ(a	NOUN
ejpam-5697	159	6	)	)	PUNCT
ejpam-5697	160	1	|	|	CCONJ
ejpam-5697	160	2	(	(	PUNCT
ejpam-5697	160	3	ρ−	ρ−	PROPN
ejpam-5697	160	4	λ	λ	PROPN
ejpam-5697	160	5	)	)	PUNCT
ejpam-5697	161	1	|κn+κ−1g(ℏ−1(λ))dλ	|κn+κ−1g(ℏ−1(λ))dλ	PROPN
ejpam-5697	161	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5697	161	3	r1	r1	PROPN
ejpam-5697	161	4	dρ	dρ	PROPN
ejpam-5697	161	5	)	)	PUNCT
ejpam-5697	161	6	1	1	NUM
ejpam-5697	161	7	r1	r1	NOUN
ejpam-5697	161	8	.	.	PUNCT
ejpam-5697	162	1	the	the	DET
ejpam-5697	162	2	generalised	generalise	VERB
ejpam-5697	162	3	minkowski	minkowski	PROPN
ejpam-5697	162	4	’s	’s	PART
ejpam-5697	162	5	inequality	inequality	NOUN
ejpam-5697	162	6	gives	give	VERB
ejpam-5697	162	7	us	we	PRON
ejpam-5697	162	8	the	the	DET
ejpam-5697	162	9	following	follow	VERB
ejpam-5697	162	10	≤	≤	NOUN
ejpam-5697	162	11	∞∑	∞∑	NUM
ejpam-5697	162	12	n=0	n=0	NUM
ejpam-5697	162	13	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	162	14	p)|n	p)|n	NOUN
ejpam-5697	162	15	|γ(κn+	|γ(κn+	VERB
ejpam-5697	162	16	κ)|	κ)|	PROPN
ejpam-5697	162	17	(	(	PUNCT
ejpam-5697	162	18	∫	∫	PROPN
ejpam-5697	162	19	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	162	20	)	)	PUNCT
ejpam-5697	162	21	ℏ(a	ℏ(a	NOUN
ejpam-5697	162	22	)	)	PUNCT
ejpam-5697	162	23	|g(ℏ−1(λ))|r1	|g(ℏ−1(λ))|r1	PROPN
ejpam-5697	162	24	∫	∫	PROPN
ejpam-5697	162	25	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	162	26	)	)	PUNCT
ejpam-5697	163	1	λ	λ	NOUN
ejpam-5697	163	2	|	|	ADV
ejpam-5697	163	3	(	(	PUNCT
ejpam-5697	163	4	ρ−	ρ−	NOUN
ejpam-5697	163	5	λ	λ	PROPN
ejpam-5697	163	6	)	)	PUNCT
ejpam-5697	163	7	|(κn+κ−1)r1dρ	|(κn+κ−1)r1dρ	NOUN
ejpam-5697	163	8	)	)	PUNCT
ejpam-5697	163	9	1	1	NUM
ejpam-5697	163	10	r1	r1	PROPN
ejpam-5697	163	11	dλ	dλ	PROPN
ejpam-5697	163	12	gauhar	gauhar	PROPN
ejpam-5697	163	13	rahman	rahman	PROPN
ejpam-5697	163	14	et	et	PROPN
ejpam-5697	163	15	al	al	PROPN
ejpam-5697	163	16	.	.	PUNCT
ejpam-5697	163	17	/	/	SYM
ejpam-5697	163	18	eur	eur	PROPN
ejpam-5697	163	19	.	.	PUNCT
ejpam-5697	164	1	j.	j.	PROPN
ejpam-5697	164	2	pure	pure	PROPN
ejpam-5697	164	3	appl	appl	PROPN
ejpam-5697	164	4	.	.	PROPN
ejpam-5697	164	5	math	math	PROPN
ejpam-5697	164	6	,	,	PUNCT
ejpam-5697	164	7	18	18	NUM
ejpam-5697	164	8	(	(	PUNCT
ejpam-5697	164	9	1	1	NUM
ejpam-5697	164	10	)	)	PUNCT
ejpam-5697	164	11	(	(	PUNCT
ejpam-5697	164	12	2025	2025	NUM
ejpam-5697	164	13	)	)	PUNCT
ejpam-5697	164	14	,	,	PUNCT
ejpam-5697	164	15	5697	5697	NUM
ejpam-5697	164	16	7	7	NUM
ejpam-5697	164	17	of	of	ADP
ejpam-5697	164	18	26	26	NUM
ejpam-5697	164	19	=	=	NOUN
ejpam-5697	164	20	∞∑	∞∑	NUM
ejpam-5697	164	21	n=0	n=0	NUM
ejpam-5697	164	22	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	164	23	p)|n	p)|n	NOUN
ejpam-5697	164	24	|γ(κn+	|γ(κn+	VERB
ejpam-5697	164	25	κ)|	κ)|	PROPN
ejpam-5697	164	26	(	(	PUNCT
ejpam-5697	164	27	∫	∫	PROPN
ejpam-5697	164	28	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	164	29	)	)	PUNCT
ejpam-5697	164	30	ℏ(a	ℏ(a	NOUN
ejpam-5697	164	31	)	)	PUNCT
ejpam-5697	165	1	|g(ℏ−1(λ))|r1	|g(ℏ−1(λ))|r1	PROPN
ejpam-5697	165	2	|	|	ADV
ejpam-5697	165	3	(	(	PUNCT
ejpam-5697	165	4	ℏ(θ)−	ℏ(θ)−	PROPN
ejpam-5697	165	5	λ	λ	PROPN
ejpam-5697	165	6	)	)	PUNCT
ejpam-5697	165	7	|(κn+κ−1)r1	|(κn+κ−1)r1	NOUN
ejpam-5697	165	8	+	+	PRON
ejpam-5697	165	9	1	1	NUM
ejpam-5697	165	10	(	(	PUNCT
ejpam-5697	165	11	κn+	κn+	PROPN
ejpam-5697	165	12	κ−	κ−	PROPN
ejpam-5697	165	13	1)r1	1)r1	NUM
ejpam-5697	165	14	+	+	CCONJ
ejpam-5697	165	15	1	1	NUM
ejpam-5697	165	16	)	)	SYM
ejpam-5697	165	17	1	1	NUM
ejpam-5697	165	18	r1	r1	PROPN
ejpam-5697	165	19	dλ	dλ	NOUN
ejpam-5697	165	20	.	.	PUNCT
ejpam-5697	166	1	with	with	ADP
ejpam-5697	166	2	the	the	DET
ejpam-5697	166	3	help	help	NOUN
ejpam-5697	166	4	of	of	ADP
ejpam-5697	166	5	hölder	hölder	NOUN
ejpam-5697	166	6	inequality	inequality	NOUN
ejpam-5697	166	7	,	,	PUNCT
ejpam-5697	166	8	we	we	PRON
ejpam-5697	166	9	have	have	VERB
ejpam-5697	166	10	≤	≤	NOUN
ejpam-5697	167	1	∞∑	∞∑	NUM
ejpam-5697	167	2	n=0	n=0	NUM
ejpam-5697	167	3	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	167	4	p)|n	p)|n	NOUN
ejpam-5697	167	5	|γ(κn+	|γ(κn+	VERB
ejpam-5697	167	6	κ)|	κ)|	PROPN
ejpam-5697	167	7	(	(	PUNCT
ejpam-5697	167	8	∫	∫	PROPN
ejpam-5697	167	9	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	167	10	)	)	PUNCT
ejpam-5697	167	11	ℏ(a	ℏ(a	NOUN
ejpam-5697	167	12	)	)	PUNCT
ejpam-5697	167	13	|g(ℏ−1(λ))|r1dλ	|g(ℏ−1(λ))|r1dλ	PUNCT
ejpam-5697	167	14	)	)	PUNCT
ejpam-5697	167	15	1	1	NUM
ejpam-5697	167	16	r1	r1	PROPN
ejpam-5697	167	17	(	(	PUNCT
ejpam-5697	167	18	∫	∫	PROPN
ejpam-5697	167	19	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	167	20	)	)	PUNCT
ejpam-5697	167	21	ℏ(a	ℏ(a	NOUN
ejpam-5697	167	22	)	)	PUNCT
ejpam-5697	167	23	(	(	PUNCT
ejpam-5697	167	24	|	|	ADV
ejpam-5697	167	25	(	(	PUNCT
ejpam-5697	167	26	ℏ(θ)−	ℏ(θ)−	PROPN
ejpam-5697	167	27	λ	λ	PROPN
ejpam-5697	167	28	)	)	PUNCT
ejpam-5697	167	29	|(κn+κ−1)r1	|(κn+κ−1)r1	NOUN
ejpam-5697	167	30	+	+	PRON
ejpam-5697	167	31	1	1	NUM
ejpam-5697	167	32	(	(	PUNCT
ejpam-5697	167	33	δn−	δn−	PROPN
ejpam-5697	167	34	1)r1	1)r1	PROPN
ejpam-5697	167	35	+	+	SYM
ejpam-5697	167	36	1	1	X
ejpam-5697	167	37	)	)	PUNCT
ejpam-5697	167	38	s1	s1	PROPN
ejpam-5697	167	39	r1	r1	PROPN
ejpam-5697	167	40	dλ	dλ	PROPN
ejpam-5697	167	41	)	)	PUNCT
ejpam-5697	167	42	1	1	NUM
ejpam-5697	167	43	s1	s1	NOUN
ejpam-5697	167	44	≤	≤	NOUN
ejpam-5697	167	45	∞∑	∞∑	NUM
ejpam-5697	167	46	n=0	n=0	NUM
ejpam-5697	167	47	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	167	48	p)|n	p)|n	NOUN
ejpam-5697	167	49	|γ(κn+	|γ(κn+	VERB
ejpam-5697	167	50	κ)|	κ)|	PROPN
ejpam-5697	167	51	(	(	PUNCT
ejpam-5697	167	52	∫	∫	PROPN
ejpam-5697	167	53	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	167	54	)	)	PUNCT
ejpam-5697	167	55	ℏ(a	ℏ(a	NOUN
ejpam-5697	167	56	)	)	PUNCT
ejpam-5697	167	57	|g(ℏ−1(λ))|r1dλ	|g(ℏ−1(λ))|r1dλ	PUNCT
ejpam-5697	167	58	)	)	PUNCT
ejpam-5697	167	59	1	1	NUM
ejpam-5697	167	60	r1	r1	NOUN
ejpam-5697	167	61	|	|	ADV
ejpam-5697	167	62	(	(	PUNCT
ejpam-5697	167	63	ℏ(θ)−	ℏ(θ)−	ADJ
ejpam-5697	167	64	ℏ(a	ℏ(a	NOUN
ejpam-5697	167	65	)	)	PUNCT
ejpam-5697	167	66	)	)	PUNCT
ejpam-5697	167	67	|(κn+κ−1	|(κn+κ−1	PROPN
ejpam-5697	167	68	)	)	PUNCT
ejpam-5697	167	69	(	(	PUNCT
ejpam-5697	167	70	κn+	κn+	PROPN
ejpam-5697	167	71	κ−	κ−	PROPN
ejpam-5697	167	72	1	1	NUM
ejpam-5697	167	73	)	)	PUNCT
ejpam-5697	167	74	,	,	PUNCT
ejpam-5697	167	75	where	where	SCONJ
ejpam-5697	167	76	1	1	NUM
ejpam-5697	167	77	r1	r1	NOUN
ejpam-5697	167	78	+	+	CCONJ
ejpam-5697	167	79	1	1	NUM
ejpam-5697	167	80	s1	s1	NOUN
ejpam-5697	167	81	=	=	SYM
ejpam-5697	167	82	1	1	X
ejpam-5697	167	83	.	.	PUNCT
ejpam-5697	167	84	by	by	ADP
ejpam-5697	167	85	substituting	substitute	VERB
ejpam-5697	167	86	ℏ−1(λ	ℏ−1(λ	NOUN
ejpam-5697	167	87	)	)	PUNCT
ejpam-5697	167	88	=	=	SYM
ejpam-5697	167	89	t	t	PROPN
ejpam-5697	167	90	,	,	PUNCT
ejpam-5697	167	91	we	we	PRON
ejpam-5697	167	92	obtain	obtain	VERB
ejpam-5697	167	93	=	=	PUNCT
ejpam-5697	167	94	∞∑	∞∑	NUM
ejpam-5697	167	95	n=0	n=0	NUM
ejpam-5697	167	96	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	167	97	p)|n	p)|n	NOUN
ejpam-5697	167	98	|γ(κn+	|γ(κn+	VERB
ejpam-5697	167	99	κ)|	κ)|	PROPN
ejpam-5697	168	1	|	|	ADV
ejpam-5697	168	2	(	(	PUNCT
ejpam-5697	168	3	ℏ(θ)−	ℏ(θ)−	ADJ
ejpam-5697	168	4	ℏ(a	ℏ(a	NOUN
ejpam-5697	168	5	)	)	PUNCT
ejpam-5697	168	6	)	)	PUNCT
ejpam-5697	168	7	|(κn+κ−1	|(κn+κ−1	PROPN
ejpam-5697	168	8	)	)	PUNCT
ejpam-5697	168	9	(	(	PUNCT
ejpam-5697	168	10	κn+	κn+	PROPN
ejpam-5697	168	11	κ−	κ−	PROPN
ejpam-5697	168	12	1	1	NUM
ejpam-5697	168	13	)	)	PUNCT
ejpam-5697	168	14	∫	∫	PROPN
ejpam-5697	168	15	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	168	16	)	)	PUNCT
ejpam-5697	168	17	ℏ(a	ℏ(a	NOUN
ejpam-5697	168	18	)	)	PUNCT
ejpam-5697	168	19	|g(ζ)|r1ℏ′(ζ)dζ	|g(ζ)|r1ℏ′(ζ)dζ	X
ejpam-5697	169	1	=	=	PUNCT
ejpam-5697	169	2	∞∑	∞∑	ADJ
ejpam-5697	169	3	n=0	n=0	NUM
ejpam-5697	169	4	|ωδ(ln	|ωδ(ln	NOUN
ejpam-5697	169	5	p)|n	p)|n	NOUN
ejpam-5697	169	6	|γ(κn+	|γ(κn+	VERB
ejpam-5697	169	7	κ)|	κ)|	PROPN
ejpam-5697	169	8	|	|	ADV
ejpam-5697	169	9	(	(	PUNCT
ejpam-5697	169	10	ℏ(θ)−	ℏ(θ)−	ADJ
ejpam-5697	169	11	ℏ(a	ℏ(a	NOUN
ejpam-5697	169	12	)	)	PUNCT
ejpam-5697	169	13	)	)	PUNCT
ejpam-5697	169	14	|(κn+κ−1	|(κn+κ−1	PROPN
ejpam-5697	169	15	)	)	PUNCT
ejpam-5697	169	16	(	(	PUNCT
ejpam-5697	169	17	κn+	κn+	PROPN
ejpam-5697	169	18	κ−	κ−	PROPN
ejpam-5697	169	19	1	1	NUM
ejpam-5697	169	20	)	)	PUNCT
ejpam-5697	169	21	||f	||f	PROPN
ejpam-5697	169	22	||xp	||xp	NOUN
ejpam-5697	169	23	.	.	PUNCT
ejpam-5697	170	1	by	by	ADP
ejpam-5697	170	2	using	use	VERB
ejpam-5697	170	3	this	this	DET
ejpam-5697	170	4	equation	equation	NOUN
ejpam-5697	170	5	in	in	ADP
ejpam-5697	170	6	(	(	PUNCT
ejpam-5697	170	7	5	5	NUM
ejpam-5697	170	8	)	)	PUNCT
ejpam-5697	170	9	,	,	PUNCT
ejpam-5697	170	10	we	we	PRON
ejpam-5697	170	11	have	have	VERB
ejpam-5697	170	12	the	the	DET
ejpam-5697	170	13	result	result	NOUN
ejpam-5697	170	14	(	(	PUNCT
ejpam-5697	170	15	4	4	NUM
ejpam-5697	170	16	)	)	PUNCT
ejpam-5697	170	17	.	.	PUNCT
ejpam-5697	171	1	now	now	ADV
ejpam-5697	171	2	,	,	PUNCT
ejpam-5697	171	3	we	we	PRON
ejpam-5697	171	4	present	present	VERB
ejpam-5697	171	5	some	some	DET
ejpam-5697	171	6	illustrative	illustrative	ADJ
ejpam-5697	171	7	examples	example	NOUN
ejpam-5697	171	8	of	of	ADP
ejpam-5697	171	9	new	new	ADJ
ejpam-5697	171	10	fractional	fractional	ADJ
ejpam-5697	171	11	derivative	derivative	ADJ
ejpam-5697	171	12	operator	operator	NOUN
ejpam-5697	171	13	.	.	PUNCT
ejpam-5697	171	14	example	example	NOUN
ejpam-5697	172	1	1	1	NUM
ejpam-5697	172	2	.	.	X
ejpam-5697	172	3	assume	assume	VERB
ejpam-5697	172	4	0	0	PUNCT
ejpam-5697	172	5	<	<	X
ejpam-5697	172	6	δ	δ	X
ejpam-5697	172	7	<	<	X
ejpam-5697	172	8	1	1	NUM
ejpam-5697	172	9	and	and	CCONJ
ejpam-5697	172	10	a	a	DET
ejpam-5697	172	11	constant	constant	ADJ
ejpam-5697	172	12	function	function	NOUN
ejpam-5697	172	13	g(ζ	g(ζ	PROPN
ejpam-5697	172	14	)	)	PUNCT
ejpam-5697	173	1	=	=	SYM
ejpam-5697	173	2	c.	c.	NOUN
ejpam-5697	173	3	the	the	DET
ejpam-5697	173	4	definition	definition	NOUN
ejpam-5697	173	5	8	8	NUM
ejpam-5697	173	6	allows	allow	VERB
ejpam-5697	173	7	us	we	PRON
ejpam-5697	173	8	to	to	PART
ejpam-5697	173	9	write	write	VERB
ejpam-5697	173	10	(	(	PUNCT
ejpam-5697	173	11	mpc	mpc	NOUN
ejpam-5697	173	12	ℏ	ℏ	NOUN
ejpam-5697	173	13	dδ;κ;p	dδ;κ;p	NOUN
ejpam-5697	173	14	a+	a+	PUNCT
ejpam-5697	173	15	c)(ζ	c)(ζ	ADV
ejpam-5697	173	16	)	)	PUNCT
ejpam-5697	173	17	=	=	SYM
ejpam-5697	173	18	r(δ	r(δ	PROPN
ejpam-5697	173	19	)	)	PUNCT
ejpam-5697	173	20	1−	1−	NUM
ejpam-5697	173	21	δ	δ	PROPN
ejpam-5697	173	22	[	[	PUNCT
ejpam-5697	173	23	c	c	NOUN
ejpam-5697	173	24	−	−	PROPN
ejpam-5697	173	25	peκ,1	peκ,1	NOUN
ejpam-5697	173	26	(	(	PUNCT
ejpam-5697	173	27	−	−	PROPN
ejpam-5697	173	28	ωδ	ωδ	X
ejpam-5697	173	29	(	(	PUNCT
ejpam-5697	173	30	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	173	31	ℏ(a	ℏ(a	NOUN
ejpam-5697	173	32	)	)	PUNCT
ejpam-5697	173	33	)	)	PUNCT
ejpam-5697	173	34	κ	κ	X
ejpam-5697	173	35	)	)	PUNCT
ejpam-5697	173	36	c	c	NOUN
ejpam-5697	173	37	−	−	PROPN
ejpam-5697	173	38	ωδ(ln	ωδ(ln	NOUN
ejpam-5697	173	39	p	p	NOUN
ejpam-5697	173	40	)	)	PUNCT
ejpam-5697	173	41	∫	∫	PROPN
ejpam-5697	174	1	ξ	ξ	PROPN
ejpam-5697	174	2	a	a	PRON
ejpam-5697	174	3	(	(	PUNCT
ejpam-5697	174	4	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	174	5	ℏ(ζ))κ−1	ℏ(ζ))κ−1	X
ejpam-5697	174	6	peκ	peκ	NOUN
ejpam-5697	174	7	,	,	PUNCT
ejpam-5697	174	8	κ	κ	X
ejpam-5697	174	9	(	(	PUNCT
ejpam-5697	174	10	−	−	PROPN
ejpam-5697	174	11	ωδ	ωδ	X
ejpam-5697	174	12	(	(	PUNCT
ejpam-5697	174	13	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	174	14	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	174	15	)	)	PUNCT
ejpam-5697	174	16	)	)	PUNCT
ejpam-5697	174	17	κ)ℏ′(ζ)cdζ	κ)ℏ′(ζ)cdζ	NOUN
ejpam-5697	174	18	]	]	PUNCT
ejpam-5697	174	19	=	=	PUNCT
ejpam-5697	174	20	r(δ	r(δ	PROPN
ejpam-5697	174	21	)	)	PUNCT
ejpam-5697	174	22	1−	1−	NUM
ejpam-5697	174	23	δ	δ	PROPN
ejpam-5697	174	24	[	[	PUNCT
ejpam-5697	174	25	c	c	NOUN
ejpam-5697	174	26	−	−	PROPN
ejpam-5697	174	27	peκ,1	peκ,1	NOUN
ejpam-5697	174	28	(	(	PUNCT
ejpam-5697	174	29	−	−	PROPN
ejpam-5697	174	30	ωδ	ωδ	X
ejpam-5697	174	31	(	(	PUNCT
ejpam-5697	174	32	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	174	33	ℏ(a	ℏ(a	NOUN
ejpam-5697	174	34	)	)	PUNCT
ejpam-5697	174	35	)	)	PUNCT
ejpam-5697	174	36	κ	κ	X
ejpam-5697	174	37	)	)	PUNCT
ejpam-5697	174	38	c	c	NOUN
ejpam-5697	174	39	−	−	PROPN
ejpam-5697	174	40	ωδ(ln	ωδ(ln	PROPN
ejpam-5697	174	41	p	p	NOUN
ejpam-5697	174	42	)	)	PUNCT
ejpam-5697	174	43	(	(	PUNCT
ejpam-5697	174	44	−1	−1	NOUN
ejpam-5697	174	45	ωδ(ln	ωδ(ln	NOUN
ejpam-5697	174	46	p	p	NOUN
ejpam-5697	174	47	)	)	PUNCT
ejpam-5697	174	48	(	(	PUNCT
ejpam-5697	174	49	peκ,1	peκ,1	NOUN
ejpam-5697	174	50	(	(	PUNCT
ejpam-5697	174	51	−	−	PROPN
ejpam-5697	174	52	ωδ	ωδ	X
ejpam-5697	174	53	(	(	PUNCT
ejpam-5697	174	54	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	174	55	ℏ(a+	ℏ(a+	PROPN
ejpam-5697	174	56	)	)	PUNCT
ejpam-5697	174	57	)	)	PUNCT
ejpam-5697	174	58	κ)−	κ)−	PROPN
ejpam-5697	174	59	1	1	NUM
ejpam-5697	174	60	)	)	PUNCT
ejpam-5697	174	61	)	)	PUNCT
ejpam-5697	175	1	c	c	NOUN
ejpam-5697	175	2	(	(	PUNCT
ejpam-5697	175	3	mabc	mabc	NOUN
ejpam-5697	175	4	ℏ	ℏ	PROPN
ejpam-5697	175	5	dδ	dδ	ADP
ejpam-5697	175	6	0c)(ζ	0c)(ζ	NUM
ejpam-5697	175	7	)	)	PUNCT
ejpam-5697	176	1	=	=	SYM
ejpam-5697	176	2	0	0	X
ejpam-5697	176	3	.	.	PUNCT
ejpam-5697	177	1	this	this	PRON
ejpam-5697	177	2	shows	show	VERB
ejpam-5697	177	3	that	that	SCONJ
ejpam-5697	177	4	the	the	DET
ejpam-5697	177	5	differentiation	differentiation	NOUN
ejpam-5697	177	6	of	of	ADP
ejpam-5697	177	7	a	a	DET
ejpam-5697	177	8	constant	constant	ADJ
ejpam-5697	177	9	is	be	AUX
ejpam-5697	177	10	zero	zero	NUM
ejpam-5697	177	11	.	.	PUNCT
ejpam-5697	177	12	example	example	NOUN
ejpam-5697	178	1	2	2	NUM
ejpam-5697	178	2	.	.	PUNCT
ejpam-5697	179	1	if	if	SCONJ
ejpam-5697	179	2	we	we	PRON
ejpam-5697	179	3	choose	choose	VERB
ejpam-5697	179	4	g(ξ	g(ξ	PROPN
ejpam-5697	179	5	)	)	PUNCT
ejpam-5697	180	1	=	=	PRON
ejpam-5697	180	2	(	(	PUNCT
ejpam-5697	180	3	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	180	4	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	180	5	)	)	PUNCT
ejpam-5697	180	6	)	)	PUNCT
ejpam-5697	181	1	ρ	ρ	PROPN
ejpam-5697	181	2	,	,	PUNCT
ejpam-5697	181	3	then	then	ADV
ejpam-5697	181	4	we	we	PRON
ejpam-5697	181	5	have	have	VERB
ejpam-5697	181	6	mpc	mpc	PROPN
ejpam-5697	181	7	ℏ	ℏ	PROPN
ejpam-5697	181	8	dδ;η;p	dδ;η;p	NOUN
ejpam-5697	181	9	a+	a+	PUNCT
ejpam-5697	181	10	g(ξ	g(ξ	PROPN
ejpam-5697	181	11	)	)	PUNCT
ejpam-5697	181	12	=	=	SYM
ejpam-5697	181	13	r(δ	r(δ	PROPN
ejpam-5697	181	14	)	)	PUNCT
ejpam-5697	181	15	1−	1−	NUM
ejpam-5697	182	1	δ	δ	NOUN
ejpam-5697	182	2	∫	∫	PROPN
ejpam-5697	182	3	ξ	ξ	PROPN
ejpam-5697	182	4	a	a	DET
ejpam-5697	182	5	peκ,1	peκ,1	NOUN
ejpam-5697	182	6	(	(	PUNCT
ejpam-5697	182	7	−	−	PROPN
ejpam-5697	182	8	ωδ	ωδ	X
ejpam-5697	182	9	(	(	PUNCT
ejpam-5697	182	10	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	182	11	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	182	12	)	)	PUNCT
ejpam-5697	182	13	)	)	PUNCT
ejpam-5697	182	14	κ	κ	X
ejpam-5697	182	15	)	)	PUNCT
ejpam-5697	182	16	d	d	X
ejpam-5697	182	17	dζ	dζ	PROPN
ejpam-5697	182	18	(	(	PUNCT
ejpam-5697	182	19	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	182	20	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	182	21	)	)	PUNCT
ejpam-5697	182	22	)	)	PUNCT
ejpam-5697	183	1	ρ	ρ	PROPN
ejpam-5697	183	2	dζ	dζ	PROPN
ejpam-5697	183	3	gauhar	gauhar	PROPN
ejpam-5697	183	4	rahman	rahman	PROPN
ejpam-5697	183	5	et	et	PROPN
ejpam-5697	183	6	al	al	PROPN
ejpam-5697	183	7	.	.	PUNCT
ejpam-5697	183	8	/	/	SYM
ejpam-5697	183	9	eur	eur	PROPN
ejpam-5697	183	10	.	.	PUNCT
ejpam-5697	184	1	j.	j.	PROPN
ejpam-5697	184	2	pure	pure	PROPN
ejpam-5697	184	3	appl	appl	PROPN
ejpam-5697	184	4	.	.	PROPN
ejpam-5697	184	5	math	math	PROPN
ejpam-5697	184	6	,	,	PUNCT
ejpam-5697	184	7	18	18	NUM
ejpam-5697	184	8	(	(	PUNCT
ejpam-5697	184	9	1	1	NUM
ejpam-5697	184	10	)	)	PUNCT
ejpam-5697	184	11	(	(	PUNCT
ejpam-5697	184	12	2025	2025	NUM
ejpam-5697	184	13	)	)	PUNCT
ejpam-5697	184	14	,	,	PUNCT
ejpam-5697	184	15	5697	5697	NUM
ejpam-5697	184	16	8	8	NUM
ejpam-5697	184	17	of	of	ADP
ejpam-5697	184	18	26	26	NUM
ejpam-5697	184	19	κ	κ	NOUN
ejpam-5697	184	20	=	=	NOUN
ejpam-5697	184	21	0.2	0.2	NUM
ejpam-5697	184	22	κ	κ	NOUN
ejpam-5697	184	23	=	=	SYM
ejpam-5697	184	24	0.5	0.5	NUM
ejpam-5697	184	25	κ	κ	NOUN
ejpam-5697	184	26	=	=	NOUN
ejpam-5697	184	27	0.8	0.8	NUM
ejpam-5697	184	28	figure	figure	NOUN
ejpam-5697	184	29	1	1	NUM
ejpam-5697	184	30	:	:	PUNCT
ejpam-5697	184	31	the	the	DET
ejpam-5697	184	32	graphical	graphical	ADJ
ejpam-5697	184	33	representation	representation	NOUN
ejpam-5697	184	34	of	of	ADP
ejpam-5697	184	35	absolute	absolute	ADJ
ejpam-5697	184	36	value	value	NOUN
ejpam-5697	184	37	of	of	ADP
ejpam-5697	184	38	(	(	PUNCT
ejpam-5697	184	39	6	6	NUM
ejpam-5697	184	40	)	)	PUNCT
ejpam-5697	184	41	corresponding	correspond	VERB
ejpam-5697	184	42	to	to	ADP
ejpam-5697	184	43	choice	choice	NOUN
ejpam-5697	184	44	0	0	NUM
ejpam-5697	184	45	≤	≤	NUM
ejpam-5697	184	46	ξ	ξ	X
ejpam-5697	184	47	≤	≤	NUM
ejpam-5697	184	48	1	1	NUM
ejpam-5697	184	49	.	.	PUNCT
ejpam-5697	185	1	=	=	SYM
ejpam-5697	185	2	−ρr(δ	−ρr(δ	NOUN
ejpam-5697	185	3	)	)	PUNCT
ejpam-5697	186	1	1−	1−	NUM
ejpam-5697	186	2	δ	δ	PROPN
ejpam-5697	186	3	∞∑	∞∑	NOUN
ejpam-5697	186	4	n=0	n=0	NUM
ejpam-5697	186	5	(	(	PUNCT
ejpam-5697	186	6	ln	ln	ADJ
ejpam-5697	186	7	p)n(−ωδ	p)n(−ωδ	NOUN
ejpam-5697	186	8	)	)	PUNCT
ejpam-5697	186	9	n	n	CCONJ
ejpam-5697	186	10	γ(κn+	γ(κn+	ADP
ejpam-5697	186	11	1	1	NUM
ejpam-5697	186	12	)	)	PUNCT
ejpam-5697	186	13	∫	∫	PROPN
ejpam-5697	187	1	ξ	ξ	PROPN
ejpam-5697	187	2	a	a	PRON
ejpam-5697	187	3	(	(	PUNCT
ejpam-5697	187	4	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	187	5	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	187	6	)	)	PUNCT
ejpam-5697	187	7	)	)	PUNCT
ejpam-5697	187	8	κn+ρ−1ℏ′(ζ)dζ	κn+ρ−1ℏ′(ζ)dζ	PROPN
ejpam-5697	187	9	=	=	SYM
ejpam-5697	187	10	ρr(δ	ρr(δ	X
ejpam-5697	187	11	)	)	PUNCT
ejpam-5697	187	12	1−	1−	NUM
ejpam-5697	188	1	δ	δ	PROPN
ejpam-5697	188	2	∞∑	∞∑	NOUN
ejpam-5697	188	3	n=0	n=0	NUM
ejpam-5697	188	4	(	(	PUNCT
ejpam-5697	188	5	−1)n+1(ln	−1)n+1(ln	X
ejpam-5697	188	6	p)n(ωδ	p)n(ωδ	NOUN
ejpam-5697	188	7	)	)	PUNCT
ejpam-5697	188	8	n	n	CCONJ
ejpam-5697	188	9	γ(κn+	γ(κn+	ADP
ejpam-5697	188	10	1	1	NUM
ejpam-5697	188	11	)	)	PUNCT
ejpam-5697	188	12	(	(	PUNCT
ejpam-5697	188	13	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	188	14	ℏ(a	ℏ(a	NOUN
ejpam-5697	188	15	)	)	PUNCT
ejpam-5697	188	16	)	)	PUNCT
ejpam-5697	189	1	κn+ρ	κn+ρ	PROPN
ejpam-5697	189	2	κn+	κn+	PROPN
ejpam-5697	189	3	ρ	ρ	PROPN
ejpam-5697	189	4	example	example	NOUN
ejpam-5697	189	5	3	3	X
ejpam-5697	189	6	.	.	PUNCT
ejpam-5697	190	1	if	if	SCONJ
ejpam-5697	190	2	we	we	PRON
ejpam-5697	190	3	choose	choose	VERB
ejpam-5697	190	4	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	190	5	)	)	PUNCT
ejpam-5697	190	6	=	=	SYM
ejpam-5697	190	7	ξ	ξ	PROPN
ejpam-5697	190	8	,	,	PUNCT
ejpam-5697	190	9	ρ	ρ	PROPN
ejpam-5697	190	10	=	=	SYM
ejpam-5697	190	11	2	2	NUM
ejpam-5697	190	12	,	,	PUNCT
ejpam-5697	190	13	r(δ	r(δ	NOUN
ejpam-5697	190	14	)	)	PUNCT
ejpam-5697	191	1	=	=	SYM
ejpam-5697	191	2	1	1	NUM
ejpam-5697	191	3	,	,	PUNCT
ejpam-5697	191	4	δ	δ	PROPN
ejpam-5697	191	5	=	=	NOUN
ejpam-5697	191	6	1	1	NUM
ejpam-5697	191	7	2	2	NUM
ejpam-5697	191	8	,	,	PUNCT
ejpam-5697	191	9	a	a	DET
ejpam-5697	191	10	=	=	SYM
ejpam-5697	191	11	0	0	NUM
ejpam-5697	191	12	,	,	PUNCT
ejpam-5697	191	13	ℏ(0	ℏ(0	PROPN
ejpam-5697	191	14	)	)	PUNCT
ejpam-5697	191	15	=	=	SYM
ejpam-5697	191	16	0	0	NUM
ejpam-5697	192	1	and	and	CCONJ
ejpam-5697	192	2	p	p	X
ejpam-5697	192	3	=	=	NOUN
ejpam-5697	192	4	2	2	NUM
ejpam-5697	192	5	in	in	ADP
ejpam-5697	192	6	example	example	NOUN
ejpam-5697	192	7	2	2	NUM
ejpam-5697	192	8	,	,	PUNCT
ejpam-5697	192	9	then	then	ADV
ejpam-5697	192	10	we	we	PRON
ejpam-5697	192	11	have	have	VERB
ejpam-5697	192	12	mpc	mpc	PROPN
ejpam-5697	192	13	ℏ	ℏ	PROPN
ejpam-5697	192	14	dδ;η;p	dδ;η;p	NOUN
ejpam-5697	192	15	a+	a+	PUNCT
ejpam-5697	192	16	f(ξ	f(ξ	PROPN
ejpam-5697	192	17	)	)	PUNCT
ejpam-5697	192	18	=	=	SYM
ejpam-5697	193	1	4	4	NUM
ejpam-5697	193	2	∞∑	∞∑	NUM
ejpam-5697	193	3	n=0	n=0	NUM
ejpam-5697	193	4	(	(	PUNCT
ejpam-5697	193	5	−1)n+1(ln	−1)n+1(ln	PROPN
ejpam-5697	193	6	2)n	2)n	NUM
ejpam-5697	193	7	γ(κn+	γ(κn+	NOUN
ejpam-5697	193	8	1	1	NUM
ejpam-5697	193	9	)	)	PUNCT
ejpam-5697	193	10	(	(	PUNCT
ejpam-5697	193	11	ξ)κn+2	ξ)κn+2	X
ejpam-5697	193	12	κn+	κn+	PROPN
ejpam-5697	193	13	2	2	NUM
ejpam-5697	193	14	.	.	PUNCT
ejpam-5697	194	1	(	(	PUNCT
ejpam-5697	194	2	6	6	NUM
ejpam-5697	194	3	)	)	PUNCT
ejpam-5697	194	4	the	the	DET
ejpam-5697	194	5	graphical	graphical	ADJ
ejpam-5697	194	6	representation	representation	NOUN
ejpam-5697	194	7	of	of	ADP
ejpam-5697	194	8	(	(	PUNCT
ejpam-5697	194	9	6	6	NUM
ejpam-5697	194	10	)	)	PUNCT
ejpam-5697	194	11	for	for	ADP
ejpam-5697	194	12	the	the	DET
ejpam-5697	194	13	choice	choice	NOUN
ejpam-5697	194	14	of	of	ADP
ejpam-5697	194	15	order	order	NOUN
ejpam-5697	194	16	κ	κ	X
ejpam-5697	194	17	=	=	SYM
ejpam-5697	194	18	0.2	0.2	NUM
ejpam-5697	194	19	,	,	PUNCT
ejpam-5697	194	20	0.5	0.5	NUM
ejpam-5697	194	21	,	,	PUNCT
ejpam-5697	194	22	0.8	0.8	NUM
ejpam-5697	194	23	,	,	PUNCT
ejpam-5697	194	24	is	be	AUX
ejpam-5697	194	25	given	give	VERB
ejpam-5697	194	26	by	by	ADP
ejpam-5697	194	27	the	the	DET
ejpam-5697	194	28	following	follow	VERB
ejpam-5697	194	29	graph	graph	NOUN
ejpam-5697	194	30	.	.	PUNCT
ejpam-5697	194	31	example	example	NOUN
ejpam-5697	195	1	4	4	NUM
ejpam-5697	195	2	.	.	PUNCT
ejpam-5697	196	1	if	if	SCONJ
ejpam-5697	196	2	we	we	PRON
ejpam-5697	196	3	choose	choose	VERB
ejpam-5697	196	4	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	196	5	)	)	PUNCT
ejpam-5697	196	6	=	=	PUNCT
ejpam-5697	196	7	ln(ξ	ln(ξ	X
ejpam-5697	197	1	+	+	NOUN
ejpam-5697	197	2	1	1	NUM
ejpam-5697	197	3	)	)	PUNCT
ejpam-5697	197	4	,	,	PUNCT
ejpam-5697	197	5	ρ	ρ	PROPN
ejpam-5697	197	6	=	=	SYM
ejpam-5697	197	7	2	2	NUM
ejpam-5697	197	8	,	,	PUNCT
ejpam-5697	197	9	r(δ	r(δ	NOUN
ejpam-5697	197	10	)	)	PUNCT
ejpam-5697	197	11	=	=	SYM
ejpam-5697	197	12	1	1	NUM
ejpam-5697	197	13	,	,	PUNCT
ejpam-5697	197	14	δ	δ	PROPN
ejpam-5697	197	15	=	=	NOUN
ejpam-5697	197	16	1	1	NUM
ejpam-5697	197	17	2	2	NUM
ejpam-5697	197	18	,	,	PUNCT
ejpam-5697	197	19	a	a	DET
ejpam-5697	197	20	=	=	SYM
ejpam-5697	197	21	0	0	NUM
ejpam-5697	197	22	,	,	PUNCT
ejpam-5697	197	23	ℏ(0	ℏ(0	PROPN
ejpam-5697	197	24	)	)	PUNCT
ejpam-5697	197	25	=	=	SYM
ejpam-5697	197	26	0	0	NUM
ejpam-5697	198	1	and	and	CCONJ
ejpam-5697	198	2	p	p	X
ejpam-5697	198	3	=	=	NOUN
ejpam-5697	198	4	2	2	NUM
ejpam-5697	198	5	in	in	ADP
ejpam-5697	198	6	example	example	NOUN
ejpam-5697	198	7	2	2	NUM
ejpam-5697	198	8	,	,	PUNCT
ejpam-5697	198	9	then	then	ADV
ejpam-5697	198	10	we	we	PRON
ejpam-5697	198	11	have	have	VERB
ejpam-5697	198	12	mpc	mpc	PROPN
ejpam-5697	198	13	ℏ	ℏ	PROPN
ejpam-5697	198	14	dδ;η;p	dδ;η;p	NOUN
ejpam-5697	198	15	a+	a+	PUNCT
ejpam-5697	198	16	f(ξ	f(ξ	PROPN
ejpam-5697	198	17	)	)	PUNCT
ejpam-5697	198	18	=	=	SYM
ejpam-5697	199	1	4	4	NUM
ejpam-5697	199	2	∞∑	∞∑	NUM
ejpam-5697	199	3	n=0	n=0	NUM
ejpam-5697	199	4	(	(	PUNCT
ejpam-5697	199	5	−1)n+1(ln	−1)n+1(ln	PROPN
ejpam-5697	199	6	2)n	2)n	NUM
ejpam-5697	199	7	γ(κn+	γ(κn+	NOUN
ejpam-5697	199	8	1	1	NUM
ejpam-5697	199	9	)	)	PUNCT
ejpam-5697	199	10	(	(	PUNCT
ejpam-5697	199	11	ln(ξ	ln(ξ	X
ejpam-5697	199	12	+	+	CCONJ
ejpam-5697	199	13	1))κn+2	1))κn+2	NUM
ejpam-5697	199	14	κn+	κn+	NOUN
ejpam-5697	199	15	2	2	NUM
ejpam-5697	199	16	.	.	PUNCT
ejpam-5697	200	1	(	(	PUNCT
ejpam-5697	200	2	7	7	X
ejpam-5697	200	3	)	)	PUNCT
ejpam-5697	200	4	the	the	DET
ejpam-5697	200	5	graphical	graphical	ADJ
ejpam-5697	200	6	representation	representation	NOUN
ejpam-5697	200	7	of	of	ADP
ejpam-5697	200	8	(	(	PUNCT
ejpam-5697	200	9	7	7	NUM
ejpam-5697	200	10	)	)	PUNCT
ejpam-5697	200	11	for	for	ADP
ejpam-5697	200	12	the	the	DET
ejpam-5697	200	13	choice	choice	NOUN
ejpam-5697	200	14	of	of	ADP
ejpam-5697	200	15	order	order	NOUN
ejpam-5697	200	16	κ	κ	X
ejpam-5697	200	17	=	=	SYM
ejpam-5697	200	18	0.2	0.2	NUM
ejpam-5697	200	19	,	,	PUNCT
ejpam-5697	200	20	0.5	0.5	NUM
ejpam-5697	200	21	,	,	PUNCT
ejpam-5697	200	22	0.8	0.8	NUM
ejpam-5697	200	23	,	,	PUNCT
ejpam-5697	200	24	is	be	AUX
ejpam-5697	200	25	given	give	VERB
ejpam-5697	200	26	by	by	ADP
ejpam-5697	200	27	the	the	DET
ejpam-5697	200	28	following	follow	VERB
ejpam-5697	200	29	graph	graph	NOUN
ejpam-5697	200	30	example	example	NOUN
ejpam-5697	200	31	5	5	NUM
ejpam-5697	200	32	.	.	PUNCT
ejpam-5697	201	1	if	if	SCONJ
ejpam-5697	201	2	we	we	PRON
ejpam-5697	201	3	choose	choose	VERB
ejpam-5697	201	4	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	201	5	)	)	PUNCT
ejpam-5697	202	1	=	=	PUNCT
ejpam-5697	203	1	√	√	NUM
ejpam-5697	203	2	ξ	ξ	X
ejpam-5697	203	3	+	+	SYM
ejpam-5697	203	4	1	1	NUM
ejpam-5697	203	5	,	,	PUNCT
ejpam-5697	203	6	ζ	ζ	NOUN
ejpam-5697	203	7	=	=	SYM
ejpam-5697	203	8	2	2	NUM
ejpam-5697	203	9	,	,	PUNCT
ejpam-5697	203	10	r(δ	r(δ	NOUN
ejpam-5697	203	11	)	)	PUNCT
ejpam-5697	203	12	=	=	SYM
ejpam-5697	203	13	1	1	NUM
ejpam-5697	203	14	,	,	PUNCT
ejpam-5697	203	15	δ	δ	PROPN
ejpam-5697	203	16	=	=	NOUN
ejpam-5697	203	17	1	1	NUM
ejpam-5697	203	18	2	2	NUM
ejpam-5697	203	19	,	,	PUNCT
ejpam-5697	203	20	a	a	DET
ejpam-5697	203	21	=	=	SYM
ejpam-5697	203	22	0	0	NUM
ejpam-5697	203	23	,	,	PUNCT
ejpam-5697	203	24	ℏ(0	ℏ(0	PROPN
ejpam-5697	203	25	)	)	PUNCT
ejpam-5697	203	26	=	=	SYM
ejpam-5697	203	27	0	0	NUM
ejpam-5697	204	1	and	and	CCONJ
ejpam-5697	204	2	p	p	X
ejpam-5697	204	3	=	=	NOUN
ejpam-5697	204	4	2	2	NUM
ejpam-5697	204	5	in	in	ADP
ejpam-5697	204	6	example	example	NOUN
ejpam-5697	204	7	2	2	NUM
ejpam-5697	204	8	,	,	PUNCT
ejpam-5697	204	9	then	then	ADV
ejpam-5697	204	10	we	we	PRON
ejpam-5697	204	11	have	have	VERB
ejpam-5697	204	12	mpc	mpc	PROPN
ejpam-5697	204	13	ℏ	ℏ	PROPN
ejpam-5697	204	14	dδ;η;p	dδ;η;p	NOUN
ejpam-5697	204	15	a+	a+	PUNCT
ejpam-5697	204	16	f(ξ	f(ξ	PROPN
ejpam-5697	204	17	)	)	PUNCT
ejpam-5697	204	18	=	=	SYM
ejpam-5697	205	1	4	4	NUM
ejpam-5697	205	2	∞∑	∞∑	NUM
ejpam-5697	205	3	n=0	n=0	NUM
ejpam-5697	205	4	(	(	PUNCT
ejpam-5697	205	5	−1)n+1(ln	−1)n+1(ln	PROPN
ejpam-5697	205	6	2)n	2)n	NUM
ejpam-5697	205	7	γ(κn+	γ(κn+	NOUN
ejpam-5697	205	8	1	1	NUM
ejpam-5697	205	9	)	)	PUNCT
ejpam-5697	205	10	(	(	PUNCT
ejpam-5697	205	11	√	√	PROPN
ejpam-5697	205	12	ξ	ξ	X
ejpam-5697	205	13	+	+	PROPN
ejpam-5697	205	14	1)κn+2	1)κn+2	NUM
ejpam-5697	205	15	κn+	κn+	NOUN
ejpam-5697	205	16	2	2	NUM
ejpam-5697	205	17	.	.	PUNCT
ejpam-5697	206	1	(	(	PUNCT
ejpam-5697	206	2	8)	8)	NUM
ejpam-5697	206	3	gauhar	gauhar	NOUN
ejpam-5697	206	4	rahman	rahman	PROPN
ejpam-5697	206	5	et	et	PROPN
ejpam-5697	206	6	al	al	PROPN
ejpam-5697	206	7	.	.	PUNCT
ejpam-5697	206	8	/	/	SYM
ejpam-5697	206	9	eur	eur	PROPN
ejpam-5697	206	10	.	.	PUNCT
ejpam-5697	207	1	j.	j.	PROPN
ejpam-5697	207	2	pure	pure	PROPN
ejpam-5697	207	3	appl	appl	PROPN
ejpam-5697	207	4	.	.	PROPN
ejpam-5697	207	5	math	math	PROPN
ejpam-5697	207	6	,	,	PUNCT
ejpam-5697	207	7	18	18	NUM
ejpam-5697	207	8	(	(	PUNCT
ejpam-5697	207	9	1	1	NUM
ejpam-5697	207	10	)	)	PUNCT
ejpam-5697	207	11	(	(	PUNCT
ejpam-5697	207	12	2025	2025	NUM
ejpam-5697	207	13	)	)	PUNCT
ejpam-5697	207	14	,	,	PUNCT
ejpam-5697	207	15	5697	5697	NUM
ejpam-5697	207	16	9	9	NUM
ejpam-5697	207	17	of	of	ADP
ejpam-5697	207	18	26	26	NUM
ejpam-5697	207	19	0.2	0.2	NUM
ejpam-5697	207	20	0.4	0.4	NUM
ejpam-5697	207	21	0.6	0.6	NUM
ejpam-5697	208	1	0.8	0.8	NUM
ejpam-5697	208	2	1.0	1.0	NUM
ejpam-5697	208	3	ξ	ξ	X
ejpam-5697	208	4	-1.2	-1.2	PUNCT
ejpam-5697	208	5	-1.0	-1.0	PROPN
ejpam-5697	208	6	-0.8	-0.8	PROPN
ejpam-5697	208	7	-0.6	-0.6	PROPN
ejpam-5697	208	8	-0.4	-0.4	X
ejpam-5697	208	9	-0.2	-0.2	NUM
ejpam-5697	208	10	_	_	PUNCT
ejpam-5697	208	11	hbar^mpc	hbar^mpc	NOUN
ejpam-5697	208	12	d	d	X
ejpam-5697	208	13	fhξl	fhξl	X
ejpam-5697	208	14	fractional	fractional	ADJ
ejpam-5697	208	15	operator	operator	NOUN
ejpam-5697	208	16	plot	plot	NOUN
ejpam-5697	208	17	h0	h0	NOUN
ejpam-5697	208	18	<	<	X
ejpam-5697	208	19	ξ	ξ	X
ejpam-5697	208	20	<	<	X
ejpam-5697	208	21	1l	1l	NUM
ejpam-5697	208	22	κ	κ	X
ejpam-5697	208	23	=	=	SYM
ejpam-5697	208	24	0.5	0.5	NUM
ejpam-5697	208	25	κ	κ	NOUN
ejpam-5697	208	26	=	=	NOUN
ejpam-5697	208	27	0.2	0.2	NUM
ejpam-5697	208	28	κ	κ	NOUN
ejpam-5697	208	29	=	=	NOUN
ejpam-5697	208	30	0.8	0.8	NUM
ejpam-5697	208	31	figure	figure	NOUN
ejpam-5697	208	32	2	2	NUM
ejpam-5697	208	33	:	:	PUNCT
ejpam-5697	208	34	the	the	DET
ejpam-5697	208	35	2	2	NUM
ejpam-5697	208	36	-	-	PUNCT
ejpam-5697	208	37	dimensional	dimensional	ADJ
ejpam-5697	208	38	graphical	graphical	ADJ
ejpam-5697	208	39	representation	representation	NOUN
ejpam-5697	208	40	of	of	ADP
ejpam-5697	208	41	(	(	PUNCT
ejpam-5697	208	42	6	6	NUM
ejpam-5697	208	43	)	)	PUNCT
ejpam-5697	208	44	corresponding	correspond	VERB
ejpam-5697	208	45	to	to	ADP
ejpam-5697	208	46	choice	choice	NOUN
ejpam-5697	208	47	0	0	NUM
ejpam-5697	208	48	≤	≤	NUM
ejpam-5697	209	1	ξ	ξ	X
ejpam-5697	209	2	≤	≤	NUM
ejpam-5697	209	3	1	1	NUM
ejpam-5697	209	4	.	.	PUNCT
ejpam-5697	210	1	the	the	DET
ejpam-5697	210	2	graphical	graphical	ADJ
ejpam-5697	210	3	representation	representation	NOUN
ejpam-5697	210	4	of	of	ADP
ejpam-5697	210	5	(	(	PUNCT
ejpam-5697	210	6	8)	8)	NUM
ejpam-5697	210	7	for	for	ADP
ejpam-5697	210	8	the	the	DET
ejpam-5697	210	9	choice	choice	NOUN
ejpam-5697	210	10	of	of	ADP
ejpam-5697	210	11	order	order	NOUN
ejpam-5697	210	12	κ	κ	X
ejpam-5697	210	13	=	=	SYM
ejpam-5697	210	14	0.2	0.2	NUM
ejpam-5697	210	15	,	,	PUNCT
ejpam-5697	210	16	0.5	0.5	NUM
ejpam-5697	210	17	,	,	PUNCT
ejpam-5697	210	18	0.8	0.8	NUM
ejpam-5697	210	19	,	,	PUNCT
ejpam-5697	210	20	is	be	AUX
ejpam-5697	210	21	given	give	VERB
ejpam-5697	210	22	by	by	ADP
ejpam-5697	210	23	the	the	DET
ejpam-5697	210	24	following	follow	VERB
ejpam-5697	210	25	graph	graph	NOUN
ejpam-5697	210	26	.	.	PUNCT
ejpam-5697	210	27	example	example	NOUN
ejpam-5697	211	1	6	6	NUM
ejpam-5697	211	2	.	.	PUNCT
ejpam-5697	211	3	suppose	suppose	VERB
ejpam-5697	211	4	that	that	SCONJ
ejpam-5697	211	5	function	function	NOUN
ejpam-5697	211	6	g	g	NOUN
ejpam-5697	211	7	be	be	VERB
ejpam-5697	211	8	piecewise	piecewise	NOUN
ejpam-5697	211	9	continuous	continuous	ADJ
ejpam-5697	211	10	g(ζ	g(ζ	PROPN
ejpam-5697	211	11	)	)	PUNCT
ejpam-5697	212	1	=	=	PRON
ejpam-5697	212	2	{	{	PUNCT
ejpam-5697	212	3	ℏ	ℏ	NOUN
ejpam-5697	212	4	−1	−1	NOUN
ejpam-5697	212	5	2	2	NUM
ejpam-5697	212	6	(	(	PUNCT
ejpam-5697	212	7	ζ	ζ	NOUN
ejpam-5697	212	8	)	)	PUNCT
ejpam-5697	212	9	,	,	PUNCT
ejpam-5697	212	10	ζ	ζ	PROPN
ejpam-5697	212	11	̸=	̸=	PROPN
ejpam-5697	212	12	0	0	NUM
ejpam-5697	212	13	;	;	PUNCT
ejpam-5697	212	14	a	a	DET
ejpam-5697	212	15	,	,	PUNCT
ejpam-5697	212	16	ζ	ζ	NOUN
ejpam-5697	212	17	=	=	SYM
ejpam-5697	212	18	0	0	NUM
ejpam-5697	212	19	.	.	PUNCT
ejpam-5697	213	1	(	(	PUNCT
ejpam-5697	213	2	9	9	X
ejpam-5697	213	3	)	)	PUNCT
ejpam-5697	213	4	putting	put	VERB
ejpam-5697	213	5	a	a	DET
ejpam-5697	213	6	∈	∈	NOUN
ejpam-5697	213	7	r	r	NOUN
ejpam-5697	213	8	\	\	PUNCT
ejpam-5697	213	9	{	{	PUNCT
ejpam-5697	213	10	0	0	NUM
ejpam-5697	213	11	}	}	PUNCT
ejpam-5697	213	12	,	,	PUNCT
ejpam-5697	213	13	now	now	ADV
ejpam-5697	213	14	κ	κ	X
ejpam-5697	213	15	=	=	SYM
ejpam-5697	213	16	1	1	NUM
ejpam-5697	213	17	2	2	NUM
ejpam-5697	213	18	=	=	SYM
ejpam-5697	213	19	δ	δ	PROPN
ejpam-5697	213	20	,	,	PUNCT
ejpam-5697	213	21	ℏ(0	ℏ(0	PROPN
ejpam-5697	213	22	)	)	PUNCT
ejpam-5697	213	23	=	=	SYM
ejpam-5697	213	24	0	0	NUM
ejpam-5697	213	25	,	,	PUNCT
ejpam-5697	213	26	uδ	uδ	NOUN
ejpam-5697	213	27	=	=	SYM
ejpam-5697	213	28	1	1	NUM
ejpam-5697	213	29	,	,	PUNCT
ejpam-5697	213	30	a	a	DET
ejpam-5697	213	31	=	=	SYM
ejpam-5697	213	32	0	0	NUM
ejpam-5697	213	33	and	and	CCONJ
ejpam-5697	213	34	r(δ	r(δ	PROPN
ejpam-5697	213	35	)	)	PUNCT
ejpam-5697	213	36	=	=	PUNCT
ejpam-5697	213	37	1	1	NUM
ejpam-5697	213	38	according	accord	VERB
ejpam-5697	213	39	to	to	ADP
ejpam-5697	213	40	definition	definition	NOUN
ejpam-5697	213	41	8	8	NUM
ejpam-5697	213	42	,	,	PUNCT
ejpam-5697	213	43	we	we	PRON
ejpam-5697	213	44	get	get	VERB
ejpam-5697	213	45	mpc	mpc	PROPN
ejpam-5697	213	46	ℏ	ℏ	PROPN
ejpam-5697	213	47	d	d	PROPN
ejpam-5697	213	48	1	1	NUM
ejpam-5697	213	49	2	2	NUM
ejpam-5697	213	50	;	;	PUNCT
ejpam-5697	213	51	1	1	NUM
ejpam-5697	213	52	2	2	NUM
ejpam-5697	213	53	;	;	PUNCT
ejpam-5697	213	54	p	p	PROPN
ejpam-5697	213	55	0	0	NUM
ejpam-5697	213	56	g(ξ	g(ξ	PROPN
ejpam-5697	213	57	)	)	PUNCT
ejpam-5697	213	58	=	=	SYM
ejpam-5697	213	59	2	2	NUM
ejpam-5697	213	60	[	[	PUNCT
ejpam-5697	213	61	g(ξ)−a	g(ξ)−a	NOUN
ejpam-5697	213	62	pe	pe	PROPN
ejpam-5697	213	63	1	1	NUM
ejpam-5697	213	64	2	2	NUM
ejpam-5697	213	65	,	,	PUNCT
ejpam-5697	213	66	1	1	NUM
ejpam-5697	213	67	(	(	PUNCT
ejpam-5697	213	68	−	−	PROPN
ejpam-5697	213	69	(	(	PUNCT
ejpam-5697	213	70	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	213	71	)	)	PUNCT
ejpam-5697	213	72	)	)	PUNCT
ejpam-5697	213	73	1	1	NUM
ejpam-5697	213	74	2	2	NUM
ejpam-5697	213	75	)	)	PUNCT
ejpam-5697	213	76	−	−	PROPN
ejpam-5697	214	1	ln	ln	ADV
ejpam-5697	214	2	p	p	NOUN
ejpam-5697	214	3	∫	∫	PROPN
ejpam-5697	214	4	ξ	ξ	X
ejpam-5697	214	5	0	0	NUM
ejpam-5697	214	6	(	(	PUNCT
ejpam-5697	214	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	214	8	ℏ(ζ))−	ℏ(ζ))−	NOUN
ejpam-5697	214	9	1	1	NUM
ejpam-5697	214	10	2	2	NUM
ejpam-5697	214	11	pe	pe	PROPN
ejpam-5697	214	12	1	1	NUM
ejpam-5697	214	13	2	2	NUM
ejpam-5697	214	14	,	,	PUNCT
ejpam-5697	214	15	1	1	NUM
ejpam-5697	214	16	2	2	NUM
ejpam-5697	214	17	(	(	PUNCT
ejpam-5697	214	18	−	−	PROPN
ejpam-5697	214	19	(	(	PUNCT
ejpam-5697	214	20	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	214	21	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	214	22	)	)	PUNCT
ejpam-5697	214	23	)	)	PUNCT
ejpam-5697	214	24	1	1	NUM
ejpam-5697	214	25	2	2	NUM
ejpam-5697	214	26	)	)	PUNCT
ejpam-5697	214	27	ℏ′(ζ)ℏ	ℏ′(ζ)ℏ	PROPN
ejpam-5697	214	28	−1	−1	NOUN
ejpam-5697	214	29	2	2	NUM
ejpam-5697	214	30	(	(	PUNCT
ejpam-5697	214	31	ζ)dζ	ζ)dζ	PROPN
ejpam-5697	214	32	]	]	PUNCT
ejpam-5697	214	33	=	=	SYM
ejpam-5697	214	34	2	2	X
ejpam-5697	214	35	[	[	PUNCT
ejpam-5697	214	36	g(ξ)−ae	g(ξ)−ae	PROPN
ejpam-5697	214	37	1	1	NUM
ejpam-5697	214	38	2	2	NUM
ejpam-5697	214	39	,	,	PUNCT
ejpam-5697	214	40	1	1	NUM
ejpam-5697	214	41	(	(	PUNCT
ejpam-5697	214	42	−	−	PROPN
ejpam-5697	214	43	(	(	PUNCT
ejpam-5697	214	44	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	214	45	)	)	PUNCT
ejpam-5697	214	46	)	)	PUNCT
ejpam-5697	214	47	1	1	NUM
ejpam-5697	214	48	2	2	NUM
ejpam-5697	214	49	)	)	PUNCT
ejpam-5697	214	50	−	−	PROPN
ejpam-5697	215	1	ln	ln	ADJ
ejpam-5697	215	2	p	p	NOUN
ejpam-5697	215	3	√	√	PROPN
ejpam-5697	215	4	π	π	INTJ
ejpam-5697	215	5	pe	pe	INTJ
ejpam-5697	215	6	1	1	NUM
ejpam-5697	215	7	2	2	NUM
ejpam-5697	215	8	,	,	PUNCT
ejpam-5697	215	9	1	1	NUM
ejpam-5697	215	10	(	(	PUNCT
ejpam-5697	215	11	−	−	PROPN
ejpam-5697	215	12	(	(	PUNCT
ejpam-5697	215	13	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	215	14	)	)	PUNCT
ejpam-5697	215	15	)	)	PUNCT
ejpam-5697	215	16	1	1	NUM
ejpam-5697	215	17	2	2	NUM
ejpam-5697	215	18	)	)	PUNCT
ejpam-5697	215	19	=	=	SYM
ejpam-5697	215	20	2	2	X
ejpam-5697	215	21	[	[	PUNCT
ejpam-5697	215	22	g(ξ)−	g(ξ)−	PROPN
ejpam-5697	215	23	(	(	PUNCT
ejpam-5697	215	24	a+	a+	PUNCT
ejpam-5697	215	25	ln	ln	PROPN
ejpam-5697	215	26	p	p	NOUN
ejpam-5697	215	27	√	√	NUM
ejpam-5697	215	28	π	π	SYM
ejpam-5697	215	29	)	)	PUNCT
ejpam-5697	215	30	pe	pe	PROPN
ejpam-5697	215	31	1	1	NUM
ejpam-5697	215	32	2	2	NUM
ejpam-5697	215	33	,	,	PUNCT
ejpam-5697	215	34	1	1	NUM
ejpam-5697	215	35	(	(	PUNCT
ejpam-5697	215	36	−	−	PROPN
ejpam-5697	215	37	(	(	PUNCT
ejpam-5697	215	38	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	215	39	)	)	PUNCT
ejpam-5697	215	40	)	)	PUNCT
ejpam-5697	215	41	1	1	NUM
ejpam-5697	215	42	2	2	NUM
ejpam-5697	215	43	)	)	PUNCT
ejpam-5697	215	44	]	]	PUNCT
ejpam-5697	215	45	.	.	PUNCT
ejpam-5697	216	1	(	(	PUNCT
ejpam-5697	216	2	10	10	NUM
ejpam-5697	216	3	)	)	PUNCT
ejpam-5697	216	4	by	by	ADP
ejpam-5697	216	5	using	use	VERB
ejpam-5697	216	6	series	series	NOUN
ejpam-5697	216	7	expansion	expansion	NOUN
ejpam-5697	216	8	of	of	ADP
ejpam-5697	216	9	pe	pe	INTJ
ejpam-5697	216	10	1	1	NUM
ejpam-5697	216	11	2	2	NUM
ejpam-5697	216	12	,	,	PUNCT
ejpam-5697	216	13	1	1	NUM
ejpam-5697	216	14	(	(	PUNCT
ejpam-5697	216	15	−	−	PROPN
ejpam-5697	216	16	(	(	PUNCT
ejpam-5697	216	17	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	216	18	)	)	PUNCT
ejpam-5697	216	19	)	)	PUNCT
ejpam-5697	216	20	1	1	NUM
ejpam-5697	216	21	2	2	NUM
ejpam-5697	216	22	)	)	PUNCT
ejpam-5697	216	23	=	=	SYM
ejpam-5697	217	1	1	1	NUM
ejpam-5697	217	2	+	+	CCONJ
ejpam-5697	217	3	(	(	PUNCT
ejpam-5697	217	4	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	217	5	)	)	PUNCT
ejpam-5697	217	6	)	)	PUNCT
ejpam-5697	217	7	1	1	NUM
ejpam-5697	217	8	2	2	NUM
ejpam-5697	217	9	ln	ln	NOUN
ejpam-5697	217	10	p	p	NOUN
ejpam-5697	217	11	γ	γ	X
ejpam-5697	217	12	(	(	PUNCT
ejpam-5697	217	13	3	3	NUM
ejpam-5697	217	14	2	2	NUM
ejpam-5697	217	15	)	)	PUNCT
ejpam-5697	217	16	+	+	CCONJ
ejpam-5697	217	17	·	·	PUNCT
ejpam-5697	217	18	·	·	PUNCT
ejpam-5697	217	19	·	·	PUNCT
ejpam-5697	217	20	,	,	PUNCT
ejpam-5697	217	21	we	we	PRON
ejpam-5697	217	22	have	have	VERB
ejpam-5697	217	23	pe	pe	PROPN
ejpam-5697	217	24	1	1	NUM
ejpam-5697	217	25	2	2	NUM
ejpam-5697	217	26	,	,	PUNCT
ejpam-5697	217	27	1	1	NUM
ejpam-5697	217	28	(	(	PUNCT
ejpam-5697	217	29	0	0	NUM
ejpam-5697	217	30	)	)	PUNCT
ejpam-5697	217	31	=	=	SYM
ejpam-5697	218	1	1	1	X
ejpam-5697	218	2	.	.	PUNCT
ejpam-5697	219	1	hence	hence	ADV
ejpam-5697	219	2	,	,	PUNCT
ejpam-5697	219	3	we	we	PRON
ejpam-5697	219	4	get	get	VERB
ejpam-5697	219	5	mabc	mabc	ADJ
ejpam-5697	219	6	ℏ	ℏ	PROPN
ejpam-5697	219	7	d	d	NOUN
ejpam-5697	219	8	1	1	NUM
ejpam-5697	219	9	2	2	NUM
ejpam-5697	219	10	;	;	PUNCT
ejpam-5697	219	11	1	1	NUM
ejpam-5697	219	12	2	2	NUM
ejpam-5697	219	13	;	;	PUNCT
ejpam-5697	219	14	p	p	PROPN
ejpam-5697	219	15	0	0	NUM
ejpam-5697	219	16	g(0	g(0	NOUN
ejpam-5697	219	17	)	)	PUNCT
ejpam-5697	219	18	=	=	SYM
ejpam-5697	220	1	−2	−2	NOUN
ejpam-5697	221	1	ln	ln	NOUN
ejpam-5697	221	2	p	p	NOUN
ejpam-5697	222	1	√	√	PROPN
ejpam-5697	222	2	π	π	PROPN
ejpam-5697	222	3	̸=	̸=	PROPN
ejpam-5697	222	4	0	0	NUM
ejpam-5697	222	5	.	.	PUNCT
ejpam-5697	223	1	remark	remark	PROPN
ejpam-5697	223	2	3	3	NUM
ejpam-5697	223	3	.	.	PUNCT
ejpam-5697	223	4	i.	i.	PROPN
ejpam-5697	224	1	if	if	SCONJ
ejpam-5697	224	2	we	we	PRON
ejpam-5697	224	3	put	put	VERB
ejpam-5697	224	4	p	p	NOUN
ejpam-5697	224	5	=	=	SYM
ejpam-5697	224	6	e	e	NOUN
ejpam-5697	224	7	,	,	PUNCT
ejpam-5697	224	8	then	then	ADV
ejpam-5697	224	9	we	we	PRON
ejpam-5697	224	10	get	get	VERB
ejpam-5697	224	11	the	the	DET
ejpam-5697	224	12	result	result	NOUN
ejpam-5697	224	13	proved	prove	VERB
ejpam-5697	224	14	by	by	ADP
ejpam-5697	224	15	huang	huang	PROPN
ejpam-5697	224	16	et	et	PROPN
ejpam-5697	224	17	al	al	PROPN
ejpam-5697	224	18	.	.	PUNCT
ejpam-5697	225	1	[	[	X
ejpam-5697	225	2	7	7	NUM
ejpam-5697	225	3	]	]	PUNCT
ejpam-5697	225	4	.	.	PUNCT
ejpam-5697	226	1	ii	ii	PROPN
ejpam-5697	226	2	.	.	PUNCT
ejpam-5697	227	1	if	if	SCONJ
ejpam-5697	227	2	we	we	PRON
ejpam-5697	227	3	put	put	VERB
ejpam-5697	227	4	p	p	NOUN
ejpam-5697	227	5	=	=	PUNCT
ejpam-5697	227	6	e	e	NOUN
ejpam-5697	227	7	and	and	CCONJ
ejpam-5697	227	8	ℏ(ξ	ℏ(ξ	VERB
ejpam-5697	227	9	)	)	PUNCT
ejpam-5697	227	10	=	=	SYM
ejpam-5697	227	11	ξ	ξ	PROPN
ejpam-5697	227	12	,	,	PUNCT
ejpam-5697	227	13	then	then	ADV
ejpam-5697	227	14	it	it	PRON
ejpam-5697	227	15	reduce	reduce	VERB
ejpam-5697	227	16	to	to	ADP
ejpam-5697	227	17	the	the	DET
ejpam-5697	227	18	example	example	NOUN
ejpam-5697	227	19	solved	solve	VERB
ejpam-5697	227	20	by	by	ADP
ejpam-5697	227	21	al	al	PROPN
ejpam-5697	227	22	-	-	PUNCT
ejpam-5697	227	23	refai	refai	PROPN
ejpam-5697	227	24	et	et	PROPN
ejpam-5697	227	25	al	al	PROPN
ejpam-5697	227	26	.	.	PUNCT
ejpam-5697	228	1	[	[	X
ejpam-5697	228	2	23	23	NUM
ejpam-5697	228	3	]	]	PUNCT
ejpam-5697	228	4	.	.	PUNCT
ejpam-5697	229	1	iii	iii	X
ejpam-5697	229	2	.	.	PUNCT
ejpam-5697	230	1	if	if	SCONJ
ejpam-5697	230	2	we	we	PRON
ejpam-5697	230	3	put	put	VERB
ejpam-5697	230	4	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	230	5	)	)	PUNCT
ejpam-5697	230	6	=	=	SYM
ejpam-5697	230	7	ξ	ξ	PROPN
ejpam-5697	230	8	,	,	PUNCT
ejpam-5697	230	9	then	then	ADV
ejpam-5697	230	10	we	we	PRON
ejpam-5697	230	11	get	get	VERB
ejpam-5697	230	12	the	the	DET
ejpam-5697	230	13	solution	solution	NOUN
ejpam-5697	230	14	of	of	ADP
ejpam-5697	230	15	the	the	DET
ejpam-5697	230	16	problem	problem	NOUN
ejpam-5697	230	17	for	for	ADP
ejpam-5697	230	18	power	power	NOUN
ejpam-5697	230	19	fractional	fractional	ADJ
ejpam-5697	230	20	derivative	derivative	NOUN
ejpam-5697	230	21	defined	define	VERB
ejpam-5697	230	22	by	by	ADP
ejpam-5697	230	23	lotfi	lotfi	PROPN
ejpam-5697	230	24	et	et	PROPN
ejpam-5697	230	25	al	al	PROPN
ejpam-5697	230	26	.	.	PUNCT
ejpam-5697	231	1	[	[	X
ejpam-5697	231	2	11	11	NUM
ejpam-5697	231	3	]	]	PUNCT
ejpam-5697	231	4	.	.	PUNCT
ejpam-5697	232	1	gauhar	gauhar	PROPN
ejpam-5697	232	2	rahman	rahman	PROPN
ejpam-5697	232	3	et	et	PROPN
ejpam-5697	232	4	al	al	PROPN
ejpam-5697	232	5	.	.	PUNCT
ejpam-5697	232	6	/	/	SYM
ejpam-5697	232	7	eur	eur	PROPN
ejpam-5697	232	8	.	.	PUNCT
ejpam-5697	233	1	j.	j.	PROPN
ejpam-5697	233	2	pure	pure	PROPN
ejpam-5697	233	3	appl	appl	PROPN
ejpam-5697	233	4	.	.	PROPN
ejpam-5697	233	5	math	math	PROPN
ejpam-5697	233	6	,	,	PUNCT
ejpam-5697	233	7	18	18	NUM
ejpam-5697	233	8	(	(	PUNCT
ejpam-5697	233	9	1	1	NUM
ejpam-5697	233	10	)	)	PUNCT
ejpam-5697	233	11	(	(	PUNCT
ejpam-5697	233	12	2025	2025	NUM
ejpam-5697	233	13	)	)	PUNCT
ejpam-5697	233	14	,	,	PUNCT
ejpam-5697	233	15	5697	5697	NUM
ejpam-5697	233	16	10	10	NUM
ejpam-5697	233	17	of	of	ADP
ejpam-5697	233	18	26	26	NUM
ejpam-5697	233	19	κ	κ	NOUN
ejpam-5697	233	20	=	=	NOUN
ejpam-5697	233	21	0.2	0.2	NUM
ejpam-5697	233	22	κ	κ	NOUN
ejpam-5697	233	23	=	=	SYM
ejpam-5697	233	24	0.5	0.5	NUM
ejpam-5697	233	25	κ	κ	NOUN
ejpam-5697	233	26	=	=	NOUN
ejpam-5697	233	27	0.8	0.8	NUM
ejpam-5697	233	28	figure	figure	NOUN
ejpam-5697	233	29	3	3	NUM
ejpam-5697	233	30	:	:	PUNCT
ejpam-5697	233	31	the	the	DET
ejpam-5697	233	32	graphical	graphical	ADJ
ejpam-5697	233	33	representation	representation	NOUN
ejpam-5697	233	34	of	of	ADP
ejpam-5697	233	35	absolute	absolute	ADJ
ejpam-5697	233	36	value	value	NOUN
ejpam-5697	233	37	of	of	ADP
ejpam-5697	233	38	(	(	PUNCT
ejpam-5697	233	39	7	7	X
ejpam-5697	233	40	)	)	PUNCT
ejpam-5697	233	41	corresponding	correspond	VERB
ejpam-5697	233	42	to	to	ADP
ejpam-5697	233	43	choice	choice	NOUN
ejpam-5697	233	44	0	0	NUM
ejpam-5697	233	45	≤	≤	NUM
ejpam-5697	234	1	ξ	ξ	X
ejpam-5697	234	2	≤	≤	NUM
ejpam-5697	234	3	1	1	NUM
ejpam-5697	234	4	.	.	PUNCT
ejpam-5697	234	5	definition	definition	NOUN
ejpam-5697	234	6	9	9	NUM
ejpam-5697	234	7	.	.	PUNCT
ejpam-5697	235	1	the	the	DET
ejpam-5697	235	2	modified	modify	VERB
ejpam-5697	235	3	power	power	NOUN
ejpam-5697	235	4	fractional	fractional	ADJ
ejpam-5697	235	5	derivative	derivative	ADJ
ejpam-5697	235	6	operator	operator	NOUN
ejpam-5697	235	7	in	in	ADP
ejpam-5697	235	8	the	the	DET
ejpam-5697	235	9	r	r	NOUN
ejpam-5697	235	10	-	-	PUNCT
ejpam-5697	235	11	l	l	NOUN
ejpam-5697	235	12	sense	sense	NOUN
ejpam-5697	235	13	of	of	ADP
ejpam-5697	235	14	order	order	NOUN
ejpam-5697	235	15	0	0	PUNCT
ejpam-5697	235	16	<	<	X
ejpam-5697	235	17	δ	δ	X
ejpam-5697	235	18	<	<	X
ejpam-5697	235	19	1	1	NUM
ejpam-5697	235	20	,	,	PUNCT
ejpam-5697	235	21	κ	κ	X
ejpam-5697	235	22	>	>	X
ejpam-5697	235	23	0	0	NUM
ejpam-5697	235	24	,	,	PUNCT
ejpam-5697	235	25	and	and	CCONJ
ejpam-5697	235	26	p	p	X
ejpam-5697	235	27	>	>	X
ejpam-5697	235	28	1	1	NUM
ejpam-5697	235	29	with	with	ADP
ejpam-5697	235	30	respect	respect	NOUN
ejpam-5697	235	31	to	to	ADP
ejpam-5697	235	32	another	another	DET
ejpam-5697	235	33	function	function	NOUN
ejpam-5697	235	34	ℏ	ℏ	PROPN
ejpam-5697	235	35	,	,	PUNCT
ejpam-5697	235	36	is	be	AUX
ejpam-5697	235	37	defined	define	VERB
ejpam-5697	235	38	as	as	SCONJ
ejpam-5697	235	39	follows	follow	VERB
ejpam-5697	235	40	,	,	PUNCT
ejpam-5697	235	41	assuming	assume	VERB
ejpam-5697	235	42	g	g	PROPN
ejpam-5697	235	43	is	be	AUX
ejpam-5697	235	44	a	a	DET
ejpam-5697	235	45	continuous	continuous	ADJ
ejpam-5697	235	46	function	function	NOUN
ejpam-5697	235	47	and	and	CCONJ
ejpam-5697	235	48	g′	g′	NOUN
ejpam-5697	235	49	∈	∈	PROPN
ejpam-5697	235	50	l1(0	l1(0	PROPN
ejpam-5697	235	51	,	,	PUNCT
ejpam-5697	235	52	t	t	PROPN
ejpam-5697	235	53	)	)	PUNCT
ejpam-5697	235	54	by	by	ADP
ejpam-5697	235	55	mprl	mprl	ADJ
ejpam-5697	235	56	ℏ	ℏ	ADJ
ejpam-5697	235	57	dδ;κ;p	dδ;κ;p	X
ejpam-5697	235	58	a+	a+	PUNCT
ejpam-5697	235	59	g(ξ	g(ξ	PROPN
ejpam-5697	235	60	)	)	PUNCT
ejpam-5697	235	61	=	=	SYM
ejpam-5697	235	62	r(δ	r(δ	PROPN
ejpam-5697	235	63	)	)	PUNCT
ejpam-5697	236	1	1−	1−	NUM
ejpam-5697	237	1	δ	δ	PROPN
ejpam-5697	237	2	d	d	PROPN
ejpam-5697	237	3	dζ	dζ	PROPN
ejpam-5697	237	4	∫	∫	PROPN
ejpam-5697	237	5	ξ	ξ	PROPN
ejpam-5697	237	6	a	a	DET
ejpam-5697	237	7	peκ,1	peκ,1	NOUN
ejpam-5697	237	8	(	(	PUNCT
ejpam-5697	237	9	−	−	PROPN
ejpam-5697	237	10	ωδ	ωδ	X
ejpam-5697	237	11	(	(	PUNCT
ejpam-5697	237	12	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	237	13	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	237	14	)	)	PUNCT
ejpam-5697	237	15	)	)	PUNCT
ejpam-5697	237	16	κ	κ	X
ejpam-5697	237	17	)	)	PUNCT
ejpam-5697	237	18	g(ζ)dζ	g(ζ)dζ	PROPN
ejpam-5697	237	19	,	,	PUNCT
ejpam-5697	237	20	ζ	ζ	X
ejpam-5697	237	21	≥	≥	NOUN
ejpam-5697	237	22	0	0	NUM
ejpam-5697	237	23	,	,	PUNCT
ejpam-5697	237	24	(	(	PUNCT
ejpam-5697	237	25	11	11	NUM
ejpam-5697	237	26	)	)	PUNCT
ejpam-5697	237	27	where	where	SCONJ
ejpam-5697	237	28	r(δ	r(δ	NOUN
ejpam-5697	237	29	)	)	PUNCT
ejpam-5697	237	30	is	be	AUX
ejpam-5697	237	31	a	a	DET
ejpam-5697	237	32	normalised	normalise	VERB
ejpam-5697	237	33	function	function	NOUN
ejpam-5697	237	34	with	with	ADP
ejpam-5697	237	35	the	the	DET
ejpam-5697	237	36	property	property	NOUN
ejpam-5697	237	37	r(0	r(0	PROPN
ejpam-5697	237	38	)	)	PUNCT
ejpam-5697	237	39	=	=	SYM
ejpam-5697	237	40	r(1	r(1	PROPN
ejpam-5697	237	41	)	)	PUNCT
ejpam-5697	237	42	=	=	SYM
ejpam-5697	238	1	1	1	NUM
ejpam-5697	238	2	,	,	PUNCT
ejpam-5697	238	3	ωδ	ωδ	ADV
ejpam-5697	238	4	=	=	SYM
ejpam-5697	238	5	δ	δ	PROPN
ejpam-5697	238	6	1−δ	1−δ	NUM
ejpam-5697	238	7	,	,	PUNCT
ejpam-5697	238	8	and	and	CCONJ
ejpam-5697	238	9	ℏ	ℏ	PROPN
ejpam-5697	238	10	is	be	AUX
ejpam-5697	238	11	a	a	DET
ejpam-5697	238	12	strictly	strictly	ADV
ejpam-5697	238	13	rising	rise	VERB
ejpam-5697	238	14	function	function	NOUN
ejpam-5697	238	15	.	.	PUNCT
ejpam-5697	239	1	remark	remark	PROPN
ejpam-5697	239	2	4	4	NUM
ejpam-5697	239	3	.	.	PUNCT
ejpam-5697	239	4	i.	i.	PROPN
ejpam-5697	240	1	if	if	SCONJ
ejpam-5697	240	2	we	we	PRON
ejpam-5697	240	3	substitute	substitute	VERB
ejpam-5697	240	4	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	240	5	)	)	PUNCT
ejpam-5697	241	1	=	=	SYM
ejpam-5697	241	2	ξ	ξ	PROPN
ejpam-5697	241	3	,	,	PUNCT
ejpam-5697	241	4	κ	κ	X
ejpam-5697	241	5	=	=	SYM
ejpam-5697	241	6	δ	δ	PROPN
ejpam-5697	241	7	and	and	CCONJ
ejpam-5697	241	8	p	p	NOUN
ejpam-5697	241	9	=	=	PUNCT
ejpam-5697	241	10	e	e	X
ejpam-5697	241	11	in	in	ADP
ejpam-5697	241	12	(	(	PUNCT
ejpam-5697	241	13	11	11	NUM
ejpam-5697	241	14	)	)	PUNCT
ejpam-5697	241	15	,	,	PUNCT
ejpam-5697	241	16	then	then	ADV
ejpam-5697	241	17	we	we	PRON
ejpam-5697	241	18	get	get	VERB
ejpam-5697	241	19	the	the	DET
ejpam-5697	241	20	well	well	ADV
ejpam-5697	241	21	-	-	PUNCT
ejpam-5697	241	22	known	know	VERB
ejpam-5697	241	23	definition	definition	NOUN
ejpam-5697	241	24	atangana	atangana	PROPN
ejpam-5697	241	25	-	-	PUNCT
ejpam-5697	241	26	baleanu	baleanu	ADJ
ejpam-5697	241	27	fractional	fractional	ADJ
ejpam-5697	241	28	derivative	derivative	ADJ
ejpam-5697	241	29	operator	operator	NOUN
ejpam-5697	241	30	in	in	ADP
ejpam-5697	241	31	the	the	DET
ejpam-5697	241	32	r	r	NOUN
ejpam-5697	241	33	-	-	PUNCT
ejpam-5697	241	34	l	l	NOUN
ejpam-5697	241	35	sense	sense	NOUN
ejpam-5697	241	36	.	.	PUNCT
ejpam-5697	242	1	ii	ii	PROPN
ejpam-5697	242	2	.	.	PUNCT
ejpam-5697	243	1	if	if	SCONJ
ejpam-5697	243	2	we	we	PRON
ejpam-5697	243	3	substitute	substitute	VERB
ejpam-5697	243	4	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	243	5	)	)	PUNCT
ejpam-5697	244	1	=	=	SYM
ejpam-5697	244	2	ξ	ξ	NOUN
ejpam-5697	244	3	,	,	PUNCT
ejpam-5697	244	4	in	in	ADP
ejpam-5697	244	5	(	(	PUNCT
ejpam-5697	244	6	11	11	NUM
ejpam-5697	244	7	)	)	PUNCT
ejpam-5697	244	8	,	,	PUNCT
ejpam-5697	244	9	then	then	ADV
ejpam-5697	244	10	we	we	PRON
ejpam-5697	244	11	get	get	VERB
ejpam-5697	244	12	definition	definition	NOUN
ejpam-5697	244	13	of	of	ADP
ejpam-5697	244	14	power	power	NOUN
ejpam-5697	244	15	fractional	fractional	ADJ
ejpam-5697	244	16	derivative	derivative	NOUN
ejpam-5697	244	17	in	in	ADP
ejpam-5697	244	18	r	r	NOUN
ejpam-5697	244	19	-	-	PUNCT
ejpam-5697	244	20	l	l	NOUN
ejpam-5697	244	21	sense	sense	NOUN
ejpam-5697	244	22	defined	define	VERB
ejpam-5697	244	23	by	by	ADP
ejpam-5697	244	24	lotfi	lotfi	PROPN
ejpam-5697	244	25	et	et	PROPN
ejpam-5697	244	26	al	al	PROPN
ejpam-5697	244	27	.	.	PUNCT
ejpam-5697	245	1	[	[	X
ejpam-5697	245	2	11	11	NUM
ejpam-5697	245	3	]	]	PUNCT
ejpam-5697	245	4	.	.	PUNCT
ejpam-5697	246	1	remark	remark	PROPN
ejpam-5697	246	2	5	5	NUM
ejpam-5697	246	3	.	.	PUNCT
ejpam-5697	247	1	the	the	DET
ejpam-5697	247	2	modified	modify	VERB
ejpam-5697	247	3	power	power	NOUN
ejpam-5697	247	4	fractional	fractional	ADJ
ejpam-5697	247	5	derivative	derivative	NOUN
ejpam-5697	247	6	in	in	ADP
ejpam-5697	247	7	r	r	NOUN
ejpam-5697	247	8	-	-	PUNCT
ejpam-5697	247	9	l	l	NOUN
ejpam-5697	247	10	sense	sense	NOUN
ejpam-5697	247	11	satisfies	satisfy	VERB
ejpam-5697	247	12	the	the	DET
ejpam-5697	247	13	following	follow	VERB
ejpam-5697	247	14	property	property	NOUN
ejpam-5697	247	15	mprl	mprl	PROPN
ejpam-5697	247	16	ℏ	ℏ	PROPN
ejpam-5697	247	17	d0;κ;p	d0;κ;p	X
ejpam-5697	247	18	a+	a+	PUNCT
ejpam-5697	247	19	g(ξ	g(ξ	PROPN
ejpam-5697	247	20	)	)	PUNCT
ejpam-5697	248	1	=	=	SYM
ejpam-5697	248	2	g(ξ	g(ξ	PROPN
ejpam-5697	248	3	)	)	PUNCT
ejpam-5697	248	4	.	.	PUNCT
ejpam-5697	249	1	theorem	theorem	NOUN
ejpam-5697	249	2	2	2	NUM
ejpam-5697	249	3	.	.	PUNCT
ejpam-5697	250	1	the	the	DET
ejpam-5697	250	2	modified	modify	VERB
ejpam-5697	250	3	fractional	fractional	ADJ
ejpam-5697	250	4	derivative	derivative	NOUN
ejpam-5697	250	5	in	in	ADP
ejpam-5697	250	6	both	both	CCONJ
ejpam-5697	250	7	caputo	caputo	PROPN
ejpam-5697	250	8	and	and	CCONJ
ejpam-5697	250	9	r	r	PROPN
ejpam-5697	250	10	-	-	PUNCT
ejpam-5697	250	11	l	l	NOUN
ejpam-5697	250	12	senses	sense	NOUN
ejpam-5697	250	13	satisfy	satisfy	VERB
ejpam-5697	250	14	the	the	DET
ejpam-5697	250	15	property	property	NOUN
ejpam-5697	250	16	of	of	ADP
ejpam-5697	250	17	linearity	linearity	NOUN
ejpam-5697	250	18	for	for	ADP
ejpam-5697	250	19	all	all	DET
ejpam-5697	250	20	α	α	NOUN
ejpam-5697	250	21	,	,	PUNCT
ejpam-5697	250	22	λ	λ	PROPN
ejpam-5697	250	23	and	and	CCONJ
ejpam-5697	250	24	f	f	NOUN
ejpam-5697	250	25	,	,	PUNCT
ejpam-5697	250	26	g	g	PROPN
ejpam-5697	250	27	∈	∈	PROPN
ejpam-5697	250	28	l1(a	l1(a	ADP
ejpam-5697	250	29	,	,	PUNCT
ejpam-5697	250	30	b	b	NOUN
ejpam-5697	250	31	)	)	PUNCT
ejpam-5697	250	32	.	.	PUNCT
ejpam-5697	251	1	proof	proof	NOUN
ejpam-5697	251	2	.	.	PUNCT
ejpam-5697	252	1	one	one	PRON
ejpam-5697	252	2	can	can	AUX
ejpam-5697	252	3	easily	easily	ADV
ejpam-5697	252	4	prove	prove	VERB
ejpam-5697	252	5	that	that	SCONJ
ejpam-5697	252	6	mpc	mpc	NOUN
ejpam-5697	252	7	ℏ	ℏ	NOUN
ejpam-5697	252	8	dδ;κ;p	dδ;κ;p	X
ejpam-5697	252	9	a+	a+	PUNCT
ejpam-5697	252	10	(	(	PUNCT
ejpam-5697	252	11	αg(ξ	αg(ξ	NUM
ejpam-5697	252	12	)	)	PUNCT
ejpam-5697	252	13	+	+	NUM
ejpam-5697	252	14	λg(ξ	λg(ξ	NOUN
ejpam-5697	252	15	)	)	PUNCT
ejpam-5697	252	16	)	)	PUNCT
ejpam-5697	253	1	=	=	PUNCT
ejpam-5697	253	2	αmpc	αmpc	NOUN
ejpam-5697	253	3	ℏ	ℏ	NOUN
ejpam-5697	253	4	dδ;κ;p	dδ;κ;p	NOUN
ejpam-5697	253	5	a+	a+	PUNCT
ejpam-5697	253	6	g(ξ	g(ξ	PROPN
ejpam-5697	253	7	)	)	PUNCT
ejpam-5697	254	1	+	+	CCONJ
ejpam-5697	254	2	λmpc	λmpc	PRON
ejpam-5697	254	3	ℏ	ℏ	NOUN
ejpam-5697	254	4	dδ;κ;p	dδ;κ;p	NOUN
ejpam-5697	254	5	a+	a+	PUNCT
ejpam-5697	254	6	g(ξ	g(ξ	PROPN
ejpam-5697	254	7	)	)	PUNCT
ejpam-5697	254	8	,	,	PUNCT
ejpam-5697	254	9	and	and	CCONJ
ejpam-5697	254	10	mprl	mprl	VERB
ejpam-5697	254	11	ℏ	ℏ	ADJ
ejpam-5697	254	12	dδ;κ;p	dδ;κ;p	X
ejpam-5697	254	13	a+	a+	PUNCT
ejpam-5697	254	14	(	(	PUNCT
ejpam-5697	254	15	αg(ξ	αg(ξ	NUM
ejpam-5697	254	16	)	)	PUNCT
ejpam-5697	254	17	+	+	NUM
ejpam-5697	254	18	λg(ξ	λg(ξ	NOUN
ejpam-5697	254	19	)	)	PUNCT
ejpam-5697	254	20	)	)	PUNCT
ejpam-5697	255	1	=	=	PUNCT
ejpam-5697	255	2	αmprl	αmprl	X
ejpam-5697	255	3	ℏ	ℏ	NOUN
ejpam-5697	255	4	dδ;κ;p	dδ;κ;p	X
ejpam-5697	255	5	a+	a+	PUNCT
ejpam-5697	255	6	g(ξ	g(ξ	PROPN
ejpam-5697	255	7	)	)	PUNCT
ejpam-5697	255	8	+	+	CCONJ
ejpam-5697	255	9	λmprl	λmprl	NOUN
ejpam-5697	255	10	ℏ	ℏ	NOUN
ejpam-5697	255	11	dδ;κ;p	dδ;κ;p	X
ejpam-5697	255	12	a+	a+	PUNCT
ejpam-5697	255	13	g(ξ	g(ξ	PROPN
ejpam-5697	255	14	)	)	PUNCT
ejpam-5697	255	15	.	.	PUNCT
ejpam-5697	256	1	gauhar	gauhar	PROPN
ejpam-5697	256	2	rahman	rahman	PROPN
ejpam-5697	256	3	et	et	PROPN
ejpam-5697	256	4	al	al	PROPN
ejpam-5697	256	5	.	.	PUNCT
ejpam-5697	256	6	/	/	SYM
ejpam-5697	256	7	eur	eur	PROPN
ejpam-5697	256	8	.	.	PUNCT
ejpam-5697	257	1	j.	j.	PROPN
ejpam-5697	257	2	pure	pure	PROPN
ejpam-5697	257	3	appl	appl	PROPN
ejpam-5697	257	4	.	.	PROPN
ejpam-5697	257	5	math	math	PROPN
ejpam-5697	257	6	,	,	PUNCT
ejpam-5697	257	7	18	18	NUM
ejpam-5697	257	8	(	(	PUNCT
ejpam-5697	257	9	1	1	NUM
ejpam-5697	257	10	)	)	PUNCT
ejpam-5697	257	11	(	(	PUNCT
ejpam-5697	257	12	2025	2025	NUM
ejpam-5697	257	13	)	)	PUNCT
ejpam-5697	257	14	,	,	PUNCT
ejpam-5697	257	15	5697	5697	NUM
ejpam-5697	257	16	11	11	NUM
ejpam-5697	257	17	of	of	ADP
ejpam-5697	257	18	26	26	NUM
ejpam-5697	257	19	0.2	0.2	NUM
ejpam-5697	257	20	0.4	0.4	NUM
ejpam-5697	257	21	0.6	0.6	NUM
ejpam-5697	257	22	0.8	0.8	NUM
ejpam-5697	257	23	1.0	1.0	NUM
ejpam-5697	257	24	ξ	ξ	PROPN
ejpam-5697	257	25	-0.6	-0.6	X
ejpam-5697	257	26	-0.5	-0.5	PROPN
ejpam-5697	257	27	-0.4	-0.4	PROPN
ejpam-5697	257	28	-0.3	-0.3	PROPN
ejpam-5697	257	29	-0.2	-0.2	PROPN
ejpam-5697	257	30	-0.1	-0.1	PROPN
ejpam-5697	257	31	_	_	PRON
ejpam-5697	257	32	hbar^mpc	hbar^mpc	NOUN
ejpam-5697	257	33	d	d	X
ejpam-5697	257	34	fhξl	fhξl	X
ejpam-5697	257	35	fractional	fractional	ADJ
ejpam-5697	257	36	operator	operator	NOUN
ejpam-5697	257	37	plot	plot	NOUN
ejpam-5697	257	38	with	with	ADP
ejpam-5697	257	39	hhξl	hhξl	NOUN
ejpam-5697	257	40	=	=	SYM
ejpam-5697	257	41	loghξ+1l	loghξ+1l	NUM
ejpam-5697	257	42	κ	κ	NOUN
ejpam-5697	257	43	=	=	PUNCT
ejpam-5697	257	44	0.2	0.2	NUM
ejpam-5697	257	45	κ	κ	NOUN
ejpam-5697	257	46	=	=	SYM
ejpam-5697	257	47	0.5	0.5	NUM
ejpam-5697	257	48	κ	κ	NOUN
ejpam-5697	257	49	=	=	NOUN
ejpam-5697	257	50	0.8	0.8	NUM
ejpam-5697	257	51	figure	figure	NOUN
ejpam-5697	257	52	4	4	NUM
ejpam-5697	257	53	:	:	PUNCT
ejpam-5697	257	54	the	the	DET
ejpam-5697	257	55	2	2	NUM
ejpam-5697	257	56	-	-	PUNCT
ejpam-5697	257	57	dimensional	dimensional	ADJ
ejpam-5697	257	58	graphical	graphical	ADJ
ejpam-5697	257	59	representation	representation	NOUN
ejpam-5697	257	60	of	of	ADP
ejpam-5697	257	61	(	(	PUNCT
ejpam-5697	257	62	7	7	X
ejpam-5697	257	63	)	)	PUNCT
ejpam-5697	257	64	corresponding	correspond	VERB
ejpam-5697	257	65	to	to	ADP
ejpam-5697	257	66	choice	choice	NOUN
ejpam-5697	257	67	0	0	NUM
ejpam-5697	257	68	≤	≤	NUM
ejpam-5697	258	1	ξ	ξ	X
ejpam-5697	258	2	≤	≤	NUM
ejpam-5697	258	3	1	1	NUM
ejpam-5697	258	4	.	.	PUNCT
ejpam-5697	258	5	definition	definition	NOUN
ejpam-5697	258	6	10	10	NUM
ejpam-5697	258	7	.	.	PUNCT
ejpam-5697	259	1	the	the	DET
ejpam-5697	259	2	laplace	laplace	NOUN
ejpam-5697	259	3	transform	transform	NOUN
ejpam-5697	259	4	of	of	ADP
ejpam-5697	259	5	ψ	ψ	NOUN
ejpam-5697	259	6	is	be	AUX
ejpam-5697	259	7	produced	produce	VERB
ejpam-5697	259	8	by	by	ADP
ejpam-5697	259	9	letting	let	VERB
ejpam-5697	259	10	ℏ	ℏ	PROPN
ejpam-5697	259	11	(	(	PUNCT
ejpam-5697	259	12	where	where	SCONJ
ejpam-5697	259	13	ℏ	ℏ	PROPN
ejpam-5697	259	14	is	be	AUX
ejpam-5697	259	15	a	a	DET
ejpam-5697	259	16	monotonically	monotonically	ADV
ejpam-5697	259	17	increasing	increase	VERB
ejpam-5697	259	18	)	)	PUNCT
ejpam-5697	259	19	and	and	CCONJ
ejpam-5697	259	20	ψ	ψ	AUX
ejpam-5697	259	21	be	be	AUX
ejpam-5697	259	22	defined	define	VERB
ejpam-5697	259	23	on	on	ADP
ejpam-5697	259	24	[	[	X
ejpam-5697	259	25	a,∞	a,∞	PROPN
ejpam-5697	259	26	)	)	PUNCT
ejpam-5697	259	27	by	by	ADP
ejpam-5697	259	28	lℏ(ψ)(s	lℏ(ψ)(s	NOUN
ejpam-5697	259	29	)	)	PUNCT
ejpam-5697	260	1	=	=	PUNCT
ejpam-5697	260	2	∞∫	∞∫	PROPN
ejpam-5697	260	3	a	a	DET
ejpam-5697	260	4	e−s(ℏ(ξ)−ℏ(a))ℏ	e−s(ℏ(ξ)−ℏ(a))ℏ	PROPN
ejpam-5697	260	5	′	′	X
ejpam-5697	260	6	(	(	PUNCT
ejpam-5697	260	7	ξ)ψ(ξ)dζ	ξ)ψ(ξ)dζ	VERB
ejpam-5697	260	8	such	such	ADJ
ejpam-5697	260	9	that	that	SCONJ
ejpam-5697	260	10	the	the	DET
ejpam-5697	260	11	equation	equation	NOUN
ejpam-5697	260	12	(	(	PUNCT
ejpam-5697	260	13	10	10	NUM
ejpam-5697	260	14	)	)	PUNCT
ejpam-5697	260	15	holds	hold	VERB
ejpam-5697	260	16	for	for	ADP
ejpam-5697	260	17	all	all	DET
ejpam-5697	260	18	values	value	NOUN
ejpam-5697	260	19	of	of	ADP
ejpam-5697	260	20	s.	s.	PROPN
ejpam-5697	260	21	definition	definition	NOUN
ejpam-5697	260	22	11	11	NUM
ejpam-5697	260	23	.	.	PUNCT
ejpam-5697	261	1	the	the	DET
ejpam-5697	261	2	convolution	convolution	NOUN
ejpam-5697	261	3	of	of	ADP
ejpam-5697	261	4	the	the	DET
ejpam-5697	261	5	function	function	NOUN
ejpam-5697	261	6	φ	φ	PROPN
ejpam-5697	261	7	and	and	CCONJ
ejpam-5697	261	8	ω	ω	PROPN
ejpam-5697	261	9	associated	associate	VERB
ejpam-5697	261	10	with	with	ADP
ejpam-5697	261	11	ϕ	ϕ	PROPN
ejpam-5697	261	12	is	be	AUX
ejpam-5697	261	13	provided	provide	VERB
ejpam-5697	261	14	by	by	ADP
ejpam-5697	261	15	(	(	PUNCT
ejpam-5697	261	16	φ	φ	PROPN
ejpam-5697	261	17	∗ϕ	∗ϕ	PROPN
ejpam-5697	261	18	ω)(ξ	ω)(ξ	NOUN
ejpam-5697	261	19	)	)	PUNCT
ejpam-5697	261	20	=	=	SYM
ejpam-5697	262	1	∫	∫	PROPN
ejpam-5697	262	2	θ	θ	PROPN
ejpam-5697	262	3	a	a	DET
ejpam-5697	262	4	φ	φ	PROPN
ejpam-5697	262	5	(	(	PUNCT
ejpam-5697	262	6	ϕ−1	ϕ−1	PROPN
ejpam-5697	262	7	(	(	PUNCT
ejpam-5697	262	8	ϕ(θ	ϕ(θ	PROPN
ejpam-5697	262	9	)	)	PUNCT
ejpam-5697	263	1	+	+	NUM
ejpam-5697	263	2	ϕ(a)−	ϕ(a)−	PROPN
ejpam-5697	263	3	ϕ(ζ	ϕ(ζ	PROPN
ejpam-5697	263	4	)	)	PUNCT
ejpam-5697	263	5	)	)	PUNCT
ejpam-5697	263	6	)	)	PUNCT
ejpam-5697	264	1	ω(ζ)ϕ	ω(ζ)ϕ	PROPN
ejpam-5697	264	2	′	′	NUM
ejpam-5697	265	1	(	(	PUNCT
ejpam-5697	265	2	ζ)dζ	ζ)dζ	PROPN
ejpam-5697	265	3	.	.	PROPN
ejpam-5697	266	1	for	for	ADP
ejpam-5697	266	2	fo	fo	INTJ
ejpam-5697	266	3	(	(	PUNCT
ejpam-5697	266	4	fractional	fractional	ADJ
ejpam-5697	266	5	operator	operator	NOUN
ejpam-5697	266	6	)	)	PUNCT
ejpam-5697	266	7	in	in	ADP
ejpam-5697	266	8	definition	definition	NOUN
ejpam-5697	266	9	8	8	NUM
ejpam-5697	266	10	,	,	PUNCT
ejpam-5697	266	11	the	the	DET
ejpam-5697	266	12	convolution	convolution	NOUN
ejpam-5697	266	13	form	form	NOUN
ejpam-5697	266	14	is	be	AUX
ejpam-5697	266	15	provided	provide	VERB
ejpam-5697	266	16	by	by	ADP
ejpam-5697	266	17	mpc	mpc	PROPN
ejpam-5697	266	18	ℏ	ℏ	NOUN
ejpam-5697	266	19	dδ;κ;p	dδ;κ;p	X
ejpam-5697	266	20	a+	a+	PUNCT
ejpam-5697	266	21	g(ξ	g(ξ	PROPN
ejpam-5697	266	22	)	)	PUNCT
ejpam-5697	266	23	=	=	SYM
ejpam-5697	266	24	r(δ	r(δ	PROPN
ejpam-5697	266	25	)	)	PUNCT
ejpam-5697	266	26	1−	1−	NUM
ejpam-5697	266	27	δ	δ	PROPN
ejpam-5697	266	28	[	[	PUNCT
ejpam-5697	266	29	g(ξ)−	g(ξ)−	NOUN
ejpam-5697	266	30	peδ,1	peδ,1	NOUN
ejpam-5697	266	31	(	(	PUNCT
ejpam-5697	266	32	−	−	PROPN
ejpam-5697	266	33	ωδ	ωδ	X
ejpam-5697	266	34	(	(	PUNCT
ejpam-5697	266	35	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	266	36	ℏ(a	ℏ(a	NOUN
ejpam-5697	266	37	)	)	PUNCT
ejpam-5697	266	38	)	)	PUNCT
ejpam-5697	266	39	κ	κ	X
ejpam-5697	266	40	)	)	PUNCT
ejpam-5697	266	41	g(a	g(a	PROPN
ejpam-5697	266	42	)	)	PUNCT
ejpam-5697	266	43	−	−	ADP
ejpam-5697	266	44	ωδ(ln	ωδ(ln	PROPN
ejpam-5697	266	45	p	p	NOUN
ejpam-5697	266	46	)	)	PUNCT
ejpam-5697	266	47	∫	∫	PROPN
ejpam-5697	267	1	ξ	ξ	PROPN
ejpam-5697	267	2	a	a	PRON
ejpam-5697	267	3	(	(	PUNCT
ejpam-5697	267	4	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	267	5	ℏ(ζ))κ−1	ℏ(ζ))κ−1	X
ejpam-5697	267	6	peκ	peκ	NOUN
ejpam-5697	267	7	,	,	PUNCT
ejpam-5697	267	8	κ	κ	X
ejpam-5697	267	9	(	(	PUNCT
ejpam-5697	267	10	−	−	PROPN
ejpam-5697	267	11	ωδ	ωδ	X
ejpam-5697	267	12	(	(	PUNCT
ejpam-5697	267	13	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	267	14	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	267	15	)	)	PUNCT
ejpam-5697	267	16	)	)	PUNCT
ejpam-5697	267	17	κ)ℏ′(ζ)g(ζ)dζ	κ)ℏ′(ζ)g(ζ)dζ	PUNCT
ejpam-5697	267	18	]	]	PUNCT
ejpam-5697	267	19	=	=	PUNCT
ejpam-5697	267	20	r(δ	r(δ	PROPN
ejpam-5697	267	21	)	)	PUNCT
ejpam-5697	267	22	1−	1−	NUM
ejpam-5697	267	23	δ	δ	PROPN
ejpam-5697	267	24	[	[	PUNCT
ejpam-5697	267	25	g(ξ)−	g(ξ)−	NOUN
ejpam-5697	267	26	peδ,1	peδ,1	NOUN
ejpam-5697	267	27	(	(	PUNCT
ejpam-5697	267	28	−	−	PROPN
ejpam-5697	267	29	ωδ	ωδ	X
ejpam-5697	267	30	(	(	PUNCT
ejpam-5697	267	31	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	267	32	ℏ(a	ℏ(a	NOUN
ejpam-5697	267	33	)	)	PUNCT
ejpam-5697	267	34	)	)	PUNCT
ejpam-5697	267	35	κ	κ	X
ejpam-5697	267	36	)	)	PUNCT
ejpam-5697	267	37	g(a	g(a	PROPN
ejpam-5697	267	38	)	)	PUNCT
ejpam-5697	267	39	−	−	ADP
ejpam-5697	267	40	ωδ(ln	ωδ(ln	NUM
ejpam-5697	267	41	p)(ℏ(ξ)−	p)(ℏ(ξ)−	NOUN
ejpam-5697	267	42	ℏ(a))κ−1	ℏ(a))κ−1	NOUN
ejpam-5697	267	43	peκ	peκ	NOUN
ejpam-5697	267	44	,	,	PUNCT
ejpam-5697	267	45	κ	κ	X
ejpam-5697	267	46	(	(	PUNCT
ejpam-5697	267	47	−	−	PROPN
ejpam-5697	267	48	ωδ	ωδ	X
ejpam-5697	267	49	(	(	PUNCT
ejpam-5697	267	50	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	267	51	ℏ(a	ℏ(a	NOUN
ejpam-5697	267	52	)	)	PUNCT
ejpam-5697	267	53	)	)	PUNCT
ejpam-5697	267	54	κ	κ	X
ejpam-5697	267	55	)	)	PUNCT
ejpam-5697	267	56	∗	∗	NOUN
ejpam-5697	267	57	g(ζ	g(ζ	PROPN
ejpam-5697	267	58	)	)	PUNCT
ejpam-5697	267	59	]	]	PUNCT
ejpam-5697	267	60	.	.	PUNCT
ejpam-5697	268	1	(	(	PUNCT
ejpam-5697	268	2	12	12	NUM
ejpam-5697	268	3	)	)	PUNCT
ejpam-5697	268	4	gauhar	gauhar	PROPN
ejpam-5697	268	5	rahman	rahman	PROPN
ejpam-5697	268	6	et	et	PROPN
ejpam-5697	268	7	al	al	PROPN
ejpam-5697	268	8	.	.	PUNCT
ejpam-5697	268	9	/	/	SYM
ejpam-5697	268	10	eur	eur	PROPN
ejpam-5697	268	11	.	.	PUNCT
ejpam-5697	269	1	j.	j.	PROPN
ejpam-5697	269	2	pure	pure	PROPN
ejpam-5697	269	3	appl	appl	PROPN
ejpam-5697	269	4	.	.	PROPN
ejpam-5697	269	5	math	math	PROPN
ejpam-5697	269	6	,	,	PUNCT
ejpam-5697	269	7	18	18	NUM
ejpam-5697	269	8	(	(	PUNCT
ejpam-5697	269	9	1	1	NUM
ejpam-5697	269	10	)	)	PUNCT
ejpam-5697	269	11	(	(	PUNCT
ejpam-5697	269	12	2025	2025	NUM
ejpam-5697	269	13	)	)	PUNCT
ejpam-5697	269	14	,	,	PUNCT
ejpam-5697	269	15	5697	5697	NUM
ejpam-5697	269	16	12	12	NUM
ejpam-5697	269	17	of	of	ADP
ejpam-5697	269	18	26	26	NUM
ejpam-5697	269	19	κ	κ	NOUN
ejpam-5697	269	20	=	=	NOUN
ejpam-5697	269	21	0.2	0.2	NUM
ejpam-5697	269	22	κ	κ	NOUN
ejpam-5697	269	23	=	=	SYM
ejpam-5697	269	24	0.5	0.5	NUM
ejpam-5697	269	25	κ	κ	NOUN
ejpam-5697	269	26	=	=	NOUN
ejpam-5697	269	27	0.8	0.8	NUM
ejpam-5697	269	28	figure	figure	NOUN
ejpam-5697	269	29	5	5	NUM
ejpam-5697	269	30	:	:	PUNCT
ejpam-5697	269	31	the	the	DET
ejpam-5697	269	32	graphical	graphical	ADJ
ejpam-5697	269	33	representation	representation	NOUN
ejpam-5697	269	34	of	of	ADP
ejpam-5697	269	35	absolute	absolute	ADJ
ejpam-5697	269	36	value	value	NOUN
ejpam-5697	269	37	of	of	ADP
ejpam-5697	269	38	(	(	PUNCT
ejpam-5697	269	39	8)	8)	NUM
ejpam-5697	269	40	corresponding	correspond	VERB
ejpam-5697	269	41	to	to	ADP
ejpam-5697	269	42	choice	choice	NOUN
ejpam-5697	269	43	0	0	NUM
ejpam-5697	269	44	≤	≤	NUM
ejpam-5697	270	1	ξ	ξ	X
ejpam-5697	270	2	≤	≤	NUM
ejpam-5697	270	3	1	1	NUM
ejpam-5697	270	4	.	.	PUNCT
ejpam-5697	271	1	the	the	DET
ejpam-5697	271	2	power	power	NOUN
ejpam-5697	271	3	m	m	PROPN
ejpam-5697	271	4	-	-	ADJ
ejpam-5697	271	5	l	l	NOUN
ejpam-5697	271	6	function	function	NOUN
ejpam-5697	271	7	involved	involve	VERB
ejpam-5697	271	8	in	in	ADP
ejpam-5697	271	9	the	the	DET
ejpam-5697	271	10	newly	newly	ADV
ejpam-5697	271	11	established	establish	VERB
ejpam-5697	271	12	operator	operator	NOUN
ejpam-5697	271	13	specified	specify	VERB
ejpam-5697	271	14	by	by	ADP
ejpam-5697	271	15	definition	definition	NOUN
ejpam-5697	271	16	8	8	NUM
ejpam-5697	271	17	is	be	AUX
ejpam-5697	271	18	then	then	ADV
ejpam-5697	271	19	evaluated	evaluate	VERB
ejpam-5697	271	20	using	use	VERB
ejpam-5697	271	21	the	the	DET
ejpam-5697	271	22	laplace	laplace	NOUN
ejpam-5697	271	23	transform	transform	NOUN
ejpam-5697	271	24	in	in	ADP
ejpam-5697	271	25	the	the	DET
ejpam-5697	271	26	subsequent	subsequent	ADJ
ejpam-5697	271	27	lemma	lemma	PROPN
ejpam-5697	271	28	.	.	PUNCT
ejpam-5697	272	1	lemma	lemma	PROPN
ejpam-5697	272	2	1	1	NUM
ejpam-5697	272	3	.	.	PUNCT
ejpam-5697	272	4	given	give	VERB
ejpam-5697	272	5	an	an	DET
ejpam-5697	272	6	increasing	increase	VERB
ejpam-5697	272	7	function	function	NOUN
ejpam-5697	272	8	ℏ	ℏ	PROPN
ejpam-5697	272	9	and	and	CCONJ
ejpam-5697	272	10	a	a	DET
ejpam-5697	272	11	range	range	NOUN
ejpam-5697	272	12	0	0	PUNCT
ejpam-5697	272	13	<	<	X
ejpam-5697	272	14	δ	δ	X
ejpam-5697	272	15	<	<	X
ejpam-5697	272	16	1	1	NUM
ejpam-5697	272	17	,	,	PUNCT
ejpam-5697	272	18	we	we	PRON
ejpam-5697	272	19	have	have	AUX
ejpam-5697	272	20	lℏ	lℏ	VERB
ejpam-5697	272	21	(	(	PUNCT
ejpam-5697	272	22	peκ,1	peκ,1	NOUN
ejpam-5697	272	23	(	(	PUNCT
ejpam-5697	272	24	−	−	PROPN
ejpam-5697	272	25	ωδ	ωδ	X
ejpam-5697	272	26	(	(	PUNCT
ejpam-5697	272	27	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	272	28	ℏ(a	ℏ(a	NOUN
ejpam-5697	272	29	)	)	PUNCT
ejpam-5697	272	30	)	)	PUNCT
ejpam-5697	272	31	κ	κ	X
ejpam-5697	272	32	)	)	PUNCT
ejpam-5697	272	33	)	)	PUNCT
ejpam-5697	273	1	(	(	PUNCT
ejpam-5697	273	2	s	s	X
ejpam-5697	273	3	)	)	PUNCT
ejpam-5697	273	4	=	=	SYM
ejpam-5697	273	5	sκ−1	sκ−1	ADJ
ejpam-5697	273	6	sκ	sκ	PROPN
ejpam-5697	274	1	+	+	X
ejpam-5697	274	2	ωδ	ωδ	INTJ
ejpam-5697	274	3	ln	ln	ADJ
ejpam-5697	274	4	p	p	NOUN
ejpam-5697	274	5	,	,	PUNCT
ejpam-5697	274	6	|ωδ	|ωδ	NUM
ejpam-5697	274	7	ln	ln	NOUN
ejpam-5697	274	8	p	p	NOUN
ejpam-5697	275	1	sκ	sκ	ADJ
ejpam-5697	275	2	|	|	ADV
ejpam-5697	275	3	<	<	X
ejpam-5697	275	4	1	1	NUM
ejpam-5697	275	5	.	.	PUNCT
ejpam-5697	275	6	(	(	PUNCT
ejpam-5697	275	7	13	13	NUM
ejpam-5697	275	8	)	)	PUNCT
ejpam-5697	275	9	proof	proof	NOUN
ejpam-5697	275	10	.	.	PUNCT
ejpam-5697	276	1	by	by	ADP
ejpam-5697	276	2	employing	employ	VERB
ejpam-5697	276	3	definition	definition	NOUN
ejpam-5697	276	4	10	10	NUM
ejpam-5697	276	5	,	,	PUNCT
ejpam-5697	276	6	we	we	PRON
ejpam-5697	276	7	have	have	AUX
ejpam-5697	276	8	lℏ	lℏ	VERB
ejpam-5697	276	9	(	(	PUNCT
ejpam-5697	276	10	peκ,1	peκ,1	NOUN
ejpam-5697	276	11	(	(	PUNCT
ejpam-5697	276	12	−	−	PROPN
ejpam-5697	276	13	ωδ	ωδ	X
ejpam-5697	276	14	(	(	PUNCT
ejpam-5697	276	15	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	276	16	ℏ(a	ℏ(a	NOUN
ejpam-5697	276	17	)	)	PUNCT
ejpam-5697	276	18	)	)	PUNCT
ejpam-5697	276	19	κ	κ	X
ejpam-5697	276	20	)	)	PUNCT
ejpam-5697	276	21	)	)	PUNCT
ejpam-5697	277	1	(	(	PUNCT
ejpam-5697	277	2	s	s	X
ejpam-5697	277	3	)	)	PUNCT
ejpam-5697	277	4	=	=	SYM
ejpam-5697	277	5	∞∫	∞∫	PROPN
ejpam-5697	277	6	a	a	DET
ejpam-5697	277	7	e−s(ℏ(ξ)−ℏ(a))ℏ	e−s(ℏ(ξ)−ℏ(a))ℏ	PROPN
ejpam-5697	277	8	′	′	X
ejpam-5697	277	9	(	(	PUNCT
ejpam-5697	277	10	ξ	ξ	NOUN
ejpam-5697	277	11	)	)	PUNCT
ejpam-5697	277	12	×	×	NOUN
ejpam-5697	277	13	peκ,1	peκ,1	NOUN
ejpam-5697	277	14	(	(	PUNCT
ejpam-5697	277	15	−	−	PROPN
ejpam-5697	277	16	ωδ	ωδ	X
ejpam-5697	277	17	(	(	PUNCT
ejpam-5697	277	18	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	277	19	ℏ(a	ℏ(a	NOUN
ejpam-5697	277	20	)	)	PUNCT
ejpam-5697	277	21	)	)	PUNCT
ejpam-5697	278	1	κ	κ	X
ejpam-5697	278	2	)	)	PUNCT
ejpam-5697	278	3	dζ	dζ	NOUN
ejpam-5697	278	4	=	=	PUNCT
ejpam-5697	278	5	∞∑	∞∑	PROPN
ejpam-5697	278	6	n=0	n=0	NUM
ejpam-5697	278	7	(	(	PUNCT
ejpam-5697	278	8	−ωδ	−ωδ	NOUN
ejpam-5697	278	9	ln	ln	NOUN
ejpam-5697	278	10	p	p	NOUN
ejpam-5697	278	11	)	)	PUNCT
ejpam-5697	278	12	n	n	NOUN
ejpam-5697	278	13	γ(κn+	γ(κn+	ADP
ejpam-5697	278	14	1	1	NUM
ejpam-5697	278	15	)	)	PUNCT
ejpam-5697	278	16	∞∫	∞∫	NOUN
ejpam-5697	278	17	a	a	DET
ejpam-5697	278	18	e−s(ℏ(ξ)−ℏ(a))ℏ	e−s(ℏ(ξ)−ℏ(a))ℏ	PROPN
ejpam-5697	278	19	′	′	X
ejpam-5697	278	20	(	(	PUNCT
ejpam-5697	278	21	ξ	ξ	NOUN
ejpam-5697	278	22	)	)	PUNCT
ejpam-5697	278	23	(	(	PUNCT
ejpam-5697	278	24	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	278	25	ℏ(a	ℏ(a	NOUN
ejpam-5697	278	26	)	)	PUNCT
ejpam-5697	278	27	)	)	PUNCT
ejpam-5697	278	28	κn	κn	PROPN
ejpam-5697	278	29	dζ	dζ	PROPN
ejpam-5697	278	30	.	.	PUNCT
ejpam-5697	279	1	substituting	substitute	VERB
ejpam-5697	279	2	(	(	PUNCT
ejpam-5697	279	3	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	279	4	ℏ(a	ℏ(a	NOUN
ejpam-5697	279	5	)	)	PUNCT
ejpam-5697	279	6	)	)	PUNCT
ejpam-5697	280	1	=	=	SYM
ejpam-5697	280	2	ζ	ζ	NOUN
ejpam-5697	280	3	,	,	PUNCT
ejpam-5697	280	4	we	we	PRON
ejpam-5697	280	5	obtain	obtain	VERB
ejpam-5697	280	6	lℏ	lℏ	X
ejpam-5697	280	7	(	(	PUNCT
ejpam-5697	280	8	peκ,1	peκ,1	NOUN
ejpam-5697	280	9	(	(	PUNCT
ejpam-5697	280	10	−	−	PROPN
ejpam-5697	280	11	ωδ	ωδ	X
ejpam-5697	280	12	(	(	PUNCT
ejpam-5697	280	13	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	280	14	ℏ(a	ℏ(a	NOUN
ejpam-5697	280	15	)	)	PUNCT
ejpam-5697	280	16	)	)	PUNCT
ejpam-5697	280	17	κ	κ	X
ejpam-5697	280	18	)	)	PUNCT
ejpam-5697	280	19	)	)	PUNCT
ejpam-5697	280	20	(	(	PUNCT
ejpam-5697	280	21	s	s	X
ejpam-5697	280	22	)	)	PUNCT
ejpam-5697	280	23	=	=	SYM
ejpam-5697	281	1	∞∑	∞∑	NUM
ejpam-5697	281	2	n=0	n=0	NUM
ejpam-5697	281	3	(	(	PUNCT
ejpam-5697	281	4	−ωδ	−ωδ	NOUN
ejpam-5697	281	5	ln	ln	NOUN
ejpam-5697	281	6	p	p	NOUN
ejpam-5697	281	7	)	)	PUNCT
ejpam-5697	281	8	n	n	PROPN
ejpam-5697	281	9	γ(δn+	γ(δn+	PROPN
ejpam-5697	281	10	1	1	NUM
ejpam-5697	281	11	)	)	PUNCT
ejpam-5697	281	12	∞∫	∞∫	PROPN
ejpam-5697	281	13	a	a	PRON
ejpam-5697	281	14	e−sζtδndζ	e−sζtδndζ	NOUN
ejpam-5697	281	15	=	=	PUNCT
ejpam-5697	282	1	∞∑	∞∑	NUM
ejpam-5697	282	2	n=0	n=0	NUM
ejpam-5697	282	3	(	(	PUNCT
ejpam-5697	282	4	−ωδ	−ωδ	NOUN
ejpam-5697	282	5	ln	ln	NOUN
ejpam-5697	282	6	p	p	NOUN
ejpam-5697	282	7	)	)	PUNCT
ejpam-5697	282	8	n	n	NOUN
ejpam-5697	282	9	γ(κn+	γ(κn+	ADP
ejpam-5697	282	10	1	1	X
ejpam-5697	282	11	)	)	PUNCT
ejpam-5697	282	12	l{tκn	l{tκn	NOUN
ejpam-5697	282	13	}	}	PUNCT
ejpam-5697	282	14	=	=	SYM
ejpam-5697	283	1	∞∑	∞∑	NUM
ejpam-5697	283	2	n=0	n=0	NUM
ejpam-5697	283	3	(	(	PUNCT
ejpam-5697	283	4	−ωδ	−ωδ	NOUN
ejpam-5697	283	5	ln	ln	NOUN
ejpam-5697	283	6	p	p	NOUN
ejpam-5697	283	7	)	)	PUNCT
ejpam-5697	283	8	n	n	PRON
ejpam-5697	283	9	sκn+1	sκn+1	NOUN
ejpam-5697	283	10	=	=	PUNCT
ejpam-5697	283	11	sκ−1	sκ−1	ADJ
ejpam-5697	283	12	sκ	sκ	PROPN
ejpam-5697	284	1	+	+	X
ejpam-5697	284	2	ωδ	ωδ	INTJ
ejpam-5697	284	3	ln	ln	ADJ
ejpam-5697	284	4	p	p	NOUN
ejpam-5697	284	5	,	,	PUNCT
ejpam-5697	284	6	which	which	PRON
ejpam-5697	284	7	gives	give	VERB
ejpam-5697	284	8	the	the	DET
ejpam-5697	284	9	desired	desire	VERB
ejpam-5697	284	10	result	result	NOUN
ejpam-5697	284	11	.	.	PUNCT
ejpam-5697	285	1	gauhar	gauhar	PROPN
ejpam-5697	285	2	rahman	rahman	PROPN
ejpam-5697	285	3	et	et	PROPN
ejpam-5697	285	4	al	al	PROPN
ejpam-5697	285	5	.	.	PUNCT
ejpam-5697	285	6	/	/	SYM
ejpam-5697	285	7	eur	eur	PROPN
ejpam-5697	285	8	.	.	PUNCT
ejpam-5697	286	1	j.	j.	PROPN
ejpam-5697	286	2	pure	pure	PROPN
ejpam-5697	286	3	appl	appl	PROPN
ejpam-5697	286	4	.	.	PROPN
ejpam-5697	286	5	math	math	PROPN
ejpam-5697	286	6	,	,	PUNCT
ejpam-5697	286	7	18	18	NUM
ejpam-5697	286	8	(	(	PUNCT
ejpam-5697	286	9	1	1	NUM
ejpam-5697	286	10	)	)	PUNCT
ejpam-5697	286	11	(	(	PUNCT
ejpam-5697	286	12	2025	2025	NUM
ejpam-5697	286	13	)	)	PUNCT
ejpam-5697	286	14	,	,	PUNCT
ejpam-5697	286	15	5697	5697	NUM
ejpam-5697	286	16	13	13	NUM
ejpam-5697	286	17	of	of	ADP
ejpam-5697	286	18	26	26	NUM
ejpam-5697	286	19	0.2	0.2	NUM
ejpam-5697	286	20	0.4	0.4	NUM
ejpam-5697	286	21	0.6	0.6	NUM
ejpam-5697	287	1	0.8	0.8	NUM
ejpam-5697	287	2	1.0	1.0	NUM
ejpam-5697	287	3	ξ	ξ	X
ejpam-5697	287	4	-2.2	-2.2	NUM
ejpam-5697	287	5	-2.0	-2.0	PROPN
ejpam-5697	287	6	-1.8	-1.8	PROPN
ejpam-5697	287	7	-1.6	-1.6	PROPN
ejpam-5697	287	8	-1.4	-1.4	PROPN
ejpam-5697	287	9	-1.2	-1.2	NOUN
ejpam-5697	287	10	_	_	PROPN
ejpam-5697	287	11	hbar^mpc	hbar^mpc	NOUN
ejpam-5697	287	12	d	d	X
ejpam-5697	287	13	fhξl	fhξl	X
ejpam-5697	287	14	fractional	fractional	ADJ
ejpam-5697	287	15	operator	operator	NOUN
ejpam-5697	287	16	plot	plot	NOUN
ejpam-5697	287	17	with	with	ADP
ejpam-5697	287	18	hhξl	hhξl	NOUN
ejpam-5697	287	19	=	=	PUNCT
ejpam-5697	287	20	sqrthξ+1l	sqrthξ+1l	PROPN
ejpam-5697	287	21	κ	κ	X
ejpam-5697	287	22	=	=	PUNCT
ejpam-5697	287	23	0.2	0.2	NUM
ejpam-5697	287	24	κ	κ	NOUN
ejpam-5697	287	25	=	=	SYM
ejpam-5697	287	26	0.5	0.5	NUM
ejpam-5697	287	27	κ	κ	NOUN
ejpam-5697	287	28	=	=	NOUN
ejpam-5697	287	29	0.8	0.8	NUM
ejpam-5697	287	30	figure	figure	NOUN
ejpam-5697	287	31	6	6	NUM
ejpam-5697	287	32	:	:	PUNCT
ejpam-5697	287	33	the	the	DET
ejpam-5697	287	34	2	2	NUM
ejpam-5697	287	35	-	-	PUNCT
ejpam-5697	287	36	dimensional	dimensional	ADJ
ejpam-5697	287	37	graphical	graphical	ADJ
ejpam-5697	287	38	representation	representation	NOUN
ejpam-5697	287	39	of	of	ADP
ejpam-5697	287	40	(	(	PUNCT
ejpam-5697	287	41	8)	8)	NUM
ejpam-5697	287	42	corresponding	correspond	VERB
ejpam-5697	287	43	to	to	ADP
ejpam-5697	287	44	choice	choice	NOUN
ejpam-5697	287	45	0	0	NUM
ejpam-5697	287	46	≤	≤	NUM
ejpam-5697	288	1	ξ	ξ	X
ejpam-5697	288	2	≤	≤	NUM
ejpam-5697	288	3	1	1	NUM
ejpam-5697	288	4	.	.	PUNCT
ejpam-5697	288	5	theorem	theorem	NOUN
ejpam-5697	288	6	3	3	NUM
ejpam-5697	288	7	.	.	X
ejpam-5697	288	8	for	for	ADP
ejpam-5697	288	9	a	a	DET
ejpam-5697	288	10	given	give	VERB
ejpam-5697	288	11	continuous	continuous	ADJ
ejpam-5697	288	12	function	function	NOUN
ejpam-5697	288	13	g	g	NOUN
ejpam-5697	288	14	and	and	CCONJ
ejpam-5697	288	15	g′	g′	PROPN
ejpam-5697	288	16	∈	∈	PROPN
ejpam-5697	288	17	l1(0	l1(0	PROPN
ejpam-5697	288	18	,	,	PUNCT
ejpam-5697	288	19	t	t	PROPN
ejpam-5697	288	20	)	)	PUNCT
ejpam-5697	288	21	,	,	PUNCT
ejpam-5697	288	22	the	the	DET
ejpam-5697	288	23	glt	glt	PROPN
ejpam-5697	288	24	of	of	ADP
ejpam-5697	288	25	the	the	DET
ejpam-5697	288	26	modified	modify	VERB
ejpam-5697	288	27	derivative	derivative	ADJ
ejpam-5697	288	28	operator	operator	NOUN
ejpam-5697	288	29	(	(	PUNCT
ejpam-5697	288	30	3	3	NUM
ejpam-5697	288	31	)	)	PUNCT
ejpam-5697	288	32	of	of	ADP
ejpam-5697	288	33	order	order	NOUN
ejpam-5697	288	34	0	0	PUNCT
ejpam-5697	288	35	<	<	X
ejpam-5697	288	36	δ	δ	X
ejpam-5697	288	37	<	<	X
ejpam-5697	288	38	1	1	NUM
ejpam-5697	288	39	can	can	AUX
ejpam-5697	288	40	be	be	AUX
ejpam-5697	288	41	defined	define	VERB
ejpam-5697	288	42	as	as	SCONJ
ejpam-5697	288	43	follows	follow	VERB
ejpam-5697	288	44	:	:	PUNCT
ejpam-5697	288	45	lℏ	lℏ	NOUN
ejpam-5697	288	46	(	(	PUNCT
ejpam-5697	288	47	mpc	mpc	NOUN
ejpam-5697	288	48	ℏ	ℏ	NOUN
ejpam-5697	288	49	dδ;κ;p	dδ;κ;p	X
ejpam-5697	288	50	a+	a+	PUNCT
ejpam-5697	288	51	g(ξ	g(ξ	PROPN
ejpam-5697	288	52	)	)	PUNCT
ejpam-5697	288	53	)	)	PUNCT
ejpam-5697	288	54	(	(	PUNCT
ejpam-5697	288	55	s	s	X
ejpam-5697	288	56	)	)	PUNCT
ejpam-5697	288	57	=	=	SYM
ejpam-5697	288	58	r(δ	r(δ	PROPN
ejpam-5697	288	59	)	)	PUNCT
ejpam-5697	288	60	1−	1−	NUM
ejpam-5697	288	61	δ	δ	PROPN
ejpam-5697	288	62	sκlℏ{g(ξ	sκlℏ{g(ξ	PROPN
ejpam-5697	288	63	)	)	PUNCT
ejpam-5697	288	64	}	}	PUNCT
ejpam-5697	288	65	−	−	PROPN
ejpam-5697	288	66	sκ−1g(a	sκ−1g(a	NUM
ejpam-5697	288	67	)	)	PUNCT
ejpam-5697	288	68	sκ	sκ	PROPN
ejpam-5697	289	1	+	+	NUM
ejpam-5697	289	2	ωδ	ωδ	INTJ
ejpam-5697	289	3	ln	ln	ADJ
ejpam-5697	289	4	p	p	NOUN
ejpam-5697	289	5	,	,	PUNCT
ejpam-5697	289	6	where	where	SCONJ
ejpam-5697	289	7	|ωδ	|ωδ	ADP
ejpam-5697	290	1	ln	ln	NOUN
ejpam-5697	290	2	p	p	NOUN
ejpam-5697	290	3	sκ	sκ	ADJ
ejpam-5697	290	4	|	|	ADV
ejpam-5697	290	5	<	<	X
ejpam-5697	290	6	1	1	NUM
ejpam-5697	290	7	.	.	PUNCT
ejpam-5697	291	1	proof	proof	NOUN
ejpam-5697	291	2	.	.	PUNCT
ejpam-5697	292	1	by	by	ADP
ejpam-5697	292	2	using	use	VERB
ejpam-5697	292	3	the	the	DET
ejpam-5697	292	4	equation	equation	NOUN
ejpam-5697	292	5	(	(	PUNCT
ejpam-5697	292	6	12	12	NUM
ejpam-5697	292	7	)	)	PUNCT
ejpam-5697	292	8	,	,	PUNCT
ejpam-5697	292	9	we	we	PRON
ejpam-5697	292	10	have	have	VERB
ejpam-5697	292	11	lℏ{mpc	lℏ{mpc	PROPN
ejpam-5697	292	12	ℏ	ℏ	NOUN
ejpam-5697	292	13	dδ;κ;p	dδ;κ;p	ADJ
ejpam-5697	292	14	a+	a+	PUNCT
ejpam-5697	292	15	g(ξ)}(s	g(ξ)}(s	NOUN
ejpam-5697	292	16	)	)	PUNCT
ejpam-5697	292	17	=	=	SYM
ejpam-5697	292	18	r(δ	r(δ	PROPN
ejpam-5697	292	19	)	)	PUNCT
ejpam-5697	292	20	1−	1−	NUM
ejpam-5697	292	21	δ	δ	PROPN
ejpam-5697	292	22	(	(	PUNCT
ejpam-5697	292	23	lℏ{g(ξ	lℏ{g(ξ	PROPN
ejpam-5697	292	24	)	)	PUNCT
ejpam-5697	292	25	}	}	PUNCT
ejpam-5697	292	26	−	−	PROPN
ejpam-5697	293	1	g(a)lℏ	g(a)lℏ	PRON
ejpam-5697	293	2	(	(	PUNCT
ejpam-5697	293	3	peκ,1	peκ,1	NOUN
ejpam-5697	293	4	(	(	PUNCT
ejpam-5697	293	5	−	−	PROPN
ejpam-5697	293	6	ωδ	ωδ	X
ejpam-5697	293	7	(	(	PUNCT
ejpam-5697	293	8	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	293	9	ℏ(a	ℏ(a	NOUN
ejpam-5697	293	10	)	)	PUNCT
ejpam-5697	293	11	)	)	PUNCT
ejpam-5697	293	12	κ	κ	X
ejpam-5697	293	13	)	)	PUNCT
ejpam-5697	293	14	)	)	PUNCT
ejpam-5697	294	1	−	−	ADP
ejpam-5697	294	2	ωδ	ωδ	ADP
ejpam-5697	294	3	ln	ln	X
ejpam-5697	294	4	plℏ	plℏ	NOUN
ejpam-5697	294	5	(	(	PUNCT
ejpam-5697	294	6	(	(	PUNCT
ejpam-5697	294	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	294	8	ℏ(a	ℏ(a	NOUN
ejpam-5697	294	9	)	)	PUNCT
ejpam-5697	294	10	)	)	PUNCT
ejpam-5697	295	1	κ−1	κ−1	PROPN
ejpam-5697	295	2	peκ,1	peκ,1	NOUN
ejpam-5697	295	3	(	(	PUNCT
ejpam-5697	295	4	−	−	PROPN
ejpam-5697	295	5	ωδ	ωδ	X
ejpam-5697	295	6	(	(	PUNCT
ejpam-5697	295	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	295	8	ℏ(a	ℏ(a	NOUN
ejpam-5697	295	9	)	)	PUNCT
ejpam-5697	295	10	)	)	PUNCT
ejpam-5697	295	11	κ	κ	X
ejpam-5697	295	12	)	)	PUNCT
ejpam-5697	295	13	∗	∗	NOUN
ejpam-5697	295	14	g(ξ	g(ξ	PROPN
ejpam-5697	295	15	)	)	PUNCT
ejpam-5697	295	16	)	)	PUNCT
ejpam-5697	295	17	)	)	PUNCT
ejpam-5697	296	1	=	=	PUNCT
ejpam-5697	296	2	r(δ	r(δ	PROPN
ejpam-5697	296	3	)	)	PUNCT
ejpam-5697	296	4	1−	1−	NUM
ejpam-5697	296	5	δ	δ	PROPN
ejpam-5697	296	6	(	(	PUNCT
ejpam-5697	296	7	lℏ{g(ξ	lℏ{g(ξ	PROPN
ejpam-5697	296	8	)	)	PUNCT
ejpam-5697	296	9	}	}	PUNCT
ejpam-5697	296	10	−	−	PROPN
ejpam-5697	296	11	g(a	g(a	PROPN
ejpam-5697	296	12	)	)	PUNCT
ejpam-5697	296	13	sκ−1	sκ−1	ADJ
ejpam-5697	296	14	sκ	sκ	PROPN
ejpam-5697	297	1	+	+	X
ejpam-5697	297	2	ωδ	ωδ	INTJ
ejpam-5697	297	3	ln	ln	ADJ
ejpam-5697	297	4	p	p	NOUN
ejpam-5697	297	5	−	−	PROPN
ejpam-5697	297	6	ωδ	ωδ	ADP
ejpam-5697	297	7	ln	ln	NOUN
ejpam-5697	297	8	p	p	NOUN
ejpam-5697	297	9	∞∑	∞∑	PROPN
ejpam-5697	297	10	n=0	n=0	NUM
ejpam-5697	297	11	(	(	PUNCT
ejpam-5697	297	12	−ωδ	−ωδ	NOUN
ejpam-5697	297	13	ln	ln	NOUN
ejpam-5697	297	14	p	p	NOUN
ejpam-5697	297	15	)	)	PUNCT
ejpam-5697	297	16	n	n	NOUN
ejpam-5697	297	17	γ(κn+	γ(κn+	ADP
ejpam-5697	297	18	κ	κ	NOUN
ejpam-5697	297	19	)	)	PUNCT
ejpam-5697	297	20	×	×	NOUN
ejpam-5697	297	21	lℏ	lℏ	NOUN
ejpam-5697	297	22	(	(	PUNCT
ejpam-5697	297	23	(	(	PUNCT
ejpam-5697	297	24	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	297	25	ℏ(a	ℏ(a	NOUN
ejpam-5697	297	26	)	)	PUNCT
ejpam-5697	297	27	)	)	PUNCT
ejpam-5697	297	28	κ(ℏ(ξ)−	κ(ℏ(ξ)−	PROPN
ejpam-5697	297	29	ℏ(a	ℏ(a	NOUN
ejpam-5697	297	30	)	)	PUNCT
ejpam-5697	297	31	)	)	PUNCT
ejpam-5697	297	32	κn−1	κn−1	PROPN
ejpam-5697	297	33	)	)	PUNCT
ejpam-5697	297	34	lℏ{g(ξ	lℏ{g(ξ	PROPN
ejpam-5697	297	35	)	)	PUNCT
ejpam-5697	297	36	}	}	PUNCT
ejpam-5697	297	37	=	=	SYM
ejpam-5697	297	38	r(δ	r(δ	NOUN
ejpam-5697	297	39	)	)	PUNCT
ejpam-5697	297	40	1−	1−	NUM
ejpam-5697	297	41	δ	δ	PROPN
ejpam-5697	297	42	(	(	PUNCT
ejpam-5697	297	43	lℏ{g(ξ	lℏ{g(ξ	PROPN
ejpam-5697	297	44	)	)	PUNCT
ejpam-5697	297	45	}	}	PUNCT
ejpam-5697	297	46	−	−	PROPN
ejpam-5697	297	47	g(a	g(a	PROPN
ejpam-5697	297	48	)	)	PUNCT
ejpam-5697	297	49	sκ−1	sκ−1	ADJ
ejpam-5697	297	50	sκ	sκ	PROPN
ejpam-5697	298	1	+	+	X
ejpam-5697	298	2	ωδ	ωδ	INTJ
ejpam-5697	298	3	ln	ln	ADJ
ejpam-5697	298	4	p	p	NOUN
ejpam-5697	298	5	−	−	PROPN
ejpam-5697	298	6	ωδ	ωδ	ADP
ejpam-5697	298	7	ln	ln	NOUN
ejpam-5697	298	8	p	p	NOUN
ejpam-5697	298	9	∞∑	∞∑	PROPN
ejpam-5697	298	10	n=0	n=0	NUM
ejpam-5697	298	11	(	(	PUNCT
ejpam-5697	298	12	−ωδ	−ωδ	NOUN
ejpam-5697	298	13	ln	ln	NOUN
ejpam-5697	298	14	p	p	NOUN
ejpam-5697	298	15	)	)	PUNCT
ejpam-5697	298	16	n	n	NOUN
ejpam-5697	298	17	γ(κn+	γ(κn+	ADP
ejpam-5697	298	18	κ	κ	NOUN
ejpam-5697	298	19	)	)	PUNCT
ejpam-5697	298	20	×	×	NOUN
ejpam-5697	298	21	lℏ	lℏ	NOUN
ejpam-5697	298	22	(	(	PUNCT
ejpam-5697	298	23	(	(	PUNCT
ejpam-5697	298	24	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	298	25	ℏ(a	ℏ(a	NOUN
ejpam-5697	298	26	)	)	PUNCT
ejpam-5697	298	27	)	)	PUNCT
ejpam-5697	298	28	κ(n+1)−1	κ(n+1)−1	PROPN
ejpam-5697	298	29	)	)	PUNCT
ejpam-5697	298	30	lℏ{g(ξ	lℏ{g(ξ	PROPN
ejpam-5697	298	31	)	)	PUNCT
ejpam-5697	298	32	}	}	PUNCT
ejpam-5697	298	33	)	)	PUNCT
ejpam-5697	298	34	gauhar	gauhar	PROPN
ejpam-5697	298	35	rahman	rahman	PROPN
ejpam-5697	298	36	et	et	PROPN
ejpam-5697	299	1	al	al	PROPN
ejpam-5697	299	2	.	.	PUNCT
ejpam-5697	299	3	/	/	SYM
ejpam-5697	299	4	eur	eur	PROPN
ejpam-5697	299	5	.	.	PUNCT
ejpam-5697	300	1	j.	j.	PROPN
ejpam-5697	300	2	pure	pure	PROPN
ejpam-5697	300	3	appl	appl	PROPN
ejpam-5697	300	4	.	.	PROPN
ejpam-5697	300	5	math	math	PROPN
ejpam-5697	300	6	,	,	PUNCT
ejpam-5697	300	7	18	18	NUM
ejpam-5697	300	8	(	(	PUNCT
ejpam-5697	300	9	1	1	NUM
ejpam-5697	300	10	)	)	PUNCT
ejpam-5697	300	11	(	(	PUNCT
ejpam-5697	300	12	2025	2025	NUM
ejpam-5697	300	13	)	)	PUNCT
ejpam-5697	300	14	,	,	PUNCT
ejpam-5697	300	15	5697	5697	NUM
ejpam-5697	300	16	14	14	NUM
ejpam-5697	300	17	of	of	ADP
ejpam-5697	300	18	26	26	NUM
ejpam-5697	300	19	=	=	SYM
ejpam-5697	300	20	r(δ	r(δ	PROPN
ejpam-5697	300	21	)	)	PUNCT
ejpam-5697	300	22	1−	1−	NUM
ejpam-5697	300	23	δ	δ	PROPN
ejpam-5697	300	24	(	(	PUNCT
ejpam-5697	300	25	lℏ{g(ξ	lℏ{g(ξ	PROPN
ejpam-5697	300	26	)	)	PUNCT
ejpam-5697	300	27	}	}	PUNCT
ejpam-5697	300	28	−	−	PROPN
ejpam-5697	300	29	g(a	g(a	PROPN
ejpam-5697	300	30	)	)	PUNCT
ejpam-5697	300	31	sκ−1	sκ−1	ADJ
ejpam-5697	300	32	sκ	sκ	PROPN
ejpam-5697	301	1	+	+	X
ejpam-5697	301	2	ωδ	ωδ	INTJ
ejpam-5697	301	3	ln	ln	ADJ
ejpam-5697	301	4	p	p	NOUN
ejpam-5697	301	5	−	−	PROPN
ejpam-5697	301	6	ωδ	ωδ	ADP
ejpam-5697	301	7	ln	ln	NOUN
ejpam-5697	301	8	p	p	NOUN
ejpam-5697	301	9	∞∑	∞∑	PROPN
ejpam-5697	301	10	n=0	n=0	NUM
ejpam-5697	301	11	(	(	PUNCT
ejpam-5697	301	12	−ωδ	−ωδ	NOUN
ejpam-5697	301	13	ln	ln	NOUN
ejpam-5697	301	14	p	p	NOUN
ejpam-5697	301	15	)	)	PUNCT
ejpam-5697	301	16	n	n	PRON
ejpam-5697	301	17	sκ(n+1	sκ(n+1	NOUN
ejpam-5697	301	18	)	)	PUNCT
ejpam-5697	301	19	lℏ{g(ξ	lℏ{g(ξ	NOUN
ejpam-5697	301	20	)	)	PUNCT
ejpam-5697	301	21	}	}	PUNCT
ejpam-5697	301	22	)	)	PUNCT
ejpam-5697	301	23	=	=	PUNCT
ejpam-5697	301	24	r(δ	r(δ	PROPN
ejpam-5697	301	25	)	)	PUNCT
ejpam-5697	301	26	1−	1−	NUM
ejpam-5697	301	27	δ	δ	PROPN
ejpam-5697	301	28	(	(	PUNCT
ejpam-5697	301	29	lℏ{g(ξ	lℏ{g(ξ	PROPN
ejpam-5697	301	30	)	)	PUNCT
ejpam-5697	301	31	}	}	PUNCT
ejpam-5697	301	32	−	−	PROPN
ejpam-5697	301	33	g(a	g(a	PROPN
ejpam-5697	301	34	)	)	PUNCT
ejpam-5697	301	35	sκ−1	sκ−1	ADJ
ejpam-5697	301	36	sκ	sκ	PROPN
ejpam-5697	302	1	+	+	X
ejpam-5697	302	2	ωδ	ωδ	INTJ
ejpam-5697	302	3	ln	ln	ADJ
ejpam-5697	302	4	p	p	NOUN
ejpam-5697	302	5	−	−	PROPN
ejpam-5697	302	6	ωδ	ωδ	ADP
ejpam-5697	302	7	ln	ln	ADJ
ejpam-5697	302	8	p	p	NOUN
ejpam-5697	303	1	sκ	sκ	PROPN
ejpam-5697	303	2	+	+	ADP
ejpam-5697	303	3	ωδ	ωδ	INTJ
ejpam-5697	303	4	ln	ln	ADJ
ejpam-5697	303	5	p	p	PROPN
ejpam-5697	303	6	lℏ{g(ξ	lℏ{g(ξ	PROPN
ejpam-5697	303	7	)	)	PUNCT
ejpam-5697	303	8	}	}	PUNCT
ejpam-5697	303	9	)	)	PUNCT
ejpam-5697	304	1	=	=	PUNCT
ejpam-5697	304	2	r(δ	r(δ	PROPN
ejpam-5697	304	3	)	)	PUNCT
ejpam-5697	304	4	1−	1−	NUM
ejpam-5697	304	5	δ	δ	PROPN
ejpam-5697	304	6	sκlℏ{g(ξ	sκlℏ{g(ξ	PROPN
ejpam-5697	304	7	)	)	PUNCT
ejpam-5697	304	8	}	}	PUNCT
ejpam-5697	304	9	−	−	PROPN
ejpam-5697	304	10	sκ−1g(a	sκ−1g(a	NUM
ejpam-5697	304	11	)	)	PUNCT
ejpam-5697	304	12	sκ	sκ	PROPN
ejpam-5697	305	1	+	+	NUM
ejpam-5697	305	2	ωδ	ωδ	INTJ
ejpam-5697	305	3	ln	ln	ADJ
ejpam-5697	305	4	p	p	NOUN
ejpam-5697	305	5	.	.	PUNCT
ejpam-5697	306	1	hence	hence	ADV
ejpam-5697	306	2	the	the	DET
ejpam-5697	306	3	result	result	NOUN
ejpam-5697	306	4	is	be	AUX
ejpam-5697	306	5	proved	prove	VERB
ejpam-5697	306	6	.	.	PUNCT
ejpam-5697	307	1	example	example	NOUN
ejpam-5697	308	1	7	7	NUM
ejpam-5697	308	2	.	.	PUNCT
ejpam-5697	309	1	when	when	SCONJ
ejpam-5697	309	2	0	0	NUM
ejpam-5697	309	3	<	<	X
ejpam-5697	309	4	δ	δ	X
ejpam-5697	309	5	<	<	X
ejpam-5697	309	6	1	1	NUM
ejpam-5697	309	7	and	and	CCONJ
ejpam-5697	309	8	κ	κ	X
ejpam-5697	309	9	>	>	X
ejpam-5697	309	10	0	0	NUM
ejpam-5697	309	11	are	be	AUX
ejpam-5697	309	12	chosen	choose	VERB
ejpam-5697	309	13	as	as	ADP
ejpam-5697	309	14	the	the	DET
ejpam-5697	309	15	parameters	parameter	NOUN
ejpam-5697	309	16	,	,	PUNCT
ejpam-5697	309	17	and	and	CCONJ
ejpam-5697	309	18	|ωδ	|ωδ	AUX
ejpam-5697	309	19	ln	ln	NOUN
ejpam-5697	309	20	p	p	NOUN
ejpam-5697	310	1	sκ	sκ	ADJ
ejpam-5697	310	2	|	|	ADV
ejpam-5697	310	3	<	<	X
ejpam-5697	310	4	1	1	NUM
ejpam-5697	310	5	,	,	PUNCT
ejpam-5697	310	6	the	the	DET
ejpam-5697	310	7	equation	equation	NOUN
ejpam-5697	310	8	’s	’s	PART
ejpam-5697	310	9	solution	solution	NOUN
ejpam-5697	310	10	mpc	mpc	PROPN
ejpam-5697	310	11	ℏ	ℏ	PROPN
ejpam-5697	310	12	dδ	dδ	ADP
ejpam-5697	310	13	0g(ξ	0g(ξ	NOUN
ejpam-5697	310	14	)	)	PUNCT
ejpam-5697	311	1	=	=	PUNCT
ejpam-5697	312	1	c	c	NOUN
ejpam-5697	312	2	is	be	AUX
ejpam-5697	312	3	provided	provide	VERB
ejpam-5697	312	4	by	by	ADP
ejpam-5697	312	5	g(ζ	g(ζ	PROPN
ejpam-5697	312	6	)	)	PUNCT
ejpam-5697	312	7	=	=	PUNCT
ejpam-5697	312	8			VERB
ejpam-5697	312	9	c(1−δ	c(1−δ	ADJ
ejpam-5697	312	10	)	)	PUNCT
ejpam-5697	312	11	r(δ	r(δ	NOUN
ejpam-5697	312	12	)	)	PUNCT
ejpam-5697	312	13	(	(	PUNCT
ejpam-5697	312	14	1	1	NUM
ejpam-5697	312	15	+	+	CCONJ
ejpam-5697	312	16	ωδ	ωδ	ADP
ejpam-5697	312	17	ln	ln	ADJ
ejpam-5697	312	18	p	p	X
ejpam-5697	312	19	(	(	PUNCT
ejpam-5697	312	20	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	312	21	)	)	PUNCT
ejpam-5697	312	22	)	)	PUNCT
ejpam-5697	312	23	κ	κ	NOUN
ejpam-5697	312	24	γ(κ+1	γ(κ+1	NUM
ejpam-5697	312	25	)	)	PUNCT
ejpam-5697	312	26	)	)	PUNCT
ejpam-5697	312	27	,	,	PUNCT
ejpam-5697	312	28	ζ	ζ	PROPN
ejpam-5697	312	29	̸=	̸=	PROPN
ejpam-5697	312	30	0	0	NUM
ejpam-5697	312	31	;	;	PUNCT
ejpam-5697	312	32	0	0	NUM
ejpam-5697	312	33	,	,	PUNCT
ejpam-5697	312	34	ζ	ζ	NOUN
ejpam-5697	312	35	=	=	SYM
ejpam-5697	312	36	0	0	NUM
ejpam-5697	312	37	.	.	PUNCT
ejpam-5697	313	1	proof	proof	NOUN
ejpam-5697	313	2	.	.	PUNCT
ejpam-5697	314	1	by	by	ADP
ejpam-5697	314	2	given	give	VERB
ejpam-5697	314	3	hypothesis	hypothesis	NOUN
ejpam-5697	314	4	g(0	g(0	NOUN
ejpam-5697	314	5	)	)	PUNCT
ejpam-5697	314	6	=	=	SYM
ejpam-5697	314	7	0	0	NUM
ejpam-5697	314	8	,	,	PUNCT
ejpam-5697	314	9	and	and	CCONJ
ejpam-5697	314	10	for	for	ADP
ejpam-5697	314	11	ζ	ζ	NOUN
ejpam-5697	314	12	>	>	SYM
ejpam-5697	314	13	0	0	NUM
ejpam-5697	314	14	,	,	PUNCT
ejpam-5697	314	15	we	we	PRON
ejpam-5697	314	16	have	have	VERB
ejpam-5697	314	17	lℏ{mpc	lℏ{mpc	NOUN
ejpam-5697	314	18	ℏ	ℏ	NOUN
ejpam-5697	314	19	dδ;κ;p	dδ;κ;p	ADJ
ejpam-5697	314	20	0	0	NUM
ejpam-5697	314	21	g(s	g(s	NOUN
ejpam-5697	314	22	)	)	PUNCT
ejpam-5697	314	23	}	}	PUNCT
ejpam-5697	315	1	=	=	X
ejpam-5697	315	2	=	=	SYM
ejpam-5697	315	3	r(δ	r(δ	PROPN
ejpam-5697	315	4	)	)	PUNCT
ejpam-5697	315	5	1−	1−	NUM
ejpam-5697	316	1	δ	δ	PROPN
ejpam-5697	316	2	sκ	sκ	PROPN
ejpam-5697	316	3	sκ	sκ	PROPN
ejpam-5697	316	4	+	+	NUM
ejpam-5697	316	5	ωδ	ωδ	INTJ
ejpam-5697	316	6	ln	ln	ADJ
ejpam-5697	316	7	p	p	X
ejpam-5697	316	8	(	(	PUNCT
ejpam-5697	316	9	lℏ{g(ζ)}(s	lℏ{g(ζ)}(s	NOUN
ejpam-5697	316	10	)	)	PUNCT
ejpam-5697	316	11	)	)	PUNCT
ejpam-5697	317	1	=	=	PUNCT
ejpam-5697	318	1	c	c	X
ejpam-5697	318	2	sκ	sκ	PROPN
ejpam-5697	318	3	sκ	sκ	PROPN
ejpam-5697	319	1	+	+	NUM
ejpam-5697	319	2	ωδ	ωδ	INTJ
ejpam-5697	319	3	ln	ln	ADJ
ejpam-5697	319	4	p	p	NOUN
ejpam-5697	319	5	lℏ	lℏ	NOUN
ejpam-5697	319	6	(	(	PUNCT
ejpam-5697	319	7	1	1	NUM
ejpam-5697	319	8	+	+	CCONJ
ejpam-5697	319	9	ωδ	ωδ	ADP
ejpam-5697	319	10	ln	ln	ADJ
ejpam-5697	319	11	p	p	X
ejpam-5697	319	12	(	(	PUNCT
ejpam-5697	319	13	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	319	14	)	)	PUNCT
ejpam-5697	319	15	)	)	PUNCT
ejpam-5697	319	16	κ	κ	PROPN
ejpam-5697	319	17	γ(κ+	γ(κ+	NUM
ejpam-5697	319	18	1	1	NUM
ejpam-5697	319	19	)	)	PUNCT
ejpam-5697	319	20	)	)	PUNCT
ejpam-5697	320	1	(	(	PUNCT
ejpam-5697	320	2	s	s	X
ejpam-5697	320	3	)	)	PUNCT
ejpam-5697	320	4	=	=	PUNCT
ejpam-5697	321	1	c	c	PROPN
ejpam-5697	321	2	sκ	sκ	PROPN
ejpam-5697	321	3	sκ	sκ	PROPN
ejpam-5697	321	4	+	+	NUM
ejpam-5697	321	5	ωδ	ωδ	INTJ
ejpam-5697	321	6	ln	ln	ADJ
ejpam-5697	321	7	p	p	X
ejpam-5697	321	8	(	(	PUNCT
ejpam-5697	321	9	1	1	NUM
ejpam-5697	321	10	s	s	NOUN
ejpam-5697	321	11	+	+	NOUN
ejpam-5697	321	12	ωδ	ωδ	ADP
ejpam-5697	321	13	ln	ln	ADJ
ejpam-5697	321	14	p	p	NOUN
ejpam-5697	321	15	sκ+1	sκ+1	NOUN
ejpam-5697	321	16	)	)	PUNCT
ejpam-5697	321	17	=	=	PUNCT
ejpam-5697	322	1	c	c	NOUN
ejpam-5697	322	2	s	s	PROPN
ejpam-5697	322	3	.	.	PUNCT
ejpam-5697	323	1	this	this	PRON
ejpam-5697	323	2	implies	imply	VERB
ejpam-5697	323	3	that	that	SCONJ
ejpam-5697	323	4	lℏ{mpc	lℏ{mpc	PROPN
ejpam-5697	323	5	ℏ	ℏ	NOUN
ejpam-5697	323	6	dδ;κ;p	dδ;κ;p	NOUN
ejpam-5697	323	7	0	0	NUM
ejpam-5697	323	8	g(s	g(s	NOUN
ejpam-5697	323	9	)	)	PUNCT
ejpam-5697	323	10	}	}	PUNCT
ejpam-5697	323	11	=	=	SYM
ejpam-5697	323	12	lℏ(c	lℏ(c	NOUN
ejpam-5697	323	13	)	)	PUNCT
ejpam-5697	323	14	.	.	PUNCT
ejpam-5697	324	1	the	the	DET
ejpam-5697	324	2	action	action	NOUN
ejpam-5697	324	3	of	of	ADP
ejpam-5697	324	4	inverse	inverse	ADJ
ejpam-5697	324	5	laplace	laplace	NOUN
ejpam-5697	324	6	will	will	AUX
ejpam-5697	324	7	give	give	VERB
ejpam-5697	324	8	the	the	DET
ejpam-5697	324	9	desired	desire	VERB
ejpam-5697	324	10	result	result	NOUN
ejpam-5697	324	11	.	.	PUNCT
ejpam-5697	325	1	theorem	theorem	ADJ
ejpam-5697	325	2	4	4	NUM
ejpam-5697	325	3	.	.	PUNCT
ejpam-5697	325	4	suppose	suppose	VERB
ejpam-5697	325	5	that	that	SCONJ
ejpam-5697	325	6	g	g	PROPN
ejpam-5697	325	7	be	be	AUX
ejpam-5697	325	8	a	a	DET
ejpam-5697	325	9	continuous	continuous	ADJ
ejpam-5697	325	10	function	function	NOUN
ejpam-5697	325	11	and	and	CCONJ
ejpam-5697	325	12	g′	g′	NOUN
ejpam-5697	325	13	∈	∈	PROPN
ejpam-5697	325	14	l1(0	l1(0	PROPN
ejpam-5697	325	15	,	,	PUNCT
ejpam-5697	325	16	t	t	PROPN
ejpam-5697	325	17	)	)	PUNCT
ejpam-5697	325	18	,	,	PUNCT
ejpam-5697	325	19	then	then	ADV
ejpam-5697	325	20	the	the	DET
ejpam-5697	325	21	glt	glt	PROPN
ejpam-5697	325	22	of	of	ADP
ejpam-5697	325	23	the	the	DET
ejpam-5697	325	24	modified	modify	VERB
ejpam-5697	325	25	fractional	fractional	ADJ
ejpam-5697	325	26	derivative	derivative	NOUN
ejpam-5697	325	27	(	(	PUNCT
ejpam-5697	325	28	11	11	NUM
ejpam-5697	325	29	)	)	PUNCT
ejpam-5697	325	30	of	of	ADP
ejpam-5697	325	31	order	order	NOUN
ejpam-5697	325	32	0	0	PUNCT
ejpam-5697	325	33	<	<	X
ejpam-5697	325	34	δ	δ	X
ejpam-5697	325	35	<	<	X
ejpam-5697	325	36	1	1	NUM
ejpam-5697	325	37	,	,	PUNCT
ejpam-5697	325	38	p	p	X
ejpam-5697	325	39	>	>	X
ejpam-5697	325	40	1	1	NUM
ejpam-5697	325	41	,	,	PUNCT
ejpam-5697	325	42	and	and	CCONJ
ejpam-5697	325	43	κ	κ	X
ejpam-5697	325	44	>	>	X
ejpam-5697	325	45	0	0	PUNCT
ejpam-5697	325	46	is	be	AUX
ejpam-5697	325	47	given	give	VERB
ejpam-5697	325	48	by	by	ADP
ejpam-5697	325	49	lℏ	lℏ	PROPN
ejpam-5697	325	50	(	(	PUNCT
ejpam-5697	325	51	mprl	mprl	NOUN
ejpam-5697	325	52	ℏ	ℏ	ADJ
ejpam-5697	325	53	dδ;κ;p	dδ;κ;p	X
ejpam-5697	325	54	a+	a+	PUNCT
ejpam-5697	325	55	g(ξ	g(ξ	PROPN
ejpam-5697	325	56	)	)	PUNCT
ejpam-5697	325	57	)	)	PUNCT
ejpam-5697	326	1	(	(	PUNCT
ejpam-5697	326	2	s	s	X
ejpam-5697	326	3	)	)	PUNCT
ejpam-5697	326	4	=	=	SYM
ejpam-5697	326	5	r(δ	r(δ	PROPN
ejpam-5697	326	6	)	)	PUNCT
ejpam-5697	326	7	1−	1−	NUM
ejpam-5697	326	8	δ	δ	PROPN
ejpam-5697	326	9	sκlℏ{g(ξ	sκlℏ{g(ξ	PROPN
ejpam-5697	326	10	)	)	PUNCT
ejpam-5697	326	11	}	}	PUNCT
ejpam-5697	327	1	sκ	sκ	PROPN
ejpam-5697	328	1	+	+	NUM
ejpam-5697	328	2	ωδ	ωδ	INTJ
ejpam-5697	328	3	ln	ln	ADJ
ejpam-5697	328	4	p	p	NOUN
ejpam-5697	328	5	,	,	PUNCT
ejpam-5697	328	6	where	where	SCONJ
ejpam-5697	328	7	|ωδ	|ωδ	ADP
ejpam-5697	329	1	ln	ln	NOUN
ejpam-5697	329	2	p	p	NOUN
ejpam-5697	329	3	sκ	sκ	ADJ
ejpam-5697	329	4	|	|	ADV
ejpam-5697	329	5	<	<	X
ejpam-5697	329	6	1	1	X
ejpam-5697	329	7	.	.	PUNCT
ejpam-5697	330	1	gauhar	gauhar	PROPN
ejpam-5697	330	2	rahman	rahman	PROPN
ejpam-5697	330	3	et	et	PROPN
ejpam-5697	330	4	al	al	PROPN
ejpam-5697	330	5	.	.	PUNCT
ejpam-5697	330	6	/	/	SYM
ejpam-5697	330	7	eur	eur	PROPN
ejpam-5697	330	8	.	.	PUNCT
ejpam-5697	331	1	j.	j.	PROPN
ejpam-5697	331	2	pure	pure	PROPN
ejpam-5697	331	3	appl	appl	PROPN
ejpam-5697	331	4	.	.	PROPN
ejpam-5697	331	5	math	math	PROPN
ejpam-5697	331	6	,	,	PUNCT
ejpam-5697	331	7	18	18	NUM
ejpam-5697	331	8	(	(	PUNCT
ejpam-5697	331	9	1	1	NUM
ejpam-5697	331	10	)	)	PUNCT
ejpam-5697	331	11	(	(	PUNCT
ejpam-5697	331	12	2025	2025	NUM
ejpam-5697	331	13	)	)	PUNCT
ejpam-5697	331	14	,	,	PUNCT
ejpam-5697	331	15	5697	5697	NUM
ejpam-5697	331	16	15	15	NUM
ejpam-5697	331	17	of	of	ADP
ejpam-5697	331	18	26	26	NUM
ejpam-5697	331	19	proof	proof	NOUN
ejpam-5697	331	20	.	.	PUNCT
ejpam-5697	332	1	applying	apply	VERB
ejpam-5697	332	2	laplace	laplace	NOUN
ejpam-5697	332	3	transformation	transformation	NOUN
ejpam-5697	332	4	on	on	ADP
ejpam-5697	332	5	both	both	DET
ejpam-5697	332	6	sides	side	NOUN
ejpam-5697	332	7	of	of	ADP
ejpam-5697	332	8	(	(	PUNCT
ejpam-5697	332	9	11	11	NUM
ejpam-5697	332	10	)	)	PUNCT
ejpam-5697	332	11	,	,	PUNCT
ejpam-5697	332	12	we	we	PRON
ejpam-5697	332	13	have	have	AUX
ejpam-5697	332	14	lℏ	lℏ	VERB
ejpam-5697	332	15	(	(	PUNCT
ejpam-5697	332	16	mprl	mprl	VERB
ejpam-5697	332	17	ℏ	ℏ	ADJ
ejpam-5697	332	18	dδ;κ;p	dδ;κ;p	X
ejpam-5697	332	19	a+	a+	PUNCT
ejpam-5697	332	20	g(ξ	g(ξ	PROPN
ejpam-5697	332	21	)	)	PUNCT
ejpam-5697	332	22	)	)	PUNCT
ejpam-5697	333	1	(	(	PUNCT
ejpam-5697	333	2	s	s	X
ejpam-5697	333	3	)	)	PUNCT
ejpam-5697	333	4	=	=	SYM
ejpam-5697	333	5	r(δ	r(δ	PROPN
ejpam-5697	333	6	)	)	PUNCT
ejpam-5697	333	7	1−	1−	NUM
ejpam-5697	333	8	δ	δ	NOUN
ejpam-5697	333	9	lℏ	lℏ	VERB
ejpam-5697	333	10	[	[	PUNCT
ejpam-5697	333	11	d	d	PROPN
ejpam-5697	333	12	dζ	dζ	PROPN
ejpam-5697	333	13	peκ,1	peκ,1	NOUN
ejpam-5697	333	14	(	(	PUNCT
ejpam-5697	333	15	−	−	PROPN
ejpam-5697	333	16	ωδ	ωδ	X
ejpam-5697	333	17	(	(	PUNCT
ejpam-5697	333	18	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	333	19	ℏ(a	ℏ(a	NOUN
ejpam-5697	333	20	)	)	PUNCT
ejpam-5697	333	21	)	)	PUNCT
ejpam-5697	333	22	κ	κ	X
ejpam-5697	333	23	)	)	PUNCT
ejpam-5697	333	24	∗	∗	NOUN
ejpam-5697	333	25	g(ξ)](s	g(ξ)](s	NUM
ejpam-5697	333	26	)	)	PUNCT
ejpam-5697	333	27	=	=	SYM
ejpam-5697	333	28	sr(δ	sr(δ	X
ejpam-5697	333	29	)	)	PUNCT
ejpam-5697	333	30	1−	1−	NUM
ejpam-5697	334	1	δ	δ	PROPN
ejpam-5697	334	2	lℏ	lℏ	NOUN
ejpam-5697	334	3	[	[	PUNCT
ejpam-5697	334	4	peκ,1	peκ,1	NOUN
ejpam-5697	334	5	(	(	PUNCT
ejpam-5697	334	6	−	−	PROPN
ejpam-5697	334	7	ωδ	ωδ	X
ejpam-5697	334	8	(	(	PUNCT
ejpam-5697	334	9	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	334	10	ℏ(a	ℏ(a	NOUN
ejpam-5697	334	11	)	)	PUNCT
ejpam-5697	334	12	)	)	PUNCT
ejpam-5697	334	13	κ	κ	X
ejpam-5697	334	14	)	)	PUNCT
ejpam-5697	334	15	∗	∗	NOUN
ejpam-5697	334	16	g(ξ)](s	g(ξ)](s	NUM
ejpam-5697	334	17	)	)	PUNCT
ejpam-5697	334	18	=	=	SYM
ejpam-5697	334	19	sr(δ	sr(δ	X
ejpam-5697	334	20	)	)	PUNCT
ejpam-5697	334	21	1−	1−	NUM
ejpam-5697	335	1	δ	δ	PROPN
ejpam-5697	335	2	lℏ	lℏ	NOUN
ejpam-5697	335	3	[	[	PUNCT
ejpam-5697	335	4	peκ,1	peκ,1	NOUN
ejpam-5697	335	5	(	(	PUNCT
ejpam-5697	335	6	−	−	PROPN
ejpam-5697	335	7	ωδ	ωδ	X
ejpam-5697	335	8	(	(	PUNCT
ejpam-5697	335	9	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	335	10	ℏ(a	ℏ(a	NOUN
ejpam-5697	335	11	)	)	PUNCT
ejpam-5697	335	12	)	)	PUNCT
ejpam-5697	335	13	κ	κ	X
ejpam-5697	335	14	)	)	PUNCT
ejpam-5697	335	15	]	]	PUNCT
ejpam-5697	335	16	(	(	PUNCT
ejpam-5697	335	17	s)lℏ	s)lℏ	PROPN
ejpam-5697	335	18	[	[	PUNCT
ejpam-5697	335	19	g(ζ	g(ζ	PROPN
ejpam-5697	335	20	)	)	PUNCT
ejpam-5697	335	21	]	]	PUNCT
ejpam-5697	335	22	(	(	PUNCT
ejpam-5697	335	23	s	s	X
ejpam-5697	335	24	)	)	PUNCT
ejpam-5697	335	25	=	=	SYM
ejpam-5697	335	26	r(δ	r(δ	PROPN
ejpam-5697	335	27	)	)	PUNCT
ejpam-5697	335	28	1−	1−	NUM
ejpam-5697	336	1	δ	δ	PROPN
ejpam-5697	336	2	sκlℏ	sκlℏ	NOUN
ejpam-5697	336	3	[	[	PUNCT
ejpam-5697	336	4	g(ζ	g(ζ	PROPN
ejpam-5697	336	5	)	)	PUNCT
ejpam-5697	336	6	]	]	PUNCT
ejpam-5697	336	7	(	(	PUNCT
ejpam-5697	336	8	s	s	X
ejpam-5697	336	9	)	)	PUNCT
ejpam-5697	336	10	sκ	sκ	PROPN
ejpam-5697	337	1	+	+	NUM
ejpam-5697	337	2	ωδ	ωδ	INTJ
ejpam-5697	337	3	ln	ln	ADJ
ejpam-5697	337	4	p	p	NOUN
ejpam-5697	337	5	.	.	PUNCT
ejpam-5697	338	1	which	which	PRON
ejpam-5697	338	2	proves	prove	VERB
ejpam-5697	338	3	the	the	DET
ejpam-5697	338	4	required	require	VERB
ejpam-5697	338	5	result	result	NOUN
ejpam-5697	338	6	.	.	PUNCT
ejpam-5697	339	1	theorem	theorem	ADJ
ejpam-5697	339	2	5	5	NUM
ejpam-5697	339	3	.	.	X
ejpam-5697	339	4	for	for	ADP
ejpam-5697	339	5	the	the	DET
ejpam-5697	339	6	following	follow	VERB
ejpam-5697	339	7	fde	fde	PROPN
ejpam-5697	339	8	(	(	PUNCT
ejpam-5697	339	9	fractional	fractional	ADJ
ejpam-5697	339	10	differential	differential	ADJ
ejpam-5697	339	11	equation	equation	NOUN
ejpam-5697	339	12	)	)	PUNCT
ejpam-5697	339	13	mprl	mprl	VERB
ejpam-5697	339	14	ℏ	ℏ	NOUN
ejpam-5697	339	15	dδ;κ;p	dδ;κ;p	X
ejpam-5697	339	16	a+	a+	PUNCT
ejpam-5697	339	17	x(ξ	x(ξ	PROPN
ejpam-5697	339	18	)	)	PUNCT
ejpam-5697	339	19	=	=	SYM
ejpam-5697	339	20	g(ξ	g(ξ	PROPN
ejpam-5697	339	21	)	)	PUNCT
ejpam-5697	339	22	,	,	PUNCT
ejpam-5697	339	23	(	(	PUNCT
ejpam-5697	339	24	14	14	NUM
ejpam-5697	339	25	)	)	PUNCT
ejpam-5697	339	26	there	there	PRON
ejpam-5697	339	27	exist	exist	VERB
ejpam-5697	339	28	a	a	DET
ejpam-5697	339	29	unique	unique	ADJ
ejpam-5697	339	30	solution	solution	NOUN
ejpam-5697	339	31	as	as	SCONJ
ejpam-5697	339	32	follows	follow	VERB
ejpam-5697	339	33	:	:	PUNCT
ejpam-5697	339	34	x(ξ	x(ξ	X
ejpam-5697	339	35	)	)	PUNCT
ejpam-5697	339	36	=	=	SYM
ejpam-5697	339	37	r(δ	r(δ	PROPN
ejpam-5697	339	38	)	)	PUNCT
ejpam-5697	339	39	1−	1−	NUM
ejpam-5697	339	40	δ	δ	PROPN
ejpam-5697	339	41	g(ξ	g(ξ	PROPN
ejpam-5697	339	42	)	)	PUNCT
ejpam-5697	340	1	+	+	NUM
ejpam-5697	340	2	δ	δ	PROPN
ejpam-5697	340	3	ln	ln	ADJ
ejpam-5697	340	4	p	p	PROPN
ejpam-5697	340	5	r(δ	r(δ	NOUN
ejpam-5697	340	6	)	)	PUNCT
ejpam-5697	340	7	rl	rl	VERB
ejpam-5697	340	8	ℏ	ℏ	PROPN
ejpam-5697	340	9	iκ0g(ξ	iκ0g(ξ	NOUN
ejpam-5697	340	10	)	)	PUNCT
ejpam-5697	340	11	,	,	PUNCT
ejpam-5697	340	12	(	(	PUNCT
ejpam-5697	340	13	15	15	NUM
ejpam-5697	340	14	)	)	PUNCT
ejpam-5697	340	15	where	where	SCONJ
ejpam-5697	340	16	rliκ0	rliκ0	PROPN
ejpam-5697	340	17	is	be	AUX
ejpam-5697	340	18	the	the	DET
ejpam-5697	340	19	generalized	generalized	ADJ
ejpam-5697	340	20	r	r	NOUN
ejpam-5697	340	21	-	-	PUNCT
ejpam-5697	340	22	l	l	NOUN
ejpam-5697	340	23	fractional	fractional	ADJ
ejpam-5697	340	24	integral	integral	ADJ
ejpam-5697	340	25	.	.	PUNCT
ejpam-5697	341	1	proof	proof	NOUN
ejpam-5697	341	2	.	.	PUNCT
ejpam-5697	342	1	by	by	ADP
ejpam-5697	342	2	applying	apply	VERB
ejpam-5697	342	3	laplace	laplace	NOUN
ejpam-5697	342	4	on	on	ADP
ejpam-5697	342	5	(	(	PUNCT
ejpam-5697	342	6	14	14	NUM
ejpam-5697	342	7	)	)	PUNCT
ejpam-5697	342	8	,	,	PUNCT
ejpam-5697	342	9	we	we	PRON
ejpam-5697	342	10	have	have	AUX
ejpam-5697	342	11	lℏ	lℏ	VERB
ejpam-5697	342	12	{	{	PUNCT
ejpam-5697	342	13	mprl	mprl	VERB
ejpam-5697	342	14	ℏ	ℏ	NOUN
ejpam-5697	342	15	dδ;κ;p	dδ;κ;p	X
ejpam-5697	342	16	a+	a+	PUNCT
ejpam-5697	342	17	x(ξ	x(ξ	PROPN
ejpam-5697	342	18	)	)	PUNCT
ejpam-5697	342	19	}	}	PUNCT
ejpam-5697	342	20	(	(	PUNCT
ejpam-5697	342	21	s	s	X
ejpam-5697	342	22	)	)	PUNCT
ejpam-5697	342	23	=	=	SYM
ejpam-5697	342	24	lℏ	lℏ	X
ejpam-5697	342	25	{	{	PUNCT
ejpam-5697	342	26	g(ξ	g(ξ	PROPN
ejpam-5697	342	27	)	)	PUNCT
ejpam-5697	342	28	}	}	PUNCT
ejpam-5697	342	29	(	(	PUNCT
ejpam-5697	342	30	s	s	NOUN
ejpam-5697	342	31	)	)	PUNCT
ejpam-5697	342	32	.	.	PUNCT
ejpam-5697	343	1	by	by	ADP
ejpam-5697	343	2	using	use	VERB
ejpam-5697	343	3	theorem	theorem	NOUN
ejpam-5697	343	4	4	4	NUM
ejpam-5697	343	5	,	,	PUNCT
ejpam-5697	343	6	we	we	PRON
ejpam-5697	343	7	obtain	obtain	VERB
ejpam-5697	343	8	lℏ	lℏ	X
ejpam-5697	343	9	{	{	PUNCT
ejpam-5697	343	10	mprl	mprl	VERB
ejpam-5697	343	11	ℏ	ℏ	NOUN
ejpam-5697	343	12	dδ;κ;p	dδ;κ;p	X
ejpam-5697	343	13	a+	a+	PUNCT
ejpam-5697	343	14	x(ξ	x(ξ	PROPN
ejpam-5697	343	15	)	)	PUNCT
ejpam-5697	343	16	}	}	PUNCT
ejpam-5697	343	17	(	(	PUNCT
ejpam-5697	343	18	s	s	X
ejpam-5697	343	19	)	)	PUNCT
ejpam-5697	343	20	=	=	SYM
ejpam-5697	343	21	r(δ	r(δ	PROPN
ejpam-5697	343	22	)	)	PUNCT
ejpam-5697	344	1	1−	1−	NUM
ejpam-5697	344	2	δ	δ	PROPN
ejpam-5697	344	3	lℏ	lℏ	VERB
ejpam-5697	344	4	{	{	PUNCT
ejpam-5697	344	5	g(ξ	g(ξ	PROPN
ejpam-5697	344	6	)	)	PUNCT
ejpam-5697	344	7	}	}	PUNCT
ejpam-5697	344	8	(	(	PUNCT
ejpam-5697	344	9	s	s	X
ejpam-5697	344	10	)	)	PUNCT
ejpam-5697	344	11	+	+	CCONJ
ejpam-5697	344	12	δ	δ	PROPN
ejpam-5697	344	13	ln	ln	NOUN
ejpam-5697	345	1	p	p	NOUN
ejpam-5697	345	2	r(δ)sκ	r(δ)sκ	PROPN
ejpam-5697	345	3	lℏ	lℏ	NOUN
ejpam-5697	345	4	{	{	PUNCT
ejpam-5697	345	5	g(ξ	g(ξ	PROPN
ejpam-5697	345	6	)	)	PUNCT
ejpam-5697	345	7	}	}	PUNCT
ejpam-5697	345	8	(	(	PUNCT
ejpam-5697	345	9	s	s	X
ejpam-5697	345	10	)	)	PUNCT
ejpam-5697	345	11	=	=	SYM
ejpam-5697	345	12	r(δ	r(δ	PROPN
ejpam-5697	345	13	)	)	PUNCT
ejpam-5697	345	14	1−	1−	NUM
ejpam-5697	346	1	δ	δ	PROPN
ejpam-5697	346	2	lℏ	lℏ	VERB
ejpam-5697	346	3	{	{	PUNCT
ejpam-5697	346	4	g(ξ	g(ξ	PROPN
ejpam-5697	346	5	)	)	PUNCT
ejpam-5697	346	6	}	}	PUNCT
ejpam-5697	346	7	(	(	PUNCT
ejpam-5697	346	8	s	s	X
ejpam-5697	346	9	)	)	PUNCT
ejpam-5697	346	10	+	+	CCONJ
ejpam-5697	346	11	δ	δ	PROPN
ejpam-5697	346	12	ln	ln	ADJ
ejpam-5697	346	13	p	p	NOUN
ejpam-5697	346	14	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	346	15	)	)	PUNCT
ejpam-5697	346	16	lℏ	lℏ	NOUN
ejpam-5697	346	17	{	{	PUNCT
ejpam-5697	346	18	(	(	PUNCT
ejpam-5697	346	19	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	346	20	)	)	PUNCT
ejpam-5697	346	21	)	)	PUNCT
ejpam-5697	347	1	λ−1	λ−1	PROPN
ejpam-5697	347	2	∗	∗	VERB
ejpam-5697	347	3	g(ξ	g(ξ	PROPN
ejpam-5697	347	4	)	)	PUNCT
ejpam-5697	347	5	}	}	PUNCT
ejpam-5697	347	6	(	(	PUNCT
ejpam-5697	347	7	s	s	X
ejpam-5697	347	8	)	)	PUNCT
ejpam-5697	348	1	=	=	SYM
ejpam-5697	348	2	lℏ	lℏ	X
ejpam-5697	348	3	{	{	PUNCT
ejpam-5697	348	4	r(δ	r(δ	PROPN
ejpam-5697	348	5	)	)	PUNCT
ejpam-5697	348	6	1−	1−	NUM
ejpam-5697	348	7	δ	δ	PROPN
ejpam-5697	348	8	g(ξ	g(ξ	PROPN
ejpam-5697	348	9	)	)	PUNCT
ejpam-5697	349	1	+	+	CCONJ
ejpam-5697	349	2	δ	δ	PROPN
ejpam-5697	349	3	ln	ln	ADJ
ejpam-5697	349	4	p	p	NOUN
ejpam-5697	349	5	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	349	6	)	)	PUNCT
ejpam-5697	349	7	(	(	PUNCT
ejpam-5697	349	8	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	349	9	)	)	PUNCT
ejpam-5697	349	10	)	)	PUNCT
ejpam-5697	350	1	λ−1	λ−1	PROPN
ejpam-5697	350	2	∗	∗	VERB
ejpam-5697	350	3	g(ξ	g(ξ	PROPN
ejpam-5697	350	4	)	)	PUNCT
ejpam-5697	350	5	}	}	PUNCT
ejpam-5697	350	6	(	(	PUNCT
ejpam-5697	350	7	s	s	NOUN
ejpam-5697	350	8	)	)	PUNCT
ejpam-5697	350	9	.	.	PUNCT
ejpam-5697	351	1	by	by	ADP
ejpam-5697	351	2	taking	take	VERB
ejpam-5697	351	3	inverse	inverse	ADJ
ejpam-5697	351	4	laplace	laplace	NOUN
ejpam-5697	351	5	transformation	transformation	NOUN
ejpam-5697	351	6	,	,	PUNCT
ejpam-5697	351	7	we	we	PRON
ejpam-5697	351	8	get	get	VERB
ejpam-5697	351	9	x(ξ	x(ξ	NOUN
ejpam-5697	351	10	)	)	PUNCT
ejpam-5697	351	11	=	=	SYM
ejpam-5697	351	12	r(δ	r(δ	PROPN
ejpam-5697	351	13	)	)	PUNCT
ejpam-5697	351	14	1−	1−	NUM
ejpam-5697	351	15	δ	δ	PROPN
ejpam-5697	351	16	g(ξ	g(ξ	PROPN
ejpam-5697	351	17	)	)	PUNCT
ejpam-5697	352	1	+	+	NUM
ejpam-5697	352	2	δ	δ	PROPN
ejpam-5697	352	3	ln	ln	ADJ
ejpam-5697	352	4	p	p	PROPN
ejpam-5697	352	5	r(δ	r(δ	NOUN
ejpam-5697	352	6	)	)	PUNCT
ejpam-5697	352	7	rl	rl	VERB
ejpam-5697	352	8	ℏ	ℏ	PROPN
ejpam-5697	352	9	iκ0g(ξ	iκ0g(ξ	PROPN
ejpam-5697	352	10	)	)	PUNCT
ejpam-5697	352	11	,	,	PUNCT
ejpam-5697	352	12	which	which	PRON
ejpam-5697	352	13	gives	give	VERB
ejpam-5697	352	14	the	the	DET
ejpam-5697	352	15	desired	desire	VERB
ejpam-5697	352	16	result	result	NOUN
ejpam-5697	352	17	.	.	PUNCT
ejpam-5697	353	1	gauhar	gauhar	PROPN
ejpam-5697	353	2	rahman	rahman	PROPN
ejpam-5697	353	3	et	et	PROPN
ejpam-5697	353	4	al	al	PROPN
ejpam-5697	353	5	.	.	PUNCT
ejpam-5697	353	6	/	/	SYM
ejpam-5697	353	7	eur	eur	PROPN
ejpam-5697	353	8	.	.	PUNCT
ejpam-5697	354	1	j.	j.	PROPN
ejpam-5697	354	2	pure	pure	PROPN
ejpam-5697	354	3	appl	appl	PROPN
ejpam-5697	354	4	.	.	PROPN
ejpam-5697	354	5	math	math	PROPN
ejpam-5697	354	6	,	,	PUNCT
ejpam-5697	354	7	18	18	NUM
ejpam-5697	354	8	(	(	PUNCT
ejpam-5697	354	9	1	1	NUM
ejpam-5697	354	10	)	)	PUNCT
ejpam-5697	354	11	(	(	PUNCT
ejpam-5697	354	12	2025	2025	NUM
ejpam-5697	354	13	)	)	PUNCT
ejpam-5697	354	14	,	,	PUNCT
ejpam-5697	354	15	5697	5697	NUM
ejpam-5697	354	16	16	16	NUM
ejpam-5697	354	17	of	of	ADP
ejpam-5697	354	18	26	26	NUM
ejpam-5697	354	19	example	example	NOUN
ejpam-5697	354	20	8	8	NUM
ejpam-5697	354	21	.	.	PUNCT
ejpam-5697	355	1	let	let	VERB
ejpam-5697	355	2	us	we	PRON
ejpam-5697	355	3	take	take	VERB
ejpam-5697	355	4	the	the	DET
ejpam-5697	355	5	following	follow	VERB
ejpam-5697	355	6	power	power	NOUN
ejpam-5697	355	7	fractional	fractional	ADJ
ejpam-5697	355	8	differential	differential	NOUN
ejpam-5697	355	9	equation	equation	NOUN
ejpam-5697	355	10	on	on	ADP
ejpam-5697	355	11	[	[	X
ejpam-5697	355	12	0	0	NUM
ejpam-5697	355	13	,	,	PUNCT
ejpam-5697	355	14	100	100	NUM
ejpam-5697	355	15	]	]	PUNCT
ejpam-5697	355	16	(	(	PUNCT
ejpam-5697	355	17	ξ	ξ	X
ejpam-5697	355	18	∈	∈	PROPN
ejpam-5697	356	1	[	[	X
ejpam-5697	356	2	0	0	NUM
ejpam-5697	356	3	,	,	PUNCT
ejpam-5697	356	4	100	100	NUM
ejpam-5697	356	5	]	]	PUNCT
ejpam-5697	356	6	)	)	PUNCT
ejpam-5697	356	7	into	into	ADP
ejpam-5697	356	8	consideration	consideration	NOUN
ejpam-5697	356	9	:	:	PUNCT
ejpam-5697	356	10	mprl	mprl	VERB
ejpam-5697	356	11	ℏ	ℏ	NOUN
ejpam-5697	356	12	dδ;κ;p	dδ;κ;p	X
ejpam-5697	356	13	a+	a+	PUNCT
ejpam-5697	356	14	x(ξ	x(ξ	PROPN
ejpam-5697	356	15	)	)	PUNCT
ejpam-5697	356	16	=	=	SYM
ejpam-5697	356	17	ℏ2(ξ	ℏ2(ξ	PROPN
ejpam-5697	356	18	)	)	PUNCT
ejpam-5697	356	19	.	.	PUNCT
ejpam-5697	357	1	(	(	PUNCT
ejpam-5697	357	2	16	16	NUM
ejpam-5697	357	3	)	)	PUNCT
ejpam-5697	357	4	by	by	ADP
ejpam-5697	357	5	employing	employ	VERB
ejpam-5697	357	6	theorem	theorem	NOUN
ejpam-5697	357	7	5	5	NUM
ejpam-5697	357	8	,	,	PUNCT
ejpam-5697	357	9	we	we	PRON
ejpam-5697	357	10	get	get	VERB
ejpam-5697	357	11	x(ξ	x(ξ	NOUN
ejpam-5697	357	12	)	)	PUNCT
ejpam-5697	357	13	=	=	SYM
ejpam-5697	357	14	r(δ	r(δ	PROPN
ejpam-5697	357	15	)	)	PUNCT
ejpam-5697	357	16	1−	1−	NUM
ejpam-5697	357	17	δ	δ	PROPN
ejpam-5697	357	18	ℏ2(ξ	ℏ2(ξ	PROPN
ejpam-5697	357	19	)	)	PUNCT
ejpam-5697	358	1	+	+	NUM
ejpam-5697	358	2	δ	δ	PROPN
ejpam-5697	358	3	ln	ln	ADJ
ejpam-5697	358	4	p	p	PROPN
ejpam-5697	358	5	r(δ	r(δ	NOUN
ejpam-5697	358	6	)	)	PUNCT
ejpam-5697	358	7	rl	rl	ADP
ejpam-5697	358	8	ℏ	ℏ	PROPN
ejpam-5697	358	9	iκ0ℏ2(ξ	iκ0ℏ2(ξ	PRON
ejpam-5697	358	10	)	)	PUNCT
ejpam-5697	358	11	=	=	SYM
ejpam-5697	358	12	r(δ	r(δ	PROPN
ejpam-5697	358	13	)	)	PUNCT
ejpam-5697	358	14	1−	1−	NUM
ejpam-5697	358	15	δ	δ	PROPN
ejpam-5697	358	16	ℏ2(ξ	ℏ2(ξ	PROPN
ejpam-5697	358	17	)	)	PUNCT
ejpam-5697	358	18	+	+	NUM
ejpam-5697	358	19	2	2	NUM
ejpam-5697	358	20	δ	δ	NOUN
ejpam-5697	358	21	ln	ln	ADJ
ejpam-5697	358	22	p	p	NOUN
ejpam-5697	358	23	r(δ	r(δ	PROPN
ejpam-5697	358	24	)	)	PUNCT
ejpam-5697	358	25	(	(	PUNCT
ejpam-5697	358	26	ℏ(ξ))κ+2	ℏ(ξ))κ+2	X
ejpam-5697	358	27	γ(κ+	γ(κ+	NUM
ejpam-5697	358	28	3	3	NUM
ejpam-5697	358	29	)	)	PUNCT
ejpam-5697	358	30	.	.	PUNCT
ejpam-5697	359	1	(	(	PUNCT
ejpam-5697	359	2	17	17	NUM
ejpam-5697	359	3	)	)	PUNCT
ejpam-5697	359	4	example	example	NOUN
ejpam-5697	359	5	9	9	NUM
ejpam-5697	359	6	.	.	X
ejpam-5697	359	7	letting	let	VERB
ejpam-5697	359	8	ℏ(ξ	ℏ(ξ	VERB
ejpam-5697	359	9	)	)	PUNCT
ejpam-5697	360	1	=	=	SYM
ejpam-5697	360	2	ξ	ξ	X
ejpam-5697	360	3	,	,	PUNCT
ejpam-5697	360	4	we	we	PRON
ejpam-5697	360	5	get	get	VERB
ejpam-5697	360	6	mprl	mprl	ADJ
ejpam-5697	360	7	ℏ	ℏ	NOUN
ejpam-5697	360	8	dδ;κ;p	dδ;κ;p	X
ejpam-5697	360	9	a+	a+	PUNCT
ejpam-5697	360	10	x(ξ	x(ξ	PROPN
ejpam-5697	360	11	)	)	PUNCT
ejpam-5697	360	12	=	=	SYM
ejpam-5697	360	13	ξ2	ξ2	NOUN
ejpam-5697	360	14	.	.	PUNCT
ejpam-5697	361	1	(	(	PUNCT
ejpam-5697	361	2	18	18	NUM
ejpam-5697	361	3	)	)	PUNCT
ejpam-5697	361	4	by	by	ADP
ejpam-5697	361	5	employing	employ	VERB
ejpam-5697	361	6	theorem	theorem	NOUN
ejpam-5697	361	7	5	5	NUM
ejpam-5697	361	8	,	,	PUNCT
ejpam-5697	361	9	we	we	PRON
ejpam-5697	361	10	get	get	VERB
ejpam-5697	361	11	x(ξ	x(ξ	NOUN
ejpam-5697	361	12	)	)	PUNCT
ejpam-5697	361	13	=	=	SYM
ejpam-5697	361	14	r(δ	r(δ	PROPN
ejpam-5697	361	15	)	)	PUNCT
ejpam-5697	362	1	1−	1−	NUM
ejpam-5697	362	2	δ	δ	NOUN
ejpam-5697	362	3	ξ2	ξ2	NOUN
ejpam-5697	362	4	+	+	CCONJ
ejpam-5697	362	5	δ	δ	PROPN
ejpam-5697	362	6	ln	ln	ADJ
ejpam-5697	362	7	p	p	PROPN
ejpam-5697	362	8	r(δ	r(δ	NOUN
ejpam-5697	362	9	)	)	PUNCT
ejpam-5697	362	10	rl	rl	ADP
ejpam-5697	362	11	ℏ	ℏ	PROPN
ejpam-5697	362	12	iκ0ξ	iκ0ξ	VERB
ejpam-5697	362	13	2	2	NUM
ejpam-5697	362	14	=	=	SYM
ejpam-5697	362	15	r(δ	r(δ	PROPN
ejpam-5697	362	16	)	)	PUNCT
ejpam-5697	362	17	1−	1−	NUM
ejpam-5697	363	1	δ	δ	NOUN
ejpam-5697	363	2	ξ2	ξ2	NOUN
ejpam-5697	363	3	+	+	CCONJ
ejpam-5697	363	4	2	2	NUM
ejpam-5697	363	5	δ	δ	PROPN
ejpam-5697	363	6	ln	ln	ADJ
ejpam-5697	363	7	p	p	NOUN
ejpam-5697	363	8	r(δ	r(δ	PROPN
ejpam-5697	363	9	)	)	PUNCT
ejpam-5697	363	10	ξκ+2	ξκ+2	X
ejpam-5697	363	11	γ(κ+	γ(κ+	NUM
ejpam-5697	363	12	3	3	NUM
ejpam-5697	363	13	)	)	PUNCT
ejpam-5697	363	14	.	.	PUNCT
ejpam-5697	364	1	(	(	PUNCT
ejpam-5697	364	2	19	19	NUM
ejpam-5697	364	3	)	)	PUNCT
ejpam-5697	364	4	example	example	NOUN
ejpam-5697	364	5	10	10	NUM
ejpam-5697	364	6	.	.	PUNCT
ejpam-5697	365	1	if	if	SCONJ
ejpam-5697	365	2	we	we	PRON
ejpam-5697	365	3	fixed	fix	VERB
ejpam-5697	365	4	r(δ	r(δ	PROPN
ejpam-5697	365	5	)	)	PUNCT
ejpam-5697	365	6	=	=	SYM
ejpam-5697	366	1	1	1	NUM
ejpam-5697	366	2	,	,	PUNCT
ejpam-5697	366	3	p	p	NOUN
ejpam-5697	366	4	=	=	SYM
ejpam-5697	366	5	2	2	NUM
ejpam-5697	366	6	,	,	PUNCT
ejpam-5697	366	7	3	3	NUM
ejpam-5697	366	8	,	,	PUNCT
ejpam-5697	366	9	4	4	NUM
ejpam-5697	366	10	,	,	PUNCT
ejpam-5697	366	11	5	5	NUM
ejpam-5697	366	12	,	,	PUNCT
ejpam-5697	366	13	0	0	PUNCT
ejpam-5697	366	14	<	<	X
ejpam-5697	366	15	κ	κ	X
ejpam-5697	366	16	<	<	X
ejpam-5697	366	17	3	3	NUM
ejpam-5697	366	18	and	and	CCONJ
ejpam-5697	366	19	δ	δ	NOUN
ejpam-5697	366	20	=	=	NOUN
ejpam-5697	366	21	1	1	NUM
ejpam-5697	366	22	2	2	NUM
ejpam-5697	366	23	in	in	ADP
ejpam-5697	366	24	example	example	NOUN
ejpam-5697	366	25	9	9	NUM
ejpam-5697	366	26	,	,	PUNCT
ejpam-5697	366	27	then	then	ADV
ejpam-5697	366	28	we	we	PRON
ejpam-5697	366	29	have	have	VERB
ejpam-5697	366	30	x(ξ	x(ξ	NOUN
ejpam-5697	366	31	)	)	PUNCT
ejpam-5697	367	1	=	=	SYM
ejpam-5697	367	2	2ξ2	2ξ2	NUM
ejpam-5697	368	1	+	+	CCONJ
ejpam-5697	368	2	ln	ln	ADJ
ejpam-5697	368	3	p	p	X
ejpam-5697	368	4	ξκ+2	ξκ+2	X
ejpam-5697	368	5	γ(κ+	γ(κ+	NUM
ejpam-5697	368	6	3	3	NUM
ejpam-5697	368	7	)	)	PUNCT
ejpam-5697	368	8	.	.	PUNCT
ejpam-5697	369	1	(	(	PUNCT
ejpam-5697	369	2	20	20	X
ejpam-5697	369	3	)	)	PUNCT
ejpam-5697	369	4	corresponding	correspond	VERB
ejpam-5697	369	5	to	to	ADP
ejpam-5697	369	6	the	the	DET
ejpam-5697	369	7	fixed	fix	VERB
ejpam-5697	369	8	values	value	NOUN
ejpam-5697	369	9	of	of	ADP
ejpam-5697	369	10	κ	κ	NOUN
ejpam-5697	369	11	=	=	PROPN
ejpam-5697	369	12	0.2	0.2	NUM
ejpam-5697	369	13	,	,	PUNCT
ejpam-5697	369	14	0.5	0.5	NUM
ejpam-5697	369	15	,	,	PUNCT
ejpam-5697	369	16	0.8	0.8	NUM
ejpam-5697	369	17	,	,	PUNCT
ejpam-5697	369	18	we	we	PRON
ejpam-5697	369	19	have	have	VERB
ejpam-5697	369	20	the	the	DET
ejpam-5697	369	21	following	follow	VERB
ejpam-5697	369	22	2	2	NUM
ejpam-5697	369	23	-	-	PUNCT
ejpam-5697	369	24	dimensional	dimensional	ADJ
ejpam-5697	369	25	p	p	NOUN
ejpam-5697	369	26	=	=	SYM
ejpam-5697	369	27	2	2	NUM
ejpam-5697	369	28	p	p	NOUN
ejpam-5697	369	29	=	=	NOUN
ejpam-5697	369	30	3	3	NUM
ejpam-5697	369	31	p	p	NOUN
ejpam-5697	369	32	=	=	NOUN
ejpam-5697	369	33	4	4	NUM
ejpam-5697	369	34	p	p	NOUN
ejpam-5697	369	35	=	=	SYM
ejpam-5697	369	36	5	5	NUM
ejpam-5697	369	37	figure	figure	NOUN
ejpam-5697	369	38	7	7	NUM
ejpam-5697	369	39	:	:	PUNCT
ejpam-5697	369	40	the	the	DET
ejpam-5697	369	41	graphical	graphical	ADJ
ejpam-5697	369	42	representation	representation	NOUN
ejpam-5697	369	43	of	of	ADP
ejpam-5697	369	44	(	(	PUNCT
ejpam-5697	369	45	20	20	NUM
ejpam-5697	369	46	)	)	PUNCT
ejpam-5697	369	47	corresponding	correspond	VERB
ejpam-5697	369	48	to	to	ADP
ejpam-5697	369	49	choice	choice	NOUN
ejpam-5697	369	50	0	0	NUM
ejpam-5697	369	51	≤	≤	NUM
ejpam-5697	370	1	ξ	ξ	X
ejpam-5697	370	2	≤	≤	NUM
ejpam-5697	370	3	100	100	NUM
ejpam-5697	370	4	.	.	PUNCT
ejpam-5697	370	5	graphical	graphical	ADJ
ejpam-5697	370	6	representation	representation	NOUN
ejpam-5697	370	7	.	.	PUNCT
ejpam-5697	371	1	gauhar	gauhar	PROPN
ejpam-5697	371	2	rahman	rahman	PROPN
ejpam-5697	371	3	et	et	PROPN
ejpam-5697	371	4	al	al	PROPN
ejpam-5697	371	5	.	.	PUNCT
ejpam-5697	371	6	/	/	SYM
ejpam-5697	371	7	eur	eur	PROPN
ejpam-5697	371	8	.	.	PUNCT
ejpam-5697	372	1	j.	j.	PROPN
ejpam-5697	372	2	pure	pure	PROPN
ejpam-5697	372	3	appl	appl	PROPN
ejpam-5697	372	4	.	.	PROPN
ejpam-5697	372	5	math	math	PROPN
ejpam-5697	372	6	,	,	PUNCT
ejpam-5697	372	7	18	18	NUM
ejpam-5697	372	8	(	(	PUNCT
ejpam-5697	372	9	1	1	NUM
ejpam-5697	372	10	)	)	PUNCT
ejpam-5697	372	11	(	(	PUNCT
ejpam-5697	372	12	2025	2025	NUM
ejpam-5697	372	13	)	)	PUNCT
ejpam-5697	372	14	,	,	PUNCT
ejpam-5697	372	15	5697	5697	NUM
ejpam-5697	372	16	17	17	NUM
ejpam-5697	372	17	of	of	ADP
ejpam-5697	372	18	26	26	NUM
ejpam-5697	372	19	20	20	NUM
ejpam-5697	372	20	40	40	NUM
ejpam-5697	372	21	60	60	NUM
ejpam-5697	372	22	80	80	NUM
ejpam-5697	372	23	100	100	NUM
ejpam-5697	372	24	ξ	ξ	SYM
ejpam-5697	372	25	50	50	NUM
ejpam-5697	372	26	000	000	NUM
ejpam-5697	372	27	100000	100000	NUM
ejpam-5697	372	28	150000	150000	NUM
ejpam-5697	372	29	xhξl	xhξl	NOUN
ejpam-5697	372	30	xhξl	xhξl	NOUN
ejpam-5697	372	31	for	for	ADP
ejpam-5697	372	32	different	different	ADJ
ejpam-5697	372	33	κ	κ	NOUN
ejpam-5697	372	34	and	and	CCONJ
ejpam-5697	372	35	p	p	PROPN
ejpam-5697	372	36	color	color	NOUN
ejpam-5697	372	37	legend	legend	NOUN
ejpam-5697	372	38	:	:	PUNCT
ejpam-5697	372	39	κ	κ	X
ejpam-5697	372	40	=	=	SYM
ejpam-5697	372	41	0.2	0.2	NUM
ejpam-5697	372	42	hbluel	hbluel	NOUN
ejpam-5697	372	43	,	,	PUNCT
ejpam-5697	372	44	κ	κ	NOUN
ejpam-5697	372	45	=	=	SYM
ejpam-5697	372	46	0.5	0.5	NUM
ejpam-5697	372	47	hgreenl	hgreenl	NOUN
ejpam-5697	372	48	,	,	PUNCT
ejpam-5697	372	49	κ	κ	X
ejpam-5697	372	50	=	=	SYM
ejpam-5697	372	51	0.8	0.8	NUM
ejpam-5697	372	52	hredl	hredl	NOUN
ejpam-5697	372	53	figure	figure	NOUN
ejpam-5697	372	54	8	8	NUM
ejpam-5697	372	55	:	:	PUNCT
ejpam-5697	372	56	the	the	DET
ejpam-5697	372	57	2	2	NUM
ejpam-5697	372	58	-	-	PUNCT
ejpam-5697	372	59	dimensional	dimensional	ADJ
ejpam-5697	372	60	graphical	graphical	ADJ
ejpam-5697	372	61	representation	representation	NOUN
ejpam-5697	372	62	of	of	ADP
ejpam-5697	372	63	(	(	PUNCT
ejpam-5697	372	64	20	20	NUM
ejpam-5697	372	65	)	)	PUNCT
ejpam-5697	372	66	corresponding	correspond	VERB
ejpam-5697	372	67	to	to	ADP
ejpam-5697	372	68	choice	choice	NOUN
ejpam-5697	372	69	0	0	NUM
ejpam-5697	372	70	≤	≤	NUM
ejpam-5697	372	71	ξ	ξ	X
ejpam-5697	372	72	≤	≤	NUM
ejpam-5697	372	73	100	100	NUM
ejpam-5697	372	74	.	.	PUNCT
ejpam-5697	372	75	example	example	NOUN
ejpam-5697	373	1	11	11	NUM
ejpam-5697	373	2	.	.	PUNCT
ejpam-5697	374	1	if	if	SCONJ
ejpam-5697	374	2	we	we	PRON
ejpam-5697	374	3	fixed	fix	VERB
ejpam-5697	374	4	r(δ	r(δ	PROPN
ejpam-5697	374	5	)	)	PUNCT
ejpam-5697	374	6	=	=	SYM
ejpam-5697	375	1	1	1	NUM
ejpam-5697	375	2	,	,	PUNCT
ejpam-5697	375	3	p	p	NOUN
ejpam-5697	375	4	=	=	SYM
ejpam-5697	375	5	2	2	NUM
ejpam-5697	375	6	,	,	PUNCT
ejpam-5697	375	7	3	3	NUM
ejpam-5697	375	8	,	,	PUNCT
ejpam-5697	375	9	4	4	NUM
ejpam-5697	375	10	,	,	PUNCT
ejpam-5697	375	11	5	5	NUM
ejpam-5697	375	12	,	,	PUNCT
ejpam-5697	375	13	0	0	PUNCT
ejpam-5697	375	14	<	<	X
ejpam-5697	375	15	κ	κ	X
ejpam-5697	375	16	<	<	X
ejpam-5697	375	17	4	4	NUM
ejpam-5697	375	18	and	and	CCONJ
ejpam-5697	375	19	δ	δ	NOUN
ejpam-5697	375	20	=	=	NOUN
ejpam-5697	375	21	1	1	NUM
ejpam-5697	375	22	2	2	NUM
ejpam-5697	375	23	in	in	ADP
ejpam-5697	375	24	example	example	NOUN
ejpam-5697	375	25	9	9	NUM
ejpam-5697	375	26	,	,	PUNCT
ejpam-5697	375	27	then	then	ADV
ejpam-5697	375	28	we	we	PRON
ejpam-5697	375	29	have	have	VERB
ejpam-5697	375	30	x(ξ	x(ξ	NOUN
ejpam-5697	375	31	)	)	PUNCT
ejpam-5697	376	1	=	=	SYM
ejpam-5697	376	2	2ξ2	2ξ2	NUM
ejpam-5697	377	1	+	+	CCONJ
ejpam-5697	377	2	ln	ln	ADJ
ejpam-5697	377	3	p	p	X
ejpam-5697	377	4	ξκ+2	ξκ+2	X
ejpam-5697	377	5	γ(κ+	γ(κ+	NUM
ejpam-5697	377	6	3	3	NUM
ejpam-5697	377	7	)	)	PUNCT
ejpam-5697	377	8	.	.	PUNCT
ejpam-5697	378	1	(	(	PUNCT
ejpam-5697	378	2	21	21	NUM
ejpam-5697	378	3	)	)	PUNCT
ejpam-5697	378	4	corresponding	correspond	VERB
ejpam-5697	378	5	to	to	ADP
ejpam-5697	378	6	the	the	DET
ejpam-5697	378	7	fixed	fix	VERB
ejpam-5697	378	8	values	value	NOUN
ejpam-5697	378	9	of	of	ADP
ejpam-5697	378	10	κ	κ	NOUN
ejpam-5697	378	11	=	=	NOUN
ejpam-5697	378	12	3.2	3.2	NUM
ejpam-5697	378	13	,	,	PUNCT
ejpam-5697	378	14	3.5	3.5	NUM
ejpam-5697	378	15	,	,	PUNCT
ejpam-5697	378	16	3.8	3.8	NUM
ejpam-5697	378	17	,	,	PUNCT
ejpam-5697	378	18	we	we	PRON
ejpam-5697	378	19	have	have	VERB
ejpam-5697	378	20	the	the	DET
ejpam-5697	378	21	following	follow	VERB
ejpam-5697	378	22	2	2	NUM
ejpam-5697	378	23	-	-	PUNCT
ejpam-5697	378	24	dimensional	dimensional	ADJ
ejpam-5697	378	25	p	p	NOUN
ejpam-5697	378	26	=	=	SYM
ejpam-5697	378	27	2	2	NUM
ejpam-5697	378	28	p	p	NOUN
ejpam-5697	378	29	=	=	NOUN
ejpam-5697	378	30	3	3	NUM
ejpam-5697	378	31	p	p	NOUN
ejpam-5697	378	32	=	=	NOUN
ejpam-5697	378	33	4	4	NUM
ejpam-5697	378	34	p	p	NOUN
ejpam-5697	378	35	=	=	SYM
ejpam-5697	378	36	5	5	NUM
ejpam-5697	378	37	figure	figure	NOUN
ejpam-5697	378	38	9	9	NUM
ejpam-5697	378	39	:	:	PUNCT
ejpam-5697	378	40	the	the	DET
ejpam-5697	378	41	graphical	graphical	ADJ
ejpam-5697	378	42	representation	representation	NOUN
ejpam-5697	378	43	of	of	ADP
ejpam-5697	378	44	(	(	PUNCT
ejpam-5697	378	45	21	21	NUM
ejpam-5697	378	46	)	)	PUNCT
ejpam-5697	378	47	corresponding	correspond	VERB
ejpam-5697	378	48	to	to	ADP
ejpam-5697	378	49	choice	choice	NOUN
ejpam-5697	378	50	0	0	NUM
ejpam-5697	378	51	≤	≤	NUM
ejpam-5697	379	1	ξ	ξ	X
ejpam-5697	379	2	≤	≤	NUM
ejpam-5697	379	3	100	100	NUM
ejpam-5697	379	4	.	.	PUNCT
ejpam-5697	379	5	graphical	graphical	ADJ
ejpam-5697	379	6	representation	representation	NOUN
ejpam-5697	379	7	example	example	NOUN
ejpam-5697	379	8	12	12	NUM
ejpam-5697	379	9	.	.	PUNCT
ejpam-5697	380	1	if	if	SCONJ
ejpam-5697	380	2	we	we	PRON
ejpam-5697	380	3	fixed	fix	VERB
ejpam-5697	380	4	r(δ	r(δ	PROPN
ejpam-5697	380	5	)	)	PUNCT
ejpam-5697	380	6	=	=	SYM
ejpam-5697	381	1	1	1	NUM
ejpam-5697	381	2	,	,	PUNCT
ejpam-5697	381	3	p	p	NOUN
ejpam-5697	381	4	=	=	SYM
ejpam-5697	381	5	2	2	NUM
ejpam-5697	381	6	,	,	PUNCT
ejpam-5697	381	7	3	3	NUM
ejpam-5697	381	8	,	,	PUNCT
ejpam-5697	381	9	4	4	NUM
ejpam-5697	381	10	,	,	PUNCT
ejpam-5697	381	11	5	5	NUM
ejpam-5697	381	12	,	,	PUNCT
ejpam-5697	381	13	0	0	PUNCT
ejpam-5697	381	14	<	<	X
ejpam-5697	381	15	κ	κ	X
ejpam-5697	381	16	<	<	X
ejpam-5697	381	17	7	7	NUM
ejpam-5697	381	18	and	and	CCONJ
ejpam-5697	381	19	δ	δ	NOUN
ejpam-5697	381	20	=	=	NOUN
ejpam-5697	381	21	1	1	NUM
ejpam-5697	381	22	2	2	NUM
ejpam-5697	381	23	in	in	ADP
ejpam-5697	381	24	example	example	NOUN
ejpam-5697	381	25	9	9	NUM
ejpam-5697	381	26	,	,	PUNCT
ejpam-5697	381	27	then	then	ADV
ejpam-5697	381	28	we	we	PRON
ejpam-5697	381	29	have	have	VERB
ejpam-5697	381	30	x(ξ	x(ξ	NOUN
ejpam-5697	381	31	)	)	PUNCT
ejpam-5697	382	1	=	=	SYM
ejpam-5697	382	2	2ξ2	2ξ2	NUM
ejpam-5697	383	1	+	+	CCONJ
ejpam-5697	383	2	ln	ln	ADJ
ejpam-5697	383	3	p	p	X
ejpam-5697	383	4	ξκ+2	ξκ+2	X
ejpam-5697	383	5	γ(κ+	γ(κ+	NUM
ejpam-5697	383	6	3	3	NUM
ejpam-5697	383	7	)	)	PUNCT
ejpam-5697	383	8	.	.	PUNCT
ejpam-5697	384	1	(	(	PUNCT
ejpam-5697	384	2	22	22	X
ejpam-5697	384	3	)	)	PUNCT
ejpam-5697	384	4	corresponding	correspond	VERB
ejpam-5697	384	5	to	to	ADP
ejpam-5697	384	6	the	the	DET
ejpam-5697	384	7	fixed	fix	VERB
ejpam-5697	384	8	values	value	NOUN
ejpam-5697	384	9	of	of	ADP
ejpam-5697	384	10	κ	κ	NOUN
ejpam-5697	384	11	=	=	NOUN
ejpam-5697	384	12	6.2	6.2	NUM
ejpam-5697	384	13	,	,	PUNCT
ejpam-5697	384	14	6.5	6.5	NUM
ejpam-5697	384	15	,	,	PUNCT
ejpam-5697	384	16	6.8	6.8	NUM
ejpam-5697	384	17	,	,	PUNCT
ejpam-5697	384	18	we	we	PRON
ejpam-5697	384	19	have	have	VERB
ejpam-5697	384	20	the	the	DET
ejpam-5697	384	21	following	follow	VERB
ejpam-5697	384	22	2	2	NUM
ejpam-5697	384	23	-	-	PUNCT
ejpam-5697	384	24	dimensional	dimensional	ADJ
ejpam-5697	384	25	graphical	graphical	ADJ
ejpam-5697	384	26	representation	representation	NOUN
ejpam-5697	384	27	.	.	PUNCT
ejpam-5697	385	1	gauhar	gauhar	PROPN
ejpam-5697	385	2	rahman	rahman	PROPN
ejpam-5697	385	3	et	et	PROPN
ejpam-5697	385	4	al	al	PROPN
ejpam-5697	385	5	.	.	PUNCT
ejpam-5697	385	6	/	/	SYM
ejpam-5697	385	7	eur	eur	PROPN
ejpam-5697	385	8	.	.	PUNCT
ejpam-5697	386	1	j.	j.	PROPN
ejpam-5697	386	2	pure	pure	PROPN
ejpam-5697	386	3	appl	appl	PROPN
ejpam-5697	386	4	.	.	PROPN
ejpam-5697	386	5	math	math	PROPN
ejpam-5697	386	6	,	,	PUNCT
ejpam-5697	386	7	18	18	NUM
ejpam-5697	386	8	(	(	PUNCT
ejpam-5697	386	9	1	1	NUM
ejpam-5697	386	10	)	)	PUNCT
ejpam-5697	386	11	(	(	PUNCT
ejpam-5697	386	12	2025	2025	NUM
ejpam-5697	386	13	)	)	PUNCT
ejpam-5697	386	14	,	,	PUNCT
ejpam-5697	386	15	5697	5697	NUM
ejpam-5697	386	16	18	18	NUM
ejpam-5697	386	17	of	of	ADP
ejpam-5697	386	18	26	26	NUM
ejpam-5697	386	19	20	20	NUM
ejpam-5697	386	20	40	40	NUM
ejpam-5697	386	21	60	60	NUM
ejpam-5697	386	22	80	80	NUM
ejpam-5697	386	23	100	100	NUM
ejpam-5697	386	24	ξ	ξ	SYM
ejpam-5697	386	25	2.0	2.0	NUM
ejpam-5697	386	26	´	´	NOUN
ejpam-5697	386	27	108	108	NUM
ejpam-5697	386	28	4.0	4.0	NUM
ejpam-5697	386	29	´	´	NOUN
ejpam-5697	386	30	108	108	NUM
ejpam-5697	386	31	6.0	6.0	NUM
ejpam-5697	386	32	´	´	NOUN
ejpam-5697	386	33	108	108	NUM
ejpam-5697	386	34	8.0	8.0	NUM
ejpam-5697	386	35	´	´	NOUN
ejpam-5697	386	36	108	108	NUM
ejpam-5697	386	37	1.0	1.0	NUM
ejpam-5697	386	38	´	´	NOUN
ejpam-5697	386	39	109	109	NUM
ejpam-5697	386	40	1.2	1.2	NUM
ejpam-5697	386	41	´	´	NOUN
ejpam-5697	386	42	109	109	NUM
ejpam-5697	386	43	xhξl	xhξl	NOUN
ejpam-5697	386	44	xhξl	xhξl	NOUN
ejpam-5697	386	45	for	for	ADP
ejpam-5697	386	46	different	different	ADJ
ejpam-5697	386	47	κ	κ	NOUN
ejpam-5697	386	48	and	and	CCONJ
ejpam-5697	386	49	p	p	PROPN
ejpam-5697	386	50	color	color	NOUN
ejpam-5697	386	51	legend	legend	NOUN
ejpam-5697	386	52	:	:	PUNCT
ejpam-5697	386	53	κ	κ	X
ejpam-5697	386	54	=	=	SYM
ejpam-5697	386	55	3.2	3.2	NUM
ejpam-5697	386	56	hbluel	hbluel	NOUN
ejpam-5697	386	57	,	,	PUNCT
ejpam-5697	386	58	κ	κ	NOUN
ejpam-5697	386	59	=	=	SYM
ejpam-5697	386	60	3.5	3.5	NUM
ejpam-5697	386	61	hgreenl	hgreenl	NOUN
ejpam-5697	386	62	,	,	PUNCT
ejpam-5697	386	63	κ	κ	X
ejpam-5697	386	64	=	=	SYM
ejpam-5697	386	65	3.8	3.8	NUM
ejpam-5697	386	66	hredl	hredl	NOUN
ejpam-5697	386	67	figure	figure	NOUN
ejpam-5697	386	68	10	10	NUM
ejpam-5697	386	69	:	:	PUNCT
ejpam-5697	386	70	the	the	DET
ejpam-5697	386	71	2	2	NUM
ejpam-5697	386	72	-	-	PUNCT
ejpam-5697	386	73	dimensional	dimensional	ADJ
ejpam-5697	386	74	graphical	graphical	ADJ
ejpam-5697	386	75	representation	representation	NOUN
ejpam-5697	386	76	of	of	ADP
ejpam-5697	386	77	(	(	PUNCT
ejpam-5697	386	78	21	21	NUM
ejpam-5697	386	79	)	)	PUNCT
ejpam-5697	386	80	corresponding	correspond	VERB
ejpam-5697	386	81	to	to	ADP
ejpam-5697	386	82	choice	choice	NOUN
ejpam-5697	386	83	0	0	NUM
ejpam-5697	386	84	≤	≤	NUM
ejpam-5697	386	85	ξ	ξ	X
ejpam-5697	386	86	≤	≤	NUM
ejpam-5697	386	87	100	100	NUM
ejpam-5697	386	88	.	.	PUNCT
ejpam-5697	387	1	p	p	X
ejpam-5697	387	2	=	=	NOUN
ejpam-5697	387	3	2	2	NUM
ejpam-5697	387	4	p	p	NOUN
ejpam-5697	387	5	=	=	NOUN
ejpam-5697	387	6	3	3	NUM
ejpam-5697	387	7	p	p	NOUN
ejpam-5697	387	8	=	=	NOUN
ejpam-5697	387	9	4	4	NUM
ejpam-5697	387	10	p	p	NOUN
ejpam-5697	387	11	=	=	SYM
ejpam-5697	387	12	5	5	NUM
ejpam-5697	387	13	figure	figure	NOUN
ejpam-5697	387	14	11	11	NUM
ejpam-5697	387	15	:	:	PUNCT
ejpam-5697	387	16	the	the	DET
ejpam-5697	387	17	graphical	graphical	ADJ
ejpam-5697	387	18	representation	representation	NOUN
ejpam-5697	387	19	of	of	ADP
ejpam-5697	387	20	(	(	PUNCT
ejpam-5697	387	21	22	22	NUM
ejpam-5697	387	22	)	)	PUNCT
ejpam-5697	387	23	corresponding	correspond	VERB
ejpam-5697	387	24	to	to	ADP
ejpam-5697	387	25	choice	choice	NOUN
ejpam-5697	387	26	0	0	NUM
ejpam-5697	387	27	≤	≤	NUM
ejpam-5697	387	28	ξ	ξ	X
ejpam-5697	387	29	≤	≤	NUM
ejpam-5697	387	30	100	100	NUM
ejpam-5697	387	31	.	.	PUNCT
ejpam-5697	388	1	20	20	NUM
ejpam-5697	388	2	40	40	NUM
ejpam-5697	388	3	60	60	NUM
ejpam-5697	388	4	80	80	NUM
ejpam-5697	388	5	100	100	NUM
ejpam-5697	388	6	ξ	ξ	SYM
ejpam-5697	388	7	5.0	5.0	NUM
ejpam-5697	388	8	´	´	NOUN
ejpam-5697	388	9	1011	1011	NUM
ejpam-5697	388	10	1.0	1.0	NUM
ejpam-5697	388	11	´	´	NOUN
ejpam-5697	388	12	1012	1012	NUM
ejpam-5697	388	13	1.5	1.5	NUM
ejpam-5697	388	14	´	´	NOUN
ejpam-5697	388	15	1012	1012	NUM
ejpam-5697	388	16	2.0	2.0	NUM
ejpam-5697	388	17	´	´	NOUN
ejpam-5697	388	18	1012	1012	NUM
ejpam-5697	388	19	2.5	2.5	NUM
ejpam-5697	388	20	´	´	NOUN
ejpam-5697	388	21	1012	1012	NUM
ejpam-5697	388	22	xhξl	xhξl	NOUN
ejpam-5697	388	23	xhξl	xhξl	NOUN
ejpam-5697	388	24	for	for	ADP
ejpam-5697	388	25	different	different	ADJ
ejpam-5697	388	26	κ	κ	NOUN
ejpam-5697	388	27	and	and	CCONJ
ejpam-5697	388	28	p	p	PROPN
ejpam-5697	388	29	color	color	NOUN
ejpam-5697	388	30	legend	legend	NOUN
ejpam-5697	388	31	:	:	PUNCT
ejpam-5697	388	32	κ	κ	X
ejpam-5697	388	33	=	=	SYM
ejpam-5697	388	34	6.2	6.2	NUM
ejpam-5697	388	35	hbluel	hbluel	NOUN
ejpam-5697	388	36	,	,	PUNCT
ejpam-5697	388	37	κ	κ	X
ejpam-5697	388	38	=	=	SYM
ejpam-5697	388	39	6.5	6.5	NUM
ejpam-5697	388	40	hgreenl	hgreenl	NOUN
ejpam-5697	388	41	,	,	PUNCT
ejpam-5697	388	42	κ	κ	X
ejpam-5697	388	43	=	=	SYM
ejpam-5697	388	44	6.8	6.8	NUM
ejpam-5697	388	45	hredl	hredl	NOUN
ejpam-5697	388	46	figure	figure	NOUN
ejpam-5697	388	47	12	12	NUM
ejpam-5697	388	48	:	:	PUNCT
ejpam-5697	388	49	the	the	DET
ejpam-5697	388	50	2	2	NUM
ejpam-5697	388	51	-	-	PUNCT
ejpam-5697	388	52	dimensional	dimensional	ADJ
ejpam-5697	388	53	graphical	graphical	ADJ
ejpam-5697	388	54	representation	representation	NOUN
ejpam-5697	388	55	of	of	ADP
ejpam-5697	388	56	(	(	PUNCT
ejpam-5697	388	57	22	22	NUM
ejpam-5697	388	58	)	)	PUNCT
ejpam-5697	388	59	corresponding	correspond	VERB
ejpam-5697	388	60	to	to	ADP
ejpam-5697	388	61	choice	choice	NOUN
ejpam-5697	388	62	0	0	NUM
ejpam-5697	388	63	≤	≤	NUM
ejpam-5697	388	64	ξ	ξ	X
ejpam-5697	388	65	≤	≤	NUM
ejpam-5697	388	66	100	100	NUM
ejpam-5697	388	67	.	.	PUNCT
ejpam-5697	389	1	gauhar	gauhar	PROPN
ejpam-5697	389	2	rahman	rahman	PROPN
ejpam-5697	389	3	et	et	PROPN
ejpam-5697	389	4	al	al	PROPN
ejpam-5697	389	5	.	.	PUNCT
ejpam-5697	389	6	/	/	SYM
ejpam-5697	389	7	eur	eur	PROPN
ejpam-5697	389	8	.	.	PUNCT
ejpam-5697	390	1	j.	j.	PROPN
ejpam-5697	390	2	pure	pure	PROPN
ejpam-5697	390	3	appl	appl	PROPN
ejpam-5697	390	4	.	.	PROPN
ejpam-5697	390	5	math	math	PROPN
ejpam-5697	390	6	,	,	PUNCT
ejpam-5697	390	7	18	18	NUM
ejpam-5697	390	8	(	(	PUNCT
ejpam-5697	390	9	1	1	NUM
ejpam-5697	390	10	)	)	PUNCT
ejpam-5697	390	11	(	(	PUNCT
ejpam-5697	390	12	2025	2025	NUM
ejpam-5697	390	13	)	)	PUNCT
ejpam-5697	390	14	,	,	PUNCT
ejpam-5697	390	15	5697	5697	NUM
ejpam-5697	390	16	19	19	NUM
ejpam-5697	390	17	of	of	ADP
ejpam-5697	390	18	26	26	NUM
ejpam-5697	390	19	example	example	NOUN
ejpam-5697	390	20	13	13	NUM
ejpam-5697	390	21	.	.	PUNCT
ejpam-5697	391	1	if	if	SCONJ
ejpam-5697	391	2	we	we	PRON
ejpam-5697	391	3	fixed	fix	VERB
ejpam-5697	391	4	r(δ	r(δ	PROPN
ejpam-5697	391	5	)	)	PUNCT
ejpam-5697	391	6	=	=	SYM
ejpam-5697	392	1	1	1	NUM
ejpam-5697	392	2	,	,	PUNCT
ejpam-5697	392	3	p	p	NOUN
ejpam-5697	392	4	=	=	SYM
ejpam-5697	392	5	2	2	NUM
ejpam-5697	392	6	,	,	PUNCT
ejpam-5697	392	7	3	3	NUM
ejpam-5697	392	8	,	,	PUNCT
ejpam-5697	392	9	4	4	NUM
ejpam-5697	392	10	,	,	PUNCT
ejpam-5697	392	11	5	5	NUM
ejpam-5697	392	12	,	,	PUNCT
ejpam-5697	392	13	0	0	PUNCT
ejpam-5697	392	14	<	<	X
ejpam-5697	392	15	κ	κ	X
ejpam-5697	392	16	<	<	X
ejpam-5697	392	17	8	8	NUM
ejpam-5697	392	18	and	and	CCONJ
ejpam-5697	392	19	δ	δ	NOUN
ejpam-5697	392	20	=	=	NOUN
ejpam-5697	392	21	1	1	NUM
ejpam-5697	392	22	2	2	NUM
ejpam-5697	392	23	in	in	ADP
ejpam-5697	392	24	example	example	NOUN
ejpam-5697	392	25	9	9	NUM
ejpam-5697	392	26	,	,	PUNCT
ejpam-5697	392	27	then	then	ADV
ejpam-5697	392	28	we	we	PRON
ejpam-5697	392	29	have	have	VERB
ejpam-5697	392	30	x(ξ	x(ξ	NOUN
ejpam-5697	392	31	)	)	PUNCT
ejpam-5697	393	1	=	=	SYM
ejpam-5697	393	2	2ξ2	2ξ2	NUM
ejpam-5697	394	1	+	+	CCONJ
ejpam-5697	394	2	ln	ln	ADJ
ejpam-5697	394	3	p	p	X
ejpam-5697	394	4	ξκ+2	ξκ+2	X
ejpam-5697	394	5	γ(κ+	γ(κ+	NUM
ejpam-5697	394	6	3	3	NUM
ejpam-5697	394	7	)	)	PUNCT
ejpam-5697	394	8	.	.	PUNCT
ejpam-5697	395	1	(	(	PUNCT
ejpam-5697	395	2	23	23	NUM
ejpam-5697	395	3	)	)	PUNCT
ejpam-5697	395	4	p	p	NOUN
ejpam-5697	395	5	=	=	SYM
ejpam-5697	395	6	2	2	NUM
ejpam-5697	395	7	p	p	NOUN
ejpam-5697	395	8	=	=	NOUN
ejpam-5697	395	9	3	3	NUM
ejpam-5697	395	10	p	p	NOUN
ejpam-5697	395	11	=	=	NOUN
ejpam-5697	395	12	4	4	NUM
ejpam-5697	395	13	p	p	NOUN
ejpam-5697	395	14	=	=	SYM
ejpam-5697	395	15	5	5	NUM
ejpam-5697	395	16	figure	figure	NOUN
ejpam-5697	395	17	13	13	NUM
ejpam-5697	395	18	:	:	PUNCT
ejpam-5697	395	19	the	the	DET
ejpam-5697	395	20	graphical	graphical	ADJ
ejpam-5697	395	21	representation	representation	NOUN
ejpam-5697	395	22	of	of	ADP
ejpam-5697	395	23	(	(	PUNCT
ejpam-5697	395	24	23	23	NUM
ejpam-5697	395	25	)	)	PUNCT
ejpam-5697	395	26	corresponding	correspond	VERB
ejpam-5697	395	27	to	to	ADP
ejpam-5697	395	28	choice	choice	NOUN
ejpam-5697	395	29	0	0	NUM
ejpam-5697	395	30	≤	≤	NUM
ejpam-5697	395	31	ξ	ξ	X
ejpam-5697	395	32	≤	≤	NUM
ejpam-5697	395	33	100	100	NUM
ejpam-5697	395	34	.	.	PUNCT
ejpam-5697	396	1	20	20	NUM
ejpam-5697	396	2	40	40	NUM
ejpam-5697	396	3	60	60	NUM
ejpam-5697	396	4	80	80	NUM
ejpam-5697	396	5	100	100	NUM
ejpam-5697	396	6	ξ	ξ	SYM
ejpam-5697	396	7	5.0	5.0	NUM
ejpam-5697	396	8	´	´	NOUN
ejpam-5697	396	9	1012	1012	NUM
ejpam-5697	396	10	1.0	1.0	NUM
ejpam-5697	396	11	´	´	NOUN
ejpam-5697	396	12	1013	1013	NUM
ejpam-5697	396	13	1.5	1.5	NUM
ejpam-5697	396	14	´	´	NOUN
ejpam-5697	396	15	1013	1013	NUM
ejpam-5697	396	16	2.0	2.0	NUM
ejpam-5697	396	17	´	´	NOUN
ejpam-5697	396	18	1013	1013	NUM
ejpam-5697	396	19	2.5	2.5	NUM
ejpam-5697	396	20	´	´	NOUN
ejpam-5697	396	21	1013	1013	NUM
ejpam-5697	396	22	xhξl	xhξl	NOUN
ejpam-5697	396	23	xhξl	xhξl	NOUN
ejpam-5697	396	24	for	for	ADP
ejpam-5697	396	25	different	different	ADJ
ejpam-5697	396	26	κ	κ	NOUN
ejpam-5697	396	27	and	and	CCONJ
ejpam-5697	396	28	p	p	PROPN
ejpam-5697	396	29	color	color	NOUN
ejpam-5697	396	30	legend	legend	NOUN
ejpam-5697	396	31	:	:	PUNCT
ejpam-5697	396	32	κ	κ	X
ejpam-5697	396	33	=	=	SYM
ejpam-5697	396	34	7.2	7.2	NUM
ejpam-5697	396	35	hbluel	hbluel	NOUN
ejpam-5697	396	36	,	,	PUNCT
ejpam-5697	396	37	κ	κ	X
ejpam-5697	396	38	=	=	SYM
ejpam-5697	396	39	7.5	7.5	NUM
ejpam-5697	396	40	hgreenl	hgreenl	NOUN
ejpam-5697	396	41	,	,	PUNCT
ejpam-5697	396	42	κ	κ	X
ejpam-5697	396	43	=	=	SYM
ejpam-5697	396	44	7.8	7.8	NUM
ejpam-5697	396	45	hredl	hredl	NOUN
ejpam-5697	396	46	figure	figure	NOUN
ejpam-5697	396	47	14	14	NUM
ejpam-5697	396	48	:	:	PUNCT
ejpam-5697	396	49	the	the	DET
ejpam-5697	396	50	2	2	NUM
ejpam-5697	396	51	-	-	PUNCT
ejpam-5697	396	52	dimensional	dimensional	ADJ
ejpam-5697	396	53	graphical	graphical	ADJ
ejpam-5697	396	54	representation	representation	NOUN
ejpam-5697	396	55	of	of	ADP
ejpam-5697	396	56	(	(	PUNCT
ejpam-5697	396	57	23	23	NUM
ejpam-5697	396	58	)	)	PUNCT
ejpam-5697	396	59	corresponding	correspond	VERB
ejpam-5697	396	60	to	to	ADP
ejpam-5697	396	61	choice	choice	NOUN
ejpam-5697	396	62	0	0	NUM
ejpam-5697	396	63	≤	≤	NUM
ejpam-5697	397	1	ξ	ξ	X
ejpam-5697	397	2	≤	≤	NUM
ejpam-5697	397	3	100	100	NUM
ejpam-5697	397	4	.	.	PUNCT
ejpam-5697	398	1	corresponding	correspond	VERB
ejpam-5697	398	2	to	to	ADP
ejpam-5697	398	3	the	the	DET
ejpam-5697	398	4	fixed	fix	VERB
ejpam-5697	398	5	values	value	NOUN
ejpam-5697	398	6	of	of	ADP
ejpam-5697	398	7	κ	κ	NOUN
ejpam-5697	398	8	=	=	SYM
ejpam-5697	398	9	7.2	7.2	NUM
ejpam-5697	398	10	,	,	PUNCT
ejpam-5697	398	11	7.5	7.5	NUM
ejpam-5697	398	12	,	,	PUNCT
ejpam-5697	398	13	7.8	7.8	NUM
ejpam-5697	398	14	,	,	PUNCT
ejpam-5697	398	15	we	we	PRON
ejpam-5697	398	16	have	have	VERB
ejpam-5697	398	17	the	the	DET
ejpam-5697	398	18	following	follow	VERB
ejpam-5697	398	19	2	2	NUM
ejpam-5697	398	20	-	-	PUNCT
ejpam-5697	398	21	dimensional	dimensional	ADJ
ejpam-5697	398	22	and	and	CCONJ
ejpam-5697	398	23	3	3	NUM
ejpam-5697	398	24	-	-	PUNCT
ejpam-5697	398	25	dimensional	dimensional	ADJ
ejpam-5697	398	26	graphical	graphical	ADJ
ejpam-5697	398	27	representation	representation	NOUN
ejpam-5697	398	28	.	.	PUNCT
ejpam-5697	399	1	the	the	DET
ejpam-5697	399	2	three	three	NUM
ejpam-5697	399	3	-	-	PUNCT
ejpam-5697	399	4	dimensional	dimensional	ADJ
ejpam-5697	399	5	and	and	CCONJ
ejpam-5697	399	6	two	two	NUM
ejpam-5697	399	7	-	-	PUNCT
ejpam-5697	399	8	dimensional	dimensional	ADJ
ejpam-5697	399	9	graphical	graphical	ADJ
ejpam-5697	399	10	representations	representation	NOUN
ejpam-5697	399	11	illustrate	illustrate	VERB
ejpam-5697	399	12	the	the	DET
ejpam-5697	399	13	convergence	convergence	NOUN
ejpam-5697	399	14	of	of	ADP
ejpam-5697	399	15	the	the	DET
ejpam-5697	399	16	solution	solution	NOUN
ejpam-5697	399	17	to	to	ADP
ejpam-5697	399	18	the	the	DET
ejpam-5697	399	19	differential	differential	ADJ
ejpam-5697	399	20	equation	equation	NOUN
ejpam-5697	399	21	.	.	PUNCT
ejpam-5697	400	1	this	this	DET
ejpam-5697	400	2	behavior	behavior	NOUN
ejpam-5697	400	3	demonstrates	demonstrate	VERB
ejpam-5697	400	4	the	the	DET
ejpam-5697	400	5	boundedness	boundedness	NOUN
ejpam-5697	400	6	and	and	CCONJ
ejpam-5697	400	7	convergence	convergence	NOUN
ejpam-5697	400	8	of	of	ADP
ejpam-5697	400	9	the	the	DET
ejpam-5697	400	10	solution	solution	NOUN
ejpam-5697	400	11	.	.	PUNCT
ejpam-5697	401	1	gauhar	gauhar	PROPN
ejpam-5697	401	2	rahman	rahman	PROPN
ejpam-5697	401	3	et	et	PROPN
ejpam-5697	401	4	al	al	PROPN
ejpam-5697	401	5	.	.	PUNCT
ejpam-5697	401	6	/	/	SYM
ejpam-5697	401	7	eur	eur	PROPN
ejpam-5697	401	8	.	.	PUNCT
ejpam-5697	402	1	j.	j.	PROPN
ejpam-5697	402	2	pure	pure	PROPN
ejpam-5697	402	3	appl	appl	PROPN
ejpam-5697	402	4	.	.	PROPN
ejpam-5697	402	5	math	math	PROPN
ejpam-5697	402	6	,	,	PUNCT
ejpam-5697	402	7	18	18	NUM
ejpam-5697	402	8	(	(	PUNCT
ejpam-5697	402	9	1	1	NUM
ejpam-5697	402	10	)	)	PUNCT
ejpam-5697	402	11	(	(	PUNCT
ejpam-5697	402	12	2025	2025	NUM
ejpam-5697	402	13	)	)	PUNCT
ejpam-5697	402	14	,	,	PUNCT
ejpam-5697	402	15	5697	5697	NUM
ejpam-5697	402	16	20	20	NUM
ejpam-5697	402	17	of	of	ADP
ejpam-5697	402	18	26	26	NUM
ejpam-5697	402	19	4	4	NUM
ejpam-5697	402	20	.	.	PUNCT
ejpam-5697	403	1	the	the	DET
ejpam-5697	403	2	modified	modify	VERB
ejpam-5697	403	3	power	power	NOUN
ejpam-5697	403	4	fractional	fractional	ADJ
ejpam-5697	403	5	integral	integral	ADJ
ejpam-5697	403	6	in	in	ADP
ejpam-5697	403	7	this	this	DET
ejpam-5697	403	8	section	section	NOUN
ejpam-5697	403	9	,	,	PUNCT
ejpam-5697	403	10	we	we	PRON
ejpam-5697	403	11	present	present	VERB
ejpam-5697	403	12	an	an	DET
ejpam-5697	403	13	modified	modify	VERB
ejpam-5697	403	14	version	version	NOUN
ejpam-5697	403	15	of	of	ADP
ejpam-5697	403	16	the	the	DET
ejpam-5697	403	17	power	power	NOUN
ejpam-5697	403	18	fractional	fractional	ADJ
ejpam-5697	403	19	integral	integral	ADJ
ejpam-5697	403	20	operator	operator	NOUN
ejpam-5697	403	21	.	.	PUNCT
ejpam-5697	404	1	also	also	ADV
ejpam-5697	404	2	,	,	PUNCT
ejpam-5697	404	3	we	we	PRON
ejpam-5697	404	4	discuss	discuss	VERB
ejpam-5697	404	5	its	its	PRON
ejpam-5697	404	6	boundedness	boundedness	NOUN
ejpam-5697	404	7	,	,	PUNCT
ejpam-5697	404	8	the	the	DET
ejpam-5697	404	9	laplace	laplace	NOUN
ejpam-5697	404	10	transform	transform	NOUN
ejpam-5697	404	11	,	,	PUNCT
ejpam-5697	404	12	and	and	CCONJ
ejpam-5697	404	13	a	a	DET
ejpam-5697	404	14	few	few	ADJ
ejpam-5697	404	15	other	other	ADJ
ejpam-5697	404	16	related	related	ADJ
ejpam-5697	404	17	features	feature	NOUN
ejpam-5697	404	18	.	.	PUNCT
ejpam-5697	405	1	definition	definition	NOUN
ejpam-5697	405	2	12	12	NUM
ejpam-5697	405	3	.	.	PUNCT
ejpam-5697	406	1	for	for	ADP
ejpam-5697	406	2	any	any	DET
ejpam-5697	406	3	g	g	PROPN
ejpam-5697	406	4	∈	∈	PROPN
ejpam-5697	406	5	l1(0	l1(0	PROPN
ejpam-5697	406	6	,	,	PUNCT
ejpam-5697	406	7	t	t	X
ejpam-5697	406	8	]	]	PUNCT
ejpam-5697	406	9	,	,	PUNCT
ejpam-5697	406	10	the	the	DET
ejpam-5697	406	11	modified	modify	VERB
ejpam-5697	406	12	power	power	NOUN
ejpam-5697	406	13	fractional	fractional	ADJ
ejpam-5697	406	14	operator	operator	NOUN
ejpam-5697	406	15	with	with	ADP
ejpam-5697	406	16	0	0	NUM
ejpam-5697	406	17	<	<	X
ejpam-5697	406	18	δ	δ	X
ejpam-5697	406	19	<	<	X
ejpam-5697	406	20	1	1	NUM
ejpam-5697	406	21	associated	associated	ADJ
ejpam-5697	406	22	ℏ	ℏ	PROPN
ejpam-5697	406	23	is	be	AUX
ejpam-5697	406	24	stated	state	VERB
ejpam-5697	406	25	by	by	ADP
ejpam-5697	406	26	as	as	ADP
ejpam-5697	406	27	mpi	mpi	PROPN
ejpam-5697	406	28	ℏ	ℏ	PROPN
ejpam-5697	406	29	iδ;κ;p	iδ;κ;p	PROPN
ejpam-5697	406	30	a+	a+	PUNCT
ejpam-5697	406	31	g(ξ	g(ξ	PROPN
ejpam-5697	406	32	)	)	PUNCT
ejpam-5697	407	1	=	=	SYM
ejpam-5697	407	2	1−	1−	NUM
ejpam-5697	407	3	δ	δ	PROPN
ejpam-5697	407	4	r(δ	r(δ	PROPN
ejpam-5697	407	5	)	)	PUNCT
ejpam-5697	407	6	g(ξ	g(ξ	PROPN
ejpam-5697	407	7	)	)	PUNCT
ejpam-5697	408	1	+	+	CCONJ
ejpam-5697	408	2	δ	δ	PROPN
ejpam-5697	408	3	ln	ln	ADJ
ejpam-5697	408	4	p	p	NOUN
ejpam-5697	408	5	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	408	6	)	)	PUNCT
ejpam-5697	408	7	∫	∫	PROPN
ejpam-5697	409	1	ξ	ξ	PROPN
ejpam-5697	409	2	a	a	DET
ejpam-5697	409	3	(	(	PUNCT
ejpam-5697	409	4	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	409	5	ℏ(ζ))κ−1ℏ	ℏ(ζ))κ−1ℏ	PROPN
ejpam-5697	409	6	′	′	NUM
ejpam-5697	409	7	(	(	PUNCT
ejpam-5697	409	8	ζ)g(ζ)dζ	ζ)g(ζ)dζ	NOUN
ejpam-5697	409	9	.	.	PUNCT
ejpam-5697	410	1	(	(	PUNCT
ejpam-5697	410	2	24	24	NUM
ejpam-5697	410	3	)	)	PUNCT
ejpam-5697	410	4	remark	remark	NOUN
ejpam-5697	410	5	6	6	NUM
ejpam-5697	410	6	.	.	PUNCT
ejpam-5697	411	1	i.	i.	PROPN
ejpam-5697	411	2	if	if	SCONJ
ejpam-5697	411	3	we	we	PRON
ejpam-5697	411	4	consider	consider	VERB
ejpam-5697	411	5	p	p	NOUN
ejpam-5697	411	6	=	=	PUNCT
ejpam-5697	411	7	e	e	X
ejpam-5697	411	8	in	in	ADP
ejpam-5697	411	9	(	(	PUNCT
ejpam-5697	411	10	24	24	NUM
ejpam-5697	411	11	)	)	PUNCT
ejpam-5697	411	12	,	,	PUNCT
ejpam-5697	411	13	we	we	PRON
ejpam-5697	411	14	get	get	VERB
ejpam-5697	411	15	the	the	DET
ejpam-5697	411	16	fractional	fractional	ADJ
ejpam-5697	411	17	integral	integral	ADJ
ejpam-5697	411	18	defined	define	VERB
ejpam-5697	411	19	by	by	ADP
ejpam-5697	411	20	[	[	X
ejpam-5697	411	21	7	7	NUM
ejpam-5697	411	22	]	]	PUNCT
ejpam-5697	411	23	.	.	PUNCT
ejpam-5697	412	1	ii	ii	PROPN
ejpam-5697	412	2	.	.	PUNCT
ejpam-5697	413	1	if	if	SCONJ
ejpam-5697	413	2	we	we	PRON
ejpam-5697	413	3	consider	consider	VERB
ejpam-5697	413	4	p	p	NOUN
ejpam-5697	413	5	=	=	SYM
ejpam-5697	413	6	e	e	X
ejpam-5697	413	7	and	and	CCONJ
ejpam-5697	413	8	ℏ(ξ	ℏ(ξ	VERB
ejpam-5697	413	9	)	)	PUNCT
ejpam-5697	413	10	=	=	SYM
ejpam-5697	414	1	ξ	ξ	X
ejpam-5697	414	2	in	in	ADP
ejpam-5697	414	3	(	(	PUNCT
ejpam-5697	414	4	24	24	NUM
ejpam-5697	414	5	)	)	PUNCT
ejpam-5697	414	6	,	,	PUNCT
ejpam-5697	414	7	we	we	PRON
ejpam-5697	414	8	get	get	VERB
ejpam-5697	414	9	the	the	DET
ejpam-5697	414	10	fractional	fractional	ADJ
ejpam-5697	414	11	integral	integral	ADJ
ejpam-5697	414	12	defined	define	VERB
ejpam-5697	414	13	by	by	ADP
ejpam-5697	414	14	[	[	X
ejpam-5697	414	15	2	2	NUM
ejpam-5697	414	16	]	]	PUNCT
ejpam-5697	414	17	.	.	PUNCT
ejpam-5697	415	1	iii	iii	X
ejpam-5697	415	2	.	.	PUNCT
ejpam-5697	416	1	if	if	SCONJ
ejpam-5697	416	2	we	we	PRON
ejpam-5697	416	3	consider	consider	VERB
ejpam-5697	416	4	ℏ(ξ	ℏ(ξ	VERB
ejpam-5697	416	5	)	)	PUNCT
ejpam-5697	416	6	=	=	SYM
ejpam-5697	417	1	ξ	ξ	X
ejpam-5697	417	2	in	in	ADP
ejpam-5697	417	3	(	(	PUNCT
ejpam-5697	417	4	24	24	NUM
ejpam-5697	417	5	)	)	PUNCT
ejpam-5697	417	6	,	,	PUNCT
ejpam-5697	417	7	we	we	PRON
ejpam-5697	417	8	get	get	VERB
ejpam-5697	417	9	the	the	DET
ejpam-5697	417	10	fractional	fractional	ADJ
ejpam-5697	417	11	integral	integral	ADJ
ejpam-5697	417	12	defined	define	VERB
ejpam-5697	417	13	by	by	ADP
ejpam-5697	417	14	[	[	PUNCT
ejpam-5697	417	15	11	11	NUM
ejpam-5697	417	16	]	]	PUNCT
ejpam-5697	417	17	.	.	PUNCT
ejpam-5697	418	1	first	first	ADV
ejpam-5697	418	2	,	,	PUNCT
ejpam-5697	418	3	we	we	PRON
ejpam-5697	418	4	establish	establish	VERB
ejpam-5697	418	5	the	the	DET
ejpam-5697	418	6	boundedness	boundedness	NOUN
ejpam-5697	418	7	of	of	ADP
ejpam-5697	418	8	this	this	DET
ejpam-5697	418	9	operator	operator	NOUN
ejpam-5697	418	10	.	.	PUNCT
ejpam-5697	419	1	theorem	theorem	VERB
ejpam-5697	419	2	6	6	NUM
ejpam-5697	419	3	.	.	PUNCT
ejpam-5697	419	4	given	give	VERB
ejpam-5697	419	5	a	a	DET
ejpam-5697	419	6	strictly	strictly	ADV
ejpam-5697	419	7	increasing	increase	VERB
ejpam-5697	419	8	function	function	NOUN
ejpam-5697	419	9	g	g	PROPN
ejpam-5697	419	10	∈	∈	PROPN
ejpam-5697	419	11	xp(0	xp(0	PROPN
ejpam-5697	419	12	,	,	PUNCT
ejpam-5697	419	13	t	t	PROPN
ejpam-5697	419	14	)	)	PUNCT
ejpam-5697	419	15	,	,	PUNCT
ejpam-5697	419	16	ℏ	ℏ	PROPN
ejpam-5697	419	17	,	,	PUNCT
ejpam-5697	419	18	we	we	PRON
ejpam-5697	419	19	get	get	VERB
ejpam-5697	419	20	ωδ	ωδ	ADP
ejpam-5697	419	21	=	=	SYM
ejpam-5697	419	22	δ	δ	PROPN
ejpam-5697	419	23	1−δ	1−δ	NUM
ejpam-5697	419	24	.if	.if	PROPN
ejpam-5697	420	1	1	1	NUM
ejpam-5697	420	2	≤	≤	NOUN
ejpam-5697	420	3	r1	r1	NOUN
ejpam-5697	420	4	<	<	X
ejpam-5697	420	5	∞	∞	PROPN
ejpam-5697	420	6	and	and	CCONJ
ejpam-5697	420	7	r(δ	r(δ	PROPN
ejpam-5697	420	8	)	)	PUNCT
ejpam-5697	420	9	,	,	PUNCT
ejpam-5697	420	10	is	be	AUX
ejpam-5697	420	11	a	a	DET
ejpam-5697	420	12	normalised	normalise	VERB
ejpam-5697	420	13	function	function	NOUN
ejpam-5697	420	14	with	with	ADP
ejpam-5697	420	15	the	the	DET
ejpam-5697	420	16	property	property	NOUN
ejpam-5697	420	17	r(0	r(0	PROPN
ejpam-5697	420	18	)	)	PUNCT
ejpam-5697	420	19	=	=	SYM
ejpam-5697	420	20	r(1	r(1	PROPN
ejpam-5697	420	21	)	)	PUNCT
ejpam-5697	421	1	=	=	PUNCT
ejpam-5697	422	1	1	1	NUM
ejpam-5697	422	2	,	,	PUNCT
ejpam-5697	422	3	then	then	ADV
ejpam-5697	422	4	the	the	DET
ejpam-5697	422	5	following	follow	VERB
ejpam-5697	422	6	inequality	inequality	NOUN
ejpam-5697	422	7	is	be	AUX
ejpam-5697	422	8	true.∥∥∥mpi	true.∥∥∥mpi	NUM
ejpam-5697	422	9	ℏ	ℏ	PRON
ejpam-5697	422	10	iδ;κ;p	iδ;κ;p	PROPN
ejpam-5697	422	11	a+	a+	PUNCT
ejpam-5697	422	12	g(ξ	g(ξ	PROPN
ejpam-5697	422	13	)	)	PUNCT
ejpam-5697	422	14	∥∥∥	∥∥∥	PROPN
ejpam-5697	422	15	xp	xp	CCONJ
ejpam-5697	422	16	≤	≤	PROPN
ejpam-5697	423	1	1−	1−	NUM
ejpam-5697	423	2	δ	δ	PROPN
ejpam-5697	423	3	r(δ	r(δ	PROPN
ejpam-5697	423	4	)	)	PUNCT
ejpam-5697	423	5	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	423	6	+	+	CCONJ
ejpam-5697	423	7	δ	δ	PROPN
ejpam-5697	423	8	ln	ln	ADJ
ejpam-5697	423	9	p	p	NOUN
ejpam-5697	423	10	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	423	11	)	)	PUNCT
ejpam-5697	423	12	∥f∥xp	∥f∥xp	NOUN
ejpam-5697	423	13	(	(	PUNCT
ejpam-5697	423	14	ℏ(θ)−	ℏ(θ)−	PROPN
ejpam-5697	423	15	ℏ(a))κ−1	ℏ(a))κ−1	X
ejpam-5697	423	16	κ−	κ−	PROPN
ejpam-5697	423	17	1	1	NUM
ejpam-5697	423	18	.	.	PUNCT
ejpam-5697	424	1	(	(	PUNCT
ejpam-5697	424	2	25	25	NUM
ejpam-5697	424	3	)	)	PUNCT
ejpam-5697	424	4	proof	proof	NOUN
ejpam-5697	424	5	.	.	PUNCT
ejpam-5697	425	1	by	by	ADP
ejpam-5697	425	2	employing	employ	VERB
ejpam-5697	425	3	the	the	DET
ejpam-5697	425	4	definition	definition	NOUN
ejpam-5697	425	5	24	24	NUM
ejpam-5697	425	6	,	,	PUNCT
ejpam-5697	425	7	we	we	PRON
ejpam-5697	425	8	have∥∥∥mpi	have∥∥∥mpi	VERB
ejpam-5697	425	9	ℏ	ℏ	PROPN
ejpam-5697	425	10	iδ;κ;p	iδ;κ;p	PROPN
ejpam-5697	425	11	a+	a+	PUNCT
ejpam-5697	425	12	g(ξ	g(ξ	PROPN
ejpam-5697	425	13	)	)	PUNCT
ejpam-5697	425	14	∥∥∥	∥∥∥	PROPN
ejpam-5697	425	15	xp	xp	CCONJ
ejpam-5697	425	16	≤	≤	PROPN
ejpam-5697	425	17	1−	1−	NUM
ejpam-5697	425	18	δ	δ	PROPN
ejpam-5697	425	19	r(δ	r(δ	PROPN
ejpam-5697	425	20	)	)	PUNCT
ejpam-5697	425	21	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	426	1	+	+	CCONJ
ejpam-5697	426	2	δ	δ	PROPN
ejpam-5697	426	3	ln	ln	ADJ
ejpam-5697	426	4	p	p	NOUN
ejpam-5697	426	5	r(δ)γ(κ)∥∥∥∥∫	r(δ)γ(κ)∥∥∥∥∫	X
ejpam-5697	426	6	ξ	ξ	X
ejpam-5697	426	7	a	a	PRON
ejpam-5697	426	8	(	(	PUNCT
ejpam-5697	426	9	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	426	10	ℏ(ζ))κ−1ℏ	ℏ(ζ))κ−1ℏ	X
ejpam-5697	426	11	′	′	NUM
ejpam-5697	426	12	(	(	PUNCT
ejpam-5697	426	13	ζ)g(ζ)dζ	ζ)g(ζ)dζ	NOUN
ejpam-5697	426	14	∥∥∥∥	∥∥∥∥	NUM
ejpam-5697	426	15	xp	xp	NOUN
ejpam-5697	427	1	=	=	SYM
ejpam-5697	428	1	1−	1−	NUM
ejpam-5697	428	2	δ	δ	PROPN
ejpam-5697	428	3	r(δ	r(δ	PROPN
ejpam-5697	428	4	)	)	PUNCT
ejpam-5697	428	5	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	428	6	+	+	CCONJ
ejpam-5697	428	7	δ	δ	PROPN
ejpam-5697	428	8	ln	ln	ADJ
ejpam-5697	428	9	p	p	NOUN
ejpam-5697	428	10	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	428	11	)	)	PUNCT
ejpam-5697	428	12	(	(	PUNCT
ejpam-5697	428	13	∫	∫	PROPN
ejpam-5697	428	14	θ	θ	PROPN
ejpam-5697	428	15	0	0	NUM
ejpam-5697	428	16	∣∣∣	∣∣∣	NOUN
ejpam-5697	428	17	∫	∫	PROPN
ejpam-5697	428	18	ξ	ξ	PROPN
ejpam-5697	428	19	a	a	PRON
ejpam-5697	428	20	(	(	PUNCT
ejpam-5697	428	21	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	428	22	ℏ(ζ))κ−1ℏ	ℏ(ζ))κ−1ℏ	PROPN
ejpam-5697	428	23	′	′	NUM
ejpam-5697	428	24	(	(	PUNCT
ejpam-5697	428	25	ζ)g(ζ)dζ	ζ)g(ζ)dζ	NOUN
ejpam-5697	428	26	∣∣∣pℏ′(ξ)du	∣∣∣pℏ′(ξ)du	PROPN
ejpam-5697	428	27	)	)	PUNCT
ejpam-5697	428	28	1	1	NUM
ejpam-5697	428	29	r1	r1	NOUN
ejpam-5697	428	30	.	.	PUNCT
ejpam-5697	429	1	substituting	substitute	VERB
ejpam-5697	429	2	ϱ	ϱ	ADP
ejpam-5697	429	3	=	=	SYM
ejpam-5697	429	4	ℏ(ξ	ℏ(ξ	PROPN
ejpam-5697	429	5	)	)	PUNCT
ejpam-5697	429	6	and	and	CCONJ
ejpam-5697	429	7	λ	λ	X
ejpam-5697	429	8	=	=	SYM
ejpam-5697	429	9	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	429	10	)	)	PUNCT
ejpam-5697	429	11	,	,	PUNCT
ejpam-5697	429	12	we	we	PRON
ejpam-5697	429	13	have∥∥∥mpi	have∥∥∥mpi	VERB
ejpam-5697	429	14	ℏ	ℏ	PROPN
ejpam-5697	429	15	iδ;κ;p	iδ;κ;p	PROPN
ejpam-5697	429	16	a+	a+	PUNCT
ejpam-5697	429	17	g(ξ	g(ξ	PROPN
ejpam-5697	429	18	)	)	PUNCT
ejpam-5697	429	19	∥∥∥	∥∥∥	PROPN
ejpam-5697	429	20	xp	xp	CCONJ
ejpam-5697	429	21	≤	≤	PROPN
ejpam-5697	430	1	1−	1−	NUM
ejpam-5697	430	2	δ	δ	PROPN
ejpam-5697	430	3	r(δ	r(δ	PROPN
ejpam-5697	430	4	)	)	PUNCT
ejpam-5697	430	5	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	430	6	+	+	CCONJ
ejpam-5697	430	7	δ	δ	PROPN
ejpam-5697	430	8	ln	ln	ADJ
ejpam-5697	430	9	p	p	NOUN
ejpam-5697	430	10	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	430	11	)	)	PUNCT
ejpam-5697	430	12	×	×	NOUN
ejpam-5697	430	13	(	(	PUNCT
ejpam-5697	430	14	∫	∫	PROPN
ejpam-5697	430	15	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	430	16	)	)	PUNCT
ejpam-5697	430	17	ℏ(a	ℏ(a	NOUN
ejpam-5697	430	18	)	)	PUNCT
ejpam-5697	430	19	∣∣∣	∣∣∣	NOUN
ejpam-5697	430	20	∫	∫	PROPN
ejpam-5697	430	21	ϱ	ϱ	ADP
ejpam-5697	430	22	ℏ(0	ℏ(0	PROPN
ejpam-5697	430	23	)	)	PUNCT
ejpam-5697	430	24	(	(	PUNCT
ejpam-5697	430	25	ϱ−	ϱ−	INTJ
ejpam-5697	430	26	λ)κ−1g(ℏ−1(λ))dλ	λ)κ−1g(ℏ−1(λ))dλ	PROPN
ejpam-5697	430	27	∣∣∣r1dϱ	∣∣∣r1dϱ	PROPN
ejpam-5697	430	28	)	)	PUNCT
ejpam-5697	430	29	1	1	NUM
ejpam-5697	430	30	r1	r1	NOUN
ejpam-5697	430	31	=	=	SYM
ejpam-5697	430	32	1−	1−	NUM
ejpam-5697	430	33	δ	δ	PROPN
ejpam-5697	430	34	r(δ	r(δ	PROPN
ejpam-5697	430	35	)	)	PUNCT
ejpam-5697	430	36	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	430	37	+	+	CCONJ
ejpam-5697	430	38	δ	δ	PROPN
ejpam-5697	430	39	ln	ln	ADJ
ejpam-5697	430	40	p	p	NOUN
ejpam-5697	430	41	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	430	42	)	)	PUNCT
ejpam-5697	430	43	×	×	NOUN
ejpam-5697	430	44	∫	∫	PROPN
ejpam-5697	430	45	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	430	46	)	)	PUNCT
ejpam-5697	430	47	ℏ(a	ℏ(a	NOUN
ejpam-5697	430	48	)	)	PUNCT
ejpam-5697	430	49	(	(	PUNCT
ejpam-5697	430	50	|g(ℏ−1(λ))|p	|g(ℏ−1(λ))|p	VERB
ejpam-5697	430	51	∣∣∣	∣∣∣	ADJ
ejpam-5697	430	52	∫	∫	PROPN
ejpam-5697	430	53	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	430	54	)	)	PUNCT
ejpam-5697	430	55	λ	λ	PROPN
ejpam-5697	430	56	(	(	PUNCT
ejpam-5697	430	57	ρ−	ρ−	PROPN
ejpam-5697	430	58	λ)κ−1	λ)κ−1	PROPN
ejpam-5697	430	59	∣∣∣r1dϱ	∣∣∣r1dϱ	PROPN
ejpam-5697	430	60	)	)	PUNCT
ejpam-5697	430	61	1	1	NUM
ejpam-5697	430	62	r1	r1	PROPN
ejpam-5697	430	63	dλ	dλ	PROPN
ejpam-5697	430	64	gauhar	gauhar	PROPN
ejpam-5697	430	65	rahman	rahman	PROPN
ejpam-5697	430	66	et	et	PROPN
ejpam-5697	430	67	al	al	PROPN
ejpam-5697	430	68	.	.	PUNCT
ejpam-5697	430	69	/	/	SYM
ejpam-5697	430	70	eur	eur	PROPN
ejpam-5697	430	71	.	.	PUNCT
ejpam-5697	431	1	j.	j.	PROPN
ejpam-5697	431	2	pure	pure	PROPN
ejpam-5697	431	3	appl	appl	PROPN
ejpam-5697	431	4	.	.	PROPN
ejpam-5697	431	5	math	math	PROPN
ejpam-5697	431	6	,	,	PUNCT
ejpam-5697	431	7	18	18	NUM
ejpam-5697	431	8	(	(	PUNCT
ejpam-5697	431	9	1	1	NUM
ejpam-5697	431	10	)	)	PUNCT
ejpam-5697	431	11	(	(	PUNCT
ejpam-5697	431	12	2025	2025	NUM
ejpam-5697	431	13	)	)	PUNCT
ejpam-5697	431	14	,	,	PUNCT
ejpam-5697	431	15	5697	5697	NUM
ejpam-5697	431	16	21	21	NUM
ejpam-5697	431	17	of	of	ADP
ejpam-5697	431	18	26	26	NUM
ejpam-5697	431	19	=	=	SYM
ejpam-5697	431	20	1−	1−	NUM
ejpam-5697	431	21	δ	δ	PROPN
ejpam-5697	431	22	r(δ	r(δ	PROPN
ejpam-5697	431	23	)	)	PUNCT
ejpam-5697	431	24	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	431	25	+	+	CCONJ
ejpam-5697	431	26	δ	δ	PROPN
ejpam-5697	431	27	ln	ln	ADJ
ejpam-5697	431	28	p	p	NOUN
ejpam-5697	431	29	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	431	30	)	)	PUNCT
ejpam-5697	431	31	×	×	NOUN
ejpam-5697	431	32	∫	∫	PROPN
ejpam-5697	431	33	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	431	34	)	)	PUNCT
ejpam-5697	431	35	ℏ(a	ℏ(a	NOUN
ejpam-5697	431	36	)	)	PUNCT
ejpam-5697	431	37	|g(ℏ−1(λ))|	|g(ℏ−1(λ))|	PROPN
ejpam-5697	431	38	(	(	PUNCT
ejpam-5697	431	39	∫	∫	PROPN
ejpam-5697	431	40	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	431	41	)	)	PUNCT
ejpam-5697	431	42	λ	λ	PROPN
ejpam-5697	431	43	(	(	PUNCT
ejpam-5697	431	44	ρ−	ρ−	NOUN
ejpam-5697	431	45	λ)r1(κ−1)dϱ	λ)r1(κ−1)dϱ	PUNCT
ejpam-5697	431	46	)	)	PUNCT
ejpam-5697	431	47	1	1	NUM
ejpam-5697	431	48	r1	r1	NOUN
ejpam-5697	431	49	dλ	dλ	NOUN
ejpam-5697	431	50	=	=	SYM
ejpam-5697	431	51	1−	1−	NUM
ejpam-5697	431	52	δ	δ	PROPN
ejpam-5697	431	53	r(δ	r(δ	PROPN
ejpam-5697	431	54	)	)	PUNCT
ejpam-5697	431	55	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	432	1	+	+	CCONJ
ejpam-5697	432	2	δ	δ	PROPN
ejpam-5697	432	3	ln	ln	ADJ
ejpam-5697	432	4	p	p	NOUN
ejpam-5697	432	5	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	432	6	)	)	PUNCT
ejpam-5697	432	7	×	×	NOUN
ejpam-5697	432	8	∫	∫	PROPN
ejpam-5697	432	9	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	432	10	)	)	PUNCT
ejpam-5697	432	11	ℏ(a	ℏ(a	NOUN
ejpam-5697	432	12	)	)	PUNCT
ejpam-5697	432	13	|g(ℏ−1(λ))|	|g(ℏ−1(λ))|	NOUN
ejpam-5697	432	14	(	(	PUNCT
ejpam-5697	432	15	(	(	PUNCT
ejpam-5697	432	16	ℏ(θ)−	ℏ(θ)−	PROPN
ejpam-5697	432	17	λ)r(κ−1)+1	λ)r(κ−1)+1	NOUN
ejpam-5697	432	18	r1(κ−	r1(κ−	NOUN
ejpam-5697	432	19	1	1	NUM
ejpam-5697	432	20	)	)	PUNCT
ejpam-5697	432	21	+	+	CCONJ
ejpam-5697	432	22	1	1	X
ejpam-5697	432	23	)	)	SYM
ejpam-5697	432	24	1	1	NUM
ejpam-5697	432	25	r1	r1	PROPN
ejpam-5697	432	26	dλ	dλ	NOUN
ejpam-5697	432	27	.	.	PUNCT
ejpam-5697	433	1	with	with	ADP
ejpam-5697	433	2	the	the	DET
ejpam-5697	433	3	help	help	NOUN
ejpam-5697	433	4	of	of	ADP
ejpam-5697	433	5	hölder	hölder	NOUN
ejpam-5697	433	6	,	,	PUNCT
ejpam-5697	433	7	inequality	inequality	NOUN
ejpam-5697	433	8	,	,	PUNCT
ejpam-5697	433	9	we	we	PRON
ejpam-5697	433	10	have∥∥∥mabc	have∥∥∥mabc	VERB
ejpam-5697	433	11	ℏ	ℏ	PROPN
ejpam-5697	433	12	iδ;κ;p	iδ;κ;p	PROPN
ejpam-5697	433	13	a+	a+	PUNCT
ejpam-5697	433	14	g(ξ	g(ξ	PROPN
ejpam-5697	433	15	)	)	PUNCT
ejpam-5697	433	16	∥∥∥	∥∥∥	PROPN
ejpam-5697	433	17	xp	xp	CCONJ
ejpam-5697	433	18	≤	≤	PROPN
ejpam-5697	433	19	1−	1−	NUM
ejpam-5697	433	20	δ	δ	PROPN
ejpam-5697	433	21	r(δ	r(δ	PROPN
ejpam-5697	433	22	)	)	PUNCT
ejpam-5697	433	23	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	434	1	+	+	CCONJ
ejpam-5697	434	2	δ	δ	PROPN
ejpam-5697	434	3	ln	ln	ADJ
ejpam-5697	434	4	p	p	NOUN
ejpam-5697	434	5	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	434	6	)	)	PUNCT
ejpam-5697	434	7	∫	∫	PROPN
ejpam-5697	434	8	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	434	9	)	)	PUNCT
ejpam-5697	434	10	ℏ(a	ℏ(a	NOUN
ejpam-5697	434	11	)	)	PUNCT
ejpam-5697	434	12	(	(	PUNCT
ejpam-5697	434	13	|g(ℏ−1(λ))|r1dλ	|g(ℏ−1(λ))|r1dλ	X
ejpam-5697	434	14	)	)	PUNCT
ejpam-5697	434	15	1	1	NUM
ejpam-5697	434	16	r1	r1	PROPN
ejpam-5697	434	17	×	×	NOUN
ejpam-5697	434	18	(	(	PUNCT
ejpam-5697	434	19	(	(	PUNCT
ejpam-5697	434	20	∫	∫	PROPN
ejpam-5697	434	21	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	434	22	)	)	PUNCT
ejpam-5697	434	23	ℏ(a	ℏ(a	NOUN
ejpam-5697	434	24	)	)	PUNCT
ejpam-5697	434	25	(	(	PUNCT
ejpam-5697	434	26	ℏ(θ)−	ℏ(θ)−	ADV
ejpam-5697	434	27	λ)r1(κ−1)+1	λ)r1(κ−1)+1	ADV
ejpam-5697	434	28	p(κ−	p(κ−	PROPN
ejpam-5697	434	29	1	1	NUM
ejpam-5697	434	30	)	)	PUNCT
ejpam-5697	434	31	+	+	CCONJ
ejpam-5697	434	32	1	1	X
ejpam-5697	434	33	)	)	PUNCT
ejpam-5697	434	34	s1	s1	PROPN
ejpam-5697	434	35	r1	r1	PROPN
ejpam-5697	434	36	dλ	dλ	PROPN
ejpam-5697	434	37	)	)	PUNCT
ejpam-5697	434	38	1	1	NUM
ejpam-5697	434	39	s1	s1	NOUN
ejpam-5697	434	40	,	,	PUNCT
ejpam-5697	434	41	where	where	SCONJ
ejpam-5697	434	42	1	1	NUM
ejpam-5697	434	43	r1	r1	NOUN
ejpam-5697	434	44	+	+	CCONJ
ejpam-5697	434	45	1	1	NUM
ejpam-5697	434	46	s1	s1	NOUN
ejpam-5697	434	47	=	=	SYM
ejpam-5697	434	48	1	1	NUM
ejpam-5697	434	49	,	,	PUNCT
ejpam-5697	434	50	now	now	ADV
ejpam-5697	434	51	substituting	substitute	VERB
ejpam-5697	434	52	ℏ−1(λ	ℏ−1(λ	NOUN
ejpam-5697	434	53	)	)	PUNCT
ejpam-5697	434	54	=	=	SYM
ejpam-5697	434	55	t	t	PROPN
ejpam-5697	434	56	,	,	PUNCT
ejpam-5697	434	57	we	we	PRON
ejpam-5697	434	58	have∥∥∥mpi	have∥∥∥mpi	VERB
ejpam-5697	434	59	ℏ	ℏ	PROPN
ejpam-5697	434	60	iδ;κ;p	iδ;κ;p	PROPN
ejpam-5697	434	61	a+	a+	PUNCT
ejpam-5697	434	62	g(ξ	g(ξ	PROPN
ejpam-5697	434	63	)	)	PUNCT
ejpam-5697	434	64	∥∥∥	∥∥∥	PROPN
ejpam-5697	434	65	xp	xp	CCONJ
ejpam-5697	434	66	≤	≤	PROPN
ejpam-5697	434	67	1−	1−	NUM
ejpam-5697	434	68	δ	δ	PROPN
ejpam-5697	434	69	r(δ	r(δ	PROPN
ejpam-5697	434	70	)	)	PUNCT
ejpam-5697	434	71	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	435	1	+	+	CCONJ
ejpam-5697	435	2	δ	δ	PROPN
ejpam-5697	435	3	ln	ln	ADJ
ejpam-5697	435	4	p	p	NOUN
ejpam-5697	435	5	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	435	6	)	)	PUNCT
ejpam-5697	435	7	∫	∫	PROPN
ejpam-5697	436	1	θ	θ	PROPN
ejpam-5697	436	2	a	a	X
ejpam-5697	436	3	(	(	PUNCT
ejpam-5697	436	4	|g(ζ)|r1ℏ′(ζ)dζ	|g(ζ)|r1ℏ′(ζ)dζ	PROPN
ejpam-5697	436	5	)	)	PUNCT
ejpam-5697	436	6	1	1	NUM
ejpam-5697	436	7	r1	r1	PROPN
ejpam-5697	436	8	×	×	NOUN
ejpam-5697	436	9	(	(	PUNCT
ejpam-5697	436	10	(	(	PUNCT
ejpam-5697	436	11	∫	∫	PROPN
ejpam-5697	436	12	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	436	13	)	)	PUNCT
ejpam-5697	436	14	ℏ(a	ℏ(a	NOUN
ejpam-5697	436	15	)	)	PUNCT
ejpam-5697	436	16	(	(	PUNCT
ejpam-5697	436	17	ℏ(θ)−	ℏ(θ)−	ADV
ejpam-5697	436	18	ℏ(ζ))r1(κ−1)+1	ℏ(ζ))r1(κ−1)+1	PRON
ejpam-5697	436	19	r1(κ−	r1(κ−	NOUN
ejpam-5697	436	20	1	1	NUM
ejpam-5697	436	21	)	)	PUNCT
ejpam-5697	436	22	+	+	CCONJ
ejpam-5697	436	23	1	1	X
ejpam-5697	436	24	)	)	PUNCT
ejpam-5697	436	25	s1	s1	PROPN
ejpam-5697	436	26	r1	r1	PROPN
ejpam-5697	436	27	ℏ′(ζ)dζ	ℏ′(ζ)dζ	PROPN
ejpam-5697	436	28	)	)	PUNCT
ejpam-5697	436	29	1	1	NUM
ejpam-5697	436	30	s1	s1	NOUN
ejpam-5697	436	31	=	=	SYM
ejpam-5697	436	32	1−	1−	NUM
ejpam-5697	436	33	δ	δ	PROPN
ejpam-5697	436	34	r(δ	r(δ	PROPN
ejpam-5697	436	35	)	)	PUNCT
ejpam-5697	436	36	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	436	37	+	+	CCONJ
ejpam-5697	436	38	δ	δ	PROPN
ejpam-5697	436	39	ln	ln	ADJ
ejpam-5697	436	40	p	p	NOUN
ejpam-5697	436	41	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	436	42	)	)	PUNCT
ejpam-5697	436	43	∫	∫	PROPN
ejpam-5697	436	44	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	436	45	)	)	PUNCT
ejpam-5697	436	46	ℏ(a	ℏ(a	NOUN
ejpam-5697	436	47	)	)	PUNCT
ejpam-5697	436	48	(	(	PUNCT
ejpam-5697	436	49	|g(ζ)|r1ℏ′(ζ)dζ	|g(ζ)|r1ℏ′(ζ)dζ	PROPN
ejpam-5697	436	50	)	)	PUNCT
ejpam-5697	436	51	1	1	NUM
ejpam-5697	436	52	r1	r1	PROPN
ejpam-5697	436	53	×	×	NOUN
ejpam-5697	436	54	(	(	PUNCT
ejpam-5697	436	55	(	(	PUNCT
ejpam-5697	436	56	∫	∫	PROPN
ejpam-5697	436	57	ℏ(θ	ℏ(θ	PROPN
ejpam-5697	436	58	)	)	PUNCT
ejpam-5697	436	59	ℏ(a	ℏ(a	NOUN
ejpam-5697	436	60	)	)	PUNCT
ejpam-5697	436	61	(	(	PUNCT
ejpam-5697	436	62	ℏ(θ)−	ℏ(θ)−	ADV
ejpam-5697	436	63	ℏ(ζ))r1(κ−1)+1	ℏ(ζ))r1(κ−1)+1	PRON
ejpam-5697	436	64	r1(κ−	r1(κ−	NOUN
ejpam-5697	436	65	1	1	NUM
ejpam-5697	436	66	)	)	PUNCT
ejpam-5697	436	67	+	+	CCONJ
ejpam-5697	436	68	1	1	X
ejpam-5697	436	69	)	)	PUNCT
ejpam-5697	436	70	s1	s1	PROPN
ejpam-5697	436	71	r1	r1	PROPN
ejpam-5697	436	72	ℏ′(ζ)dζ	ℏ′(ζ)dζ	PROPN
ejpam-5697	436	73	)	)	PUNCT
ejpam-5697	436	74	1	1	NUM
ejpam-5697	436	75	s1	s1	NOUN
ejpam-5697	436	76	≤	≤	NUM
ejpam-5697	436	77	1−	1−	NUM
ejpam-5697	436	78	δ	δ	PROPN
ejpam-5697	436	79	r(δ	r(δ	PROPN
ejpam-5697	436	80	)	)	PUNCT
ejpam-5697	436	81	∥g(ξ)∥xp	∥g(ξ)∥xp	NOUN
ejpam-5697	436	82	+	+	CCONJ
ejpam-5697	436	83	δ	δ	PROPN
ejpam-5697	436	84	ln	ln	ADJ
ejpam-5697	436	85	p	p	NOUN
ejpam-5697	436	86	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	436	87	)	)	PUNCT
ejpam-5697	436	88	(	(	PUNCT
ejpam-5697	436	89	ℏ(θ)−	ℏ(θ)−	PROPN
ejpam-5697	436	90	ℏ(a))κ−1	ℏ(a))κ−1	X
ejpam-5697	436	91	κ−	κ−	PROPN
ejpam-5697	436	92	1	1	NUM
ejpam-5697	436	93	∥f∥xp	∥f∥xp	NOUN
ejpam-5697	436	94	.	.	PUNCT
ejpam-5697	437	1	next	next	ADV
ejpam-5697	437	2	,	,	PUNCT
ejpam-5697	437	3	we	we	PRON
ejpam-5697	437	4	determine	determine	VERB
ejpam-5697	437	5	our	our	PRON
ejpam-5697	437	6	generalised	generalise	VERB
ejpam-5697	437	7	fractional	fractional	ADJ
ejpam-5697	437	8	integral	integral	ADJ
ejpam-5697	437	9	operator	operator	NOUN
ejpam-5697	437	10	’s	’s	PART
ejpam-5697	437	11	laplace	laplace	NOUN
ejpam-5697	437	12	transform	transform	NOUN
ejpam-5697	437	13	.	.	PUNCT
ejpam-5697	438	1	theorem	theorem	VERB
ejpam-5697	438	2	7	7	NUM
ejpam-5697	438	3	.	.	PUNCT
ejpam-5697	439	1	the	the	DET
ejpam-5697	439	2	modified	modify	VERB
ejpam-5697	439	3	fractional	fractional	ADJ
ejpam-5697	439	4	integral	integral	ADJ
ejpam-5697	439	5	of	of	ADP
ejpam-5697	439	6	order	order	NOUN
ejpam-5697	439	7	0	0	PUNCT
ejpam-5697	439	8	<	<	X
ejpam-5697	439	9	δ	δ	X
ejpam-5697	439	10	<	<	X
ejpam-5697	439	11	1	1	NUM
ejpam-5697	439	12	,	,	PUNCT
ejpam-5697	439	13	κ	κ	X
ejpam-5697	439	14	>	>	X
ejpam-5697	439	15	0	0	NUM
ejpam-5697	439	16	associated	associate	VERB
ejpam-5697	439	17	with	with	ADP
ejpam-5697	439	18	ℏ	ℏ	PROPN
ejpam-5697	439	19	is	be	AUX
ejpam-5697	439	20	defined	define	VERB
ejpam-5697	439	21	for	for	ADP
ejpam-5697	439	22	g	g	PROPN
ejpam-5697	439	23	∈	∈	PROPN
ejpam-5697	439	24	l1(0	l1(0	PROPN
ejpam-5697	439	25	,	,	PUNCT
ejpam-5697	439	26	t	t	X
ejpam-5697	439	27	]	]	PUNCT
ejpam-5697	439	28	as	as	SCONJ
ejpam-5697	439	29	follows	follow	VERB
ejpam-5697	439	30	:	:	PUNCT
ejpam-5697	439	31	lℏ	lℏ	X
ejpam-5697	439	32	(	(	PUNCT
ejpam-5697	439	33	mpi	mpi	PROPN
ejpam-5697	439	34	ℏ	ℏ	PROPN
ejpam-5697	439	35	iδ;κ;p	iδ;κ;p	PROPN
ejpam-5697	439	36	a+	a+	PUNCT
ejpam-5697	439	37	g(ξ	g(ξ	PROPN
ejpam-5697	439	38	)	)	PUNCT
ejpam-5697	439	39	)	)	PUNCT
ejpam-5697	440	1	=	=	SYM
ejpam-5697	440	2	1−	1−	NUM
ejpam-5697	440	3	δ	δ	NOUN
ejpam-5697	440	4	r(δ	r(δ	PROPN
ejpam-5697	440	5	)	)	PUNCT
ejpam-5697	440	6	sκ	sκ	PROPN
ejpam-5697	441	1	+	+	NUM
ejpam-5697	441	2	ωδ	ωδ	INTJ
ejpam-5697	441	3	ln	ln	ADJ
ejpam-5697	441	4	p	p	X
ejpam-5697	441	5	sκ	sκ	PROPN
ejpam-5697	441	6	lℏ(g(ξ	lℏ(g(ξ	X
ejpam-5697	441	7	)	)	PUNCT
ejpam-5697	441	8	)	)	PUNCT
ejpam-5697	441	9	.	.	PUNCT
ejpam-5697	442	1	proof	proof	NOUN
ejpam-5697	442	2	.	.	PUNCT
ejpam-5697	443	1	through	through	ADP
ejpam-5697	443	2	application	application	NOUN
ejpam-5697	443	3	of	of	ADP
ejpam-5697	443	4	definition	definition	NOUN
ejpam-5697	443	5	24	24	NUM
ejpam-5697	443	6	,	,	PUNCT
ejpam-5697	443	7	we	we	PRON
ejpam-5697	443	8	have	have	AUX
ejpam-5697	443	9	lℏ	lℏ	VERB
ejpam-5697	443	10	(	(	PUNCT
ejpam-5697	443	11	mpi	mpi	PROPN
ejpam-5697	443	12	ℏ	ℏ	PROPN
ejpam-5697	443	13	iδ;κ;pa	iδ;κ;pa	PROPN
ejpam-5697	443	14	g(ξ	g(ξ	PROPN
ejpam-5697	443	15	)	)	PUNCT
ejpam-5697	443	16	)	)	PUNCT
ejpam-5697	444	1	=	=	SYM
ejpam-5697	444	2	1−	1−	NUM
ejpam-5697	444	3	δ	δ	PROPN
ejpam-5697	444	4	r(δ	r(δ	PROPN
ejpam-5697	444	5	)	)	PUNCT
ejpam-5697	444	6	lℏ(g(ξ	lℏ(g(ξ	NUM
ejpam-5697	444	7	)	)	PUNCT
ejpam-5697	444	8	)	)	PUNCT
ejpam-5697	445	1	+	+	CCONJ
ejpam-5697	445	2	δ	δ	PROPN
ejpam-5697	445	3	ln	ln	ADJ
ejpam-5697	445	4	p	p	NOUN
ejpam-5697	445	5	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	445	6	)	)	PUNCT
ejpam-5697	445	7	lℏ	lℏ	NOUN
ejpam-5697	445	8	(	(	PUNCT
ejpam-5697	445	9	(	(	PUNCT
ejpam-5697	445	10	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	445	11	ℏ(a))κ−1	ℏ(a))κ−1	X
ejpam-5697	445	12	∗	∗	NOUN
ejpam-5697	445	13	g(ξ	g(ξ	PROPN
ejpam-5697	445	14	)	)	PUNCT
ejpam-5697	445	15	)	)	PUNCT
ejpam-5697	446	1	gauhar	gauhar	PROPN
ejpam-5697	446	2	rahman	rahman	PROPN
ejpam-5697	446	3	et	et	PROPN
ejpam-5697	446	4	al	al	PROPN
ejpam-5697	446	5	.	.	PUNCT
ejpam-5697	446	6	/	/	SYM
ejpam-5697	446	7	eur	eur	PROPN
ejpam-5697	446	8	.	.	PUNCT
ejpam-5697	447	1	j.	j.	PROPN
ejpam-5697	447	2	pure	pure	PROPN
ejpam-5697	447	3	appl	appl	PROPN
ejpam-5697	447	4	.	.	PROPN
ejpam-5697	447	5	math	math	PROPN
ejpam-5697	447	6	,	,	PUNCT
ejpam-5697	447	7	18	18	NUM
ejpam-5697	447	8	(	(	PUNCT
ejpam-5697	447	9	1	1	NUM
ejpam-5697	447	10	)	)	PUNCT
ejpam-5697	447	11	(	(	PUNCT
ejpam-5697	447	12	2025	2025	NUM
ejpam-5697	447	13	)	)	PUNCT
ejpam-5697	447	14	,	,	PUNCT
ejpam-5697	447	15	5697	5697	NUM
ejpam-5697	447	16	22	22	NUM
ejpam-5697	447	17	of	of	ADP
ejpam-5697	447	18	26	26	NUM
ejpam-5697	447	19	=	=	SYM
ejpam-5697	447	20	1−	1−	NUM
ejpam-5697	447	21	δ	δ	PROPN
ejpam-5697	447	22	r(δ	r(δ	PROPN
ejpam-5697	447	23	)	)	PUNCT
ejpam-5697	447	24	lℏ(g(ξ	lℏ(g(ξ	NUM
ejpam-5697	447	25	)	)	PUNCT
ejpam-5697	447	26	)	)	PUNCT
ejpam-5697	448	1	+	+	CCONJ
ejpam-5697	448	2	δ	δ	PROPN
ejpam-5697	448	3	ln	ln	ADJ
ejpam-5697	448	4	p	p	NOUN
ejpam-5697	448	5	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	448	6	)	)	PUNCT
ejpam-5697	448	7	lℏ	lℏ	NOUN
ejpam-5697	448	8	(	(	PUNCT
ejpam-5697	448	9	(	(	PUNCT
ejpam-5697	448	10	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	448	11	ℏ(a))κ−1	ℏ(a))κ−1	X
ejpam-5697	448	12	)	)	PUNCT
ejpam-5697	448	13	lℏ(g(ξ	lℏ(g(ξ	NUM
ejpam-5697	448	14	)	)	PUNCT
ejpam-5697	448	15	)	)	PUNCT
ejpam-5697	449	1	=	=	SYM
ejpam-5697	449	2	1−	1−	NUM
ejpam-5697	449	3	δ	δ	PROPN
ejpam-5697	449	4	r(δ	r(δ	PROPN
ejpam-5697	449	5	)	)	PUNCT
ejpam-5697	449	6	lℏ(g(ξ	lℏ(g(ξ	NUM
ejpam-5697	449	7	)	)	PUNCT
ejpam-5697	449	8	)	)	PUNCT
ejpam-5697	450	1	+	+	CCONJ
ejpam-5697	450	2	δ	δ	PROPN
ejpam-5697	450	3	ln	ln	ADJ
ejpam-5697	450	4	p	p	NOUN
ejpam-5697	450	5	r(δ)sκ	r(δ)sκ	NUM
ejpam-5697	450	6	lℏ(g(ξ	lℏ(g(ξ	NUM
ejpam-5697	450	7	)	)	PUNCT
ejpam-5697	450	8	)	)	PUNCT
ejpam-5697	451	1	=	=	SYM
ejpam-5697	452	1	1−	1−	NUM
ejpam-5697	452	2	δ	δ	NOUN
ejpam-5697	452	3	r(δ	r(δ	PROPN
ejpam-5697	452	4	)	)	PUNCT
ejpam-5697	453	1	sκ	sκ	PROPN
ejpam-5697	454	1	+	+	NUM
ejpam-5697	454	2	ωδ	ωδ	INTJ
ejpam-5697	454	3	ln	ln	ADJ
ejpam-5697	454	4	p	p	X
ejpam-5697	454	5	sκ	sκ	PROPN
ejpam-5697	454	6	lℏ(g(ξ	lℏ(g(ξ	X
ejpam-5697	454	7	)	)	PUNCT
ejpam-5697	454	8	)	)	PUNCT
ejpam-5697	454	9	,	,	PUNCT
ejpam-5697	454	10	which	which	PRON
ejpam-5697	454	11	gives	give	VERB
ejpam-5697	454	12	the	the	DET
ejpam-5697	454	13	desired	desire	VERB
ejpam-5697	454	14	result	result	NOUN
ejpam-5697	454	15	.	.	PUNCT
ejpam-5697	455	1	theorem	theorem	ADJ
ejpam-5697	455	2	8	8	NUM
ejpam-5697	455	3	.	.	PUNCT
ejpam-5697	455	4	assuming	assume	VERB
ejpam-5697	455	5	g′	g′	PROPN
ejpam-5697	455	6	∈	∈	PROPN
ejpam-5697	455	7	l1(0	l1(0	PROPN
ejpam-5697	455	8	,	,	PUNCT
ejpam-5697	455	9	t	t	PROPN
ejpam-5697	455	10	)	)	PUNCT
ejpam-5697	455	11	,	,	PUNCT
ejpam-5697	455	12	and	and	CCONJ
ejpam-5697	455	13	0	0	NUM
ejpam-5697	455	14	<	<	X
ejpam-5697	455	15	δ	δ	X
ejpam-5697	455	16	<	<	X
ejpam-5697	455	17	1	1	NUM
ejpam-5697	455	18	,	,	PUNCT
ejpam-5697	455	19	the	the	DET
ejpam-5697	455	20	following	follow	VERB
ejpam-5697	455	21	outcome	outcome	NOUN
ejpam-5697	455	22	can	can	AUX
ejpam-5697	455	23	be	be	AUX
ejpam-5697	455	24	obtained	obtain	VERB
ejpam-5697	455	25	.	.	PUNCT
ejpam-5697	456	1	mpc	mpc	NOUN
ejpam-5697	456	2	ℏ	ℏ	NOUN
ejpam-5697	456	3	dδ;κ;p	dδ;κ;p	NOUN
ejpam-5697	456	4	a+	a+	PUNCT
ejpam-5697	456	5	(	(	PUNCT
ejpam-5697	456	6	mpi	mpi	PROPN
ejpam-5697	456	7	ℏ	ℏ	PROPN
ejpam-5697	456	8	iδ;κ;p	iδ;κ;p	PROPN
ejpam-5697	456	9	a+	a+	PUNCT
ejpam-5697	456	10	)	)	PUNCT
ejpam-5697	456	11	g(ξ	g(ξ	PROPN
ejpam-5697	456	12	)	)	PUNCT
ejpam-5697	457	1	=	=	NOUN
ejpam-5697	457	2	g(ξ)−	g(ξ)−	PROPN
ejpam-5697	457	3	g(0	g(0	PROPN
ejpam-5697	457	4	)	)	PUNCT
ejpam-5697	457	5	peκ,1	peκ,1	NOUN
ejpam-5697	457	6	(	(	PUNCT
ejpam-5697	457	7	−	−	PROPN
ejpam-5697	457	8	ωδ	ωδ	X
ejpam-5697	457	9	(	(	PUNCT
ejpam-5697	457	10	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	457	11	ℏ(a	ℏ(a	NOUN
ejpam-5697	457	12	)	)	PUNCT
ejpam-5697	457	13	)	)	PUNCT
ejpam-5697	457	14	κ	κ	X
ejpam-5697	457	15	)	)	PUNCT
ejpam-5697	457	16	.	.	PUNCT
ejpam-5697	458	1	(	(	PUNCT
ejpam-5697	458	2	26	26	NUM
ejpam-5697	458	3	)	)	PUNCT
ejpam-5697	458	4	proof	proof	NOUN
ejpam-5697	458	5	.	.	PUNCT
ejpam-5697	459	1	using	use	VERB
ejpam-5697	459	2	the	the	DET
ejpam-5697	459	3	laplace	laplace	NOUN
ejpam-5697	459	4	transform	transform	NOUN
ejpam-5697	459	5	definition	definition	NOUN
ejpam-5697	459	6	,	,	PUNCT
ejpam-5697	459	7	we	we	PRON
ejpam-5697	459	8	have	have	AUX
ejpam-5697	459	9	lℏ	lℏ	VERB
ejpam-5697	459	10	(	(	PUNCT
ejpam-5697	459	11	mpc	mpc	NOUN
ejpam-5697	459	12	ℏ	ℏ	NOUN
ejpam-5697	459	13	dδ;κ;p	dδ;κ;p	NUM
ejpam-5697	459	14	a+	a+	PUNCT
ejpam-5697	459	15	(	(	PUNCT
ejpam-5697	459	16	mpc	mpc	PROPN
ejpam-5697	459	17	ℏ	ℏ	PROPN
ejpam-5697	459	18	iδ;κ;pa	iδ;κ;pa	PROPN
ejpam-5697	459	19	)	)	PUNCT
ejpam-5697	459	20	g(ξ	g(ξ	PROPN
ejpam-5697	459	21	)	)	PUNCT
ejpam-5697	459	22	)	)	PUNCT
ejpam-5697	460	1	=	=	PUNCT
ejpam-5697	460	2	r(δ	r(δ	PROPN
ejpam-5697	460	3	)	)	PUNCT
ejpam-5697	460	4	1−	1−	NUM
ejpam-5697	461	1	δ	δ	PROPN
ejpam-5697	461	2	sκ	sκ	PROPN
ejpam-5697	461	3	sκ	sκ	PROPN
ejpam-5697	462	1	+	+	NUM
ejpam-5697	462	2	ωδ	ωδ	INTJ
ejpam-5697	462	3	ln	ln	ADJ
ejpam-5697	462	4	p	p	NOUN
ejpam-5697	462	5	lℏ	lℏ	NOUN
ejpam-5697	462	6	(	(	PUNCT
ejpam-5697	462	7	mpi	mpi	PROPN
ejpam-5697	462	8	ℏ	ℏ	PROPN
ejpam-5697	462	9	iδ;κ;pa	iδ;κ;pa	PROPN
ejpam-5697	462	10	g(ξ	g(ξ	PROPN
ejpam-5697	462	11	)	)	PUNCT
ejpam-5697	462	12	)	)	PUNCT
ejpam-5697	463	1	−	−	ADP
ejpam-5697	463	2	r(δ	r(δ	PROPN
ejpam-5697	463	3	)	)	PUNCT
ejpam-5697	463	4	1−	1−	NUM
ejpam-5697	463	5	δ	δ	PROPN
ejpam-5697	463	6	sκ−1	sκ−1	PROPN
ejpam-5697	463	7	sκ	sκ	PROPN
ejpam-5697	463	8	+	+	ADP
ejpam-5697	463	9	ωδ	ωδ	INTJ
ejpam-5697	463	10	ln	ln	ADJ
ejpam-5697	463	11	p	p	X
ejpam-5697	463	12	(	(	PUNCT
ejpam-5697	463	13	mpi	mpi	PROPN
ejpam-5697	463	14	ℏ	ℏ	PROPN
ejpam-5697	463	15	iδ;κ;pa	iδ;κ;pa	PROPN
ejpam-5697	463	16	g(0	g(0	NOUN
ejpam-5697	463	17	)	)	PUNCT
ejpam-5697	463	18	)	)	PUNCT
ejpam-5697	464	1	=	=	PUNCT
ejpam-5697	464	2	sκ	sκ	PROPN
ejpam-5697	464	3	sκ	sκ	PROPN
ejpam-5697	464	4	+	+	NUM
ejpam-5697	464	5	ωδ	ωδ	INTJ
ejpam-5697	464	6	ln	ln	ADJ
ejpam-5697	464	7	p	p	X
ejpam-5697	464	8	(	(	PUNCT
ejpam-5697	464	9	sκ	sκ	PROPN
ejpam-5697	464	10	+	+	ADP
ejpam-5697	464	11	ωδ	ωδ	INTJ
ejpam-5697	464	12	ln	ln	ADJ
ejpam-5697	464	13	p	p	NOUN
ejpam-5697	464	14	sκ	sκ	PROPN
ejpam-5697	464	15	)	)	PUNCT
ejpam-5697	464	16	lℏ(g(ξ))−	lℏ(g(ξ))−	PROPN
ejpam-5697	464	17	sκ−1	sκ−1	ADJ
ejpam-5697	464	18	sκ	sκ	ADJ
ejpam-5697	465	1	+	+	ADP
ejpam-5697	465	2	ωδ	ωδ	INTJ
ejpam-5697	465	3	ln	ln	ADJ
ejpam-5697	465	4	p	p	NOUN
ejpam-5697	465	5	g(0	g(0	NOUN
ejpam-5697	465	6	)	)	PUNCT
ejpam-5697	465	7	=	=	PUNCT
ejpam-5697	466	1	lℏ(g(ξ))−	lℏ(g(ξ))−	PROPN
ejpam-5697	466	2	sκ−1	sκ−1	ADJ
ejpam-5697	467	1	sκ	sκ	PROPN
ejpam-5697	467	2	+	+	ADP
ejpam-5697	467	3	ωδ	ωδ	INTJ
ejpam-5697	467	4	ln	ln	ADJ
ejpam-5697	467	5	p	p	NOUN
ejpam-5697	467	6	g(0	g(0	PROPN
ejpam-5697	467	7	)	)	PUNCT
ejpam-5697	467	8	.	.	PUNCT
ejpam-5697	468	1	utilising	utilise	VERB
ejpam-5697	468	2	the	the	DET
ejpam-5697	468	3	inverse	inverse	ADJ
ejpam-5697	468	4	laplace	laplace	NOUN
ejpam-5697	468	5	transform	transform	NOUN
ejpam-5697	468	6	,	,	PUNCT
ejpam-5697	468	7	we	we	PRON
ejpam-5697	468	8	arrive	arrive	VERB
ejpam-5697	468	9	at	at	ADP
ejpam-5697	468	10	(	(	PUNCT
ejpam-5697	468	11	mpc	mpc	PROPN
ejpam-5697	468	12	ℏ	ℏ	NOUN
ejpam-5697	468	13	dδ;κ;p	dδ;κ;p	NUM
ejpam-5697	468	14	a	a	DET
ejpam-5697	468	15	(	(	PUNCT
ejpam-5697	468	16	mpi	mpi	PROPN
ejpam-5697	468	17	ℏ	ℏ	PROPN
ejpam-5697	468	18	iδ;κ;pa	iδ;κ;pa	PROPN
ejpam-5697	468	19	)	)	PUNCT
ejpam-5697	468	20	g(ξ	g(ξ	PROPN
ejpam-5697	468	21	)	)	PUNCT
ejpam-5697	468	22	)	)	PUNCT
ejpam-5697	469	1	=	=	NOUN
ejpam-5697	469	2	g(ξ)−	g(ξ)−	PROPN
ejpam-5697	469	3	g(0	g(0	PROPN
ejpam-5697	469	4	)	)	PUNCT
ejpam-5697	469	5	peκ,1	peκ,1	NOUN
ejpam-5697	469	6	(	(	PUNCT
ejpam-5697	469	7	−	−	PROPN
ejpam-5697	469	8	ωδ	ωδ	X
ejpam-5697	469	9	(	(	PUNCT
ejpam-5697	469	10	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	469	11	ℏ(a	ℏ(a	NOUN
ejpam-5697	469	12	)	)	PUNCT
ejpam-5697	469	13	)	)	PUNCT
ejpam-5697	469	14	κ	κ	X
ejpam-5697	469	15	)	)	PUNCT
ejpam-5697	469	16	,	,	PUNCT
ejpam-5697	469	17	which	which	PRON
ejpam-5697	469	18	completes	complete	VERB
ejpam-5697	469	19	the	the	DET
ejpam-5697	469	20	required	require	VERB
ejpam-5697	469	21	result	result	NOUN
ejpam-5697	469	22	.	.	PUNCT
ejpam-5697	470	1	theorem	theorem	NOUN
ejpam-5697	470	2	9	9	NUM
ejpam-5697	470	3	.	.	PUNCT
ejpam-5697	470	4	assuming	assume	VERB
ejpam-5697	470	5	that	that	SCONJ
ejpam-5697	470	6	g′	g′	PROPN
ejpam-5697	470	7	∈	∈	PROPN
ejpam-5697	470	8	l1(0	l1(0	PROPN
ejpam-5697	470	9	,	,	PUNCT
ejpam-5697	470	10	t	t	PROPN
ejpam-5697	470	11	)	)	PUNCT
ejpam-5697	470	12	,	,	PUNCT
ejpam-5697	470	13	a	a	DET
ejpam-5697	470	14	=	=	NOUN
ejpam-5697	470	15	0	0	NUM
ejpam-5697	470	16	,	,	PUNCT
ejpam-5697	470	17	and	and	CCONJ
ejpam-5697	470	18	0	0	NUM
ejpam-5697	470	19	<	<	X
ejpam-5697	470	20	δ	δ	X
ejpam-5697	470	21	<	<	X
ejpam-5697	470	22	1	1	NUM
ejpam-5697	470	23	,	,	PUNCT
ejpam-5697	470	24	the	the	DET
ejpam-5697	470	25	following	follow	VERB
ejpam-5697	470	26	outcome	outcome	NOUN
ejpam-5697	470	27	can	can	AUX
ejpam-5697	470	28	be	be	AUX
ejpam-5697	470	29	obtained	obtain	VERB
ejpam-5697	470	30	.	.	PUNCT
ejpam-5697	471	1	mpi	mpi	PROPN
ejpam-5697	471	2	ℏ	ℏ	PROPN
ejpam-5697	471	3	iδ;κ;p0	iδ;κ;p0	PROPN
ejpam-5697	471	4	(	(	PUNCT
ejpam-5697	471	5	mpc	mpc	NOUN
ejpam-5697	471	6	ℏ	ℏ	NOUN
ejpam-5697	471	7	dδ;κ;p	dδ;κ;p	NUM
ejpam-5697	471	8	0	0	NUM
ejpam-5697	471	9	)	)	PUNCT
ejpam-5697	471	10	g(ξ	g(ξ	PROPN
ejpam-5697	471	11	)	)	PUNCT
ejpam-5697	472	1	=	=	NOUN
ejpam-5697	472	2	g(ξ)−	g(ξ)−	PROPN
ejpam-5697	472	3	g(0	g(0	PROPN
ejpam-5697	472	4	)	)	PUNCT
ejpam-5697	472	5	.	.	PUNCT
ejpam-5697	473	1	proof	proof	NOUN
ejpam-5697	473	2	.	.	PUNCT
ejpam-5697	474	1	by	by	ADP
ejpam-5697	474	2	using	use	VERB
ejpam-5697	474	3	the	the	DET
ejpam-5697	474	4	definition	definition	NOUN
ejpam-5697	474	5	8	8	NUM
ejpam-5697	474	6	and	and	CCONJ
ejpam-5697	474	7	24	24	NUM
ejpam-5697	474	8	,	,	PUNCT
ejpam-5697	474	9	we	we	PRON
ejpam-5697	474	10	have	have	VERB
ejpam-5697	474	11	mpi	mpi	PROPN
ejpam-5697	474	12	ℏ	ℏ	PROPN
ejpam-5697	474	13	iδ;κ;p0	iδ;κ;p0	PROPN
ejpam-5697	474	14	(	(	PUNCT
ejpam-5697	474	15	mpc	mpc	NOUN
ejpam-5697	474	16	ℏ	ℏ	NOUN
ejpam-5697	474	17	dδ;κ;p	dδ;κ;p	NUM
ejpam-5697	474	18	0	0	NUM
ejpam-5697	474	19	)	)	PUNCT
ejpam-5697	474	20	g(ξ	g(ξ	PROPN
ejpam-5697	474	21	)	)	PUNCT
ejpam-5697	474	22	=	=	SYM
ejpam-5697	474	23	1−δ	1−δ	NUM
ejpam-5697	474	24	r(δ	r(δ	NOUN
ejpam-5697	474	25	)	)	PUNCT
ejpam-5697	474	26	(	(	PUNCT
ejpam-5697	474	27	mpc	mpc	NOUN
ejpam-5697	474	28	ℏ	ℏ	NOUN
ejpam-5697	474	29	dδ;κ;p	dδ;κ;p	NUM
ejpam-5697	474	30	0	0	NUM
ejpam-5697	474	31	)	)	PUNCT
ejpam-5697	474	32	g(ξ	g(ξ	PROPN
ejpam-5697	474	33	)	)	PUNCT
ejpam-5697	475	1	+	+	CCONJ
ejpam-5697	475	2	δ	δ	PROPN
ejpam-5697	475	3	ln	ln	ADJ
ejpam-5697	475	4	p	p	NOUN
ejpam-5697	475	5	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	475	6	)	)	PUNCT
ejpam-5697	476	1	∫	∫	PROPN
ejpam-5697	476	2	t	t	PROPN
ejpam-5697	476	3	0	0	NUM
ejpam-5697	476	4	(	(	PUNCT
ejpam-5697	476	5	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	476	6	ℏ(ζ))κ−1	ℏ(ζ))κ−1	PROPN
ejpam-5697	476	7	×ℏ′	×ℏ′	ADV
ejpam-5697	476	8	(	(	PUNCT
ejpam-5697	476	9	ζ	ζ	NOUN
ejpam-5697	476	10	)	)	PUNCT
ejpam-5697	476	11	(	(	PUNCT
ejpam-5697	476	12	mpc	mpc	NOUN
ejpam-5697	476	13	ℏ	ℏ	NOUN
ejpam-5697	476	14	dδ;κ;p	dδ;κ;p	NUM
ejpam-5697	476	15	0	0	NUM
ejpam-5697	476	16	)	)	PUNCT
ejpam-5697	476	17	g(ζ)dζ	g(ζ)dζ	PROPN
ejpam-5697	477	1	=	=	SYM
ejpam-5697	477	2	∫	∫	PROPN
ejpam-5697	477	3	ξ	ξ	SYM
ejpam-5697	477	4	0	0	NUM
ejpam-5697	477	5	peκ,1	peκ,1	NOUN
ejpam-5697	477	6	(	(	PUNCT
ejpam-5697	477	7	−	−	PROPN
ejpam-5697	477	8	ωδ	ωδ	X
ejpam-5697	477	9	(	(	PUNCT
ejpam-5697	477	10	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	477	11	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	477	12	)	)	PUNCT
ejpam-5697	477	13	)	)	PUNCT
ejpam-5697	477	14	κ	κ	X
ejpam-5697	477	15	)	)	PUNCT
ejpam-5697	477	16	g′(ζ)dζ	g′(ζ)dζ	PROPN
ejpam-5697	477	17	+	+	CCONJ
ejpam-5697	477	18	r(δ	r(δ	PROPN
ejpam-5697	477	19	)	)	PUNCT
ejpam-5697	477	20	1−δ	1−δ	NUM
ejpam-5697	478	1	δ	δ	X
ejpam-5697	478	2	ln	ln	ADJ
ejpam-5697	478	3	p	p	NOUN
ejpam-5697	478	4	r(δ)γ(κ	r(δ)γ(κ	NOUN
ejpam-5697	478	5	)	)	PUNCT
ejpam-5697	478	6	∫	∫	PROPN
ejpam-5697	479	1	ξ	ξ	X
ejpam-5697	479	2	0	0	NUM
ejpam-5697	479	3	(	(	PUNCT
ejpam-5697	479	4	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	479	5	ℏ(ζ))κ−1	ℏ(ζ))κ−1	PROPN
ejpam-5697	479	6	×ℏ′	×ℏ′	ADV
ejpam-5697	479	7	(	(	PUNCT
ejpam-5697	479	8	ζ	ζ	NOUN
ejpam-5697	479	9	)	)	PUNCT
ejpam-5697	479	10	∫	∫	PROPN
ejpam-5697	479	11	t	t	PROPN
ejpam-5697	479	12	0	0	NUM
ejpam-5697	479	13	peκ,1	peκ,1	NOUN
ejpam-5697	479	14	(	(	PUNCT
ejpam-5697	479	15	−	−	NUM
ejpam-5697	479	16	ωκ,1	ωκ,1	NUM
ejpam-5697	479	17	(	(	PUNCT
ejpam-5697	479	18	ℏ(ζ)−	ℏ(ζ)−	VERB
ejpam-5697	479	19	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-5697	479	20	)	)	PUNCT
ejpam-5697	479	21	)	)	PUNCT
ejpam-5697	479	22	κ	κ	X
ejpam-5697	479	23	)	)	PUNCT
ejpam-5697	479	24	g′(ϑ)dϑ	g′(ϑ)dϑ	PROPN
ejpam-5697	479	25	gauhar	gauhar	PROPN
ejpam-5697	479	26	rahman	rahman	PROPN
ejpam-5697	479	27	et	et	PROPN
ejpam-5697	479	28	al	al	PROPN
ejpam-5697	479	29	.	.	PUNCT
ejpam-5697	479	30	/	/	SYM
ejpam-5697	479	31	eur	eur	PROPN
ejpam-5697	479	32	.	.	PUNCT
ejpam-5697	480	1	j.	j.	PROPN
ejpam-5697	480	2	pure	pure	PROPN
ejpam-5697	480	3	appl	appl	PROPN
ejpam-5697	480	4	.	.	PROPN
ejpam-5697	480	5	math	math	PROPN
ejpam-5697	480	6	,	,	PUNCT
ejpam-5697	480	7	18	18	NUM
ejpam-5697	480	8	(	(	PUNCT
ejpam-5697	480	9	1	1	NUM
ejpam-5697	480	10	)	)	PUNCT
ejpam-5697	480	11	(	(	PUNCT
ejpam-5697	480	12	2025	2025	NUM
ejpam-5697	480	13	)	)	PUNCT
ejpam-5697	480	14	,	,	PUNCT
ejpam-5697	480	15	5697	5697	NUM
ejpam-5697	480	16	23	23	NUM
ejpam-5697	480	17	of	of	ADP
ejpam-5697	480	18	26	26	NUM
ejpam-5697	480	19	=	=	SYM
ejpam-5697	480	20	∫	∫	PROPN
ejpam-5697	480	21	ξ	ξ	SYM
ejpam-5697	480	22	0	0	NUM
ejpam-5697	480	23	peκ	peκ	NOUN
ejpam-5697	480	24	(	(	PUNCT
ejpam-5697	480	25	−	−	NOUN
ejpam-5697	480	26	ωδ	ωδ	X
ejpam-5697	480	27	(	(	PUNCT
ejpam-5697	480	28	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	480	29	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	480	30	)	)	PUNCT
ejpam-5697	480	31	)	)	PUNCT
ejpam-5697	480	32	κ	κ	X
ejpam-5697	480	33	)	)	PUNCT
ejpam-5697	480	34	g′(ζ)dζ	g′(ζ)dζ	PROPN
ejpam-5697	480	35	+	+	CCONJ
ejpam-5697	480	36	δ	δ	PROPN
ejpam-5697	480	37	ln	ln	ADJ
ejpam-5697	480	38	p	p	X
ejpam-5697	480	39	(	(	PUNCT
ejpam-5697	480	40	1−δ)γ(κ	1−δ)γ(κ	NUM
ejpam-5697	480	41	)	)	PUNCT
ejpam-5697	481	1	×	×	NOUN
ejpam-5697	482	1	∫	∫	PROPN
ejpam-5697	483	1	ξ	ξ	SYM
ejpam-5697	483	2	0	0	NUM
ejpam-5697	483	3	g	g	NOUN
ejpam-5697	483	4	′(ϑ	′(ϑ	NOUN
ejpam-5697	483	5	)	)	PUNCT
ejpam-5697	483	6	∫	∫	PROPN
ejpam-5697	484	1	ξ	ξ	X
ejpam-5697	484	2	z	z	PROPN
ejpam-5697	484	3	(	(	PUNCT
ejpam-5697	484	4	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	484	5	ℏ(ζ))κ−1ℏ′	ℏ(ζ))κ−1ℏ′	ADJ
ejpam-5697	484	6	(	(	PUNCT
ejpam-5697	484	7	ζ	ζ	NOUN
ejpam-5697	484	8	)	)	PUNCT
ejpam-5697	484	9	peκ,1	peκ,1	NOUN
ejpam-5697	484	10	(	(	PUNCT
ejpam-5697	484	11	−	−	PROPN
ejpam-5697	484	12	ωδ	ωδ	ADV
ejpam-5697	484	13	(	(	PUNCT
ejpam-5697	484	14	ℏ(ζ)−	ℏ(ζ)−	PROPN
ejpam-5697	484	15	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-5697	484	16	)	)	PUNCT
ejpam-5697	484	17	)	)	PUNCT
ejpam-5697	484	18	κ	κ	X
ejpam-5697	484	19	)	)	PUNCT
ejpam-5697	484	20	dζdϑ	dζdϑ	NOUN
ejpam-5697	484	21	=	=	PUNCT
ejpam-5697	484	22	∫	∫	PROPN
ejpam-5697	484	23	ξ	ξ	SYM
ejpam-5697	484	24	0	0	NUM
ejpam-5697	484	25	peκ,1	peκ,1	NOUN
ejpam-5697	484	26	(	(	PUNCT
ejpam-5697	484	27	−	−	PROPN
ejpam-5697	484	28	ωδ	ωδ	X
ejpam-5697	484	29	(	(	PUNCT
ejpam-5697	484	30	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	484	31	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	484	32	)	)	PUNCT
ejpam-5697	484	33	)	)	PUNCT
ejpam-5697	484	34	κ	κ	X
ejpam-5697	484	35	)	)	PUNCT
ejpam-5697	484	36	g′(ζ)dζ	g′(ζ)dζ	PROPN
ejpam-5697	484	37	+	+	CCONJ
ejpam-5697	484	38	δ	δ	PROPN
ejpam-5697	484	39	ln	ln	ADJ
ejpam-5697	484	40	p	p	X
ejpam-5697	484	41	(	(	PUNCT
ejpam-5697	484	42	1−δ)γ(κ	1−δ)γ(κ	NUM
ejpam-5697	484	43	)	)	PUNCT
ejpam-5697	484	44	∑∞	∑∞	NOUN
ejpam-5697	484	45	n=0	n=0	NUM
ejpam-5697	484	46	(	(	PUNCT
ejpam-5697	484	47	−ωδ	−ωδ	X
ejpam-5697	484	48	ln	ln	ADJ
ejpam-5697	484	49	p)n	p)n	NOUN
ejpam-5697	484	50	γ(κn+1	γ(κn+1	X
ejpam-5697	484	51	)	)	PUNCT
ejpam-5697	485	1	×	×	NOUN
ejpam-5697	485	2	∫	∫	PROPN
ejpam-5697	485	3	ξ	ξ	SYM
ejpam-5697	485	4	0	0	NUM
ejpam-5697	485	5	g	g	NOUN
ejpam-5697	485	6	′(ϑ	′(ϑ	NOUN
ejpam-5697	485	7	)	)	PUNCT
ejpam-5697	485	8	∫	∫	PROPN
ejpam-5697	486	1	ξ	ξ	X
ejpam-5697	486	2	z	z	PROPN
ejpam-5697	486	3	(	(	PUNCT
ejpam-5697	486	4	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	486	5	ℏ(ζ))κ−1ℏ′	ℏ(ζ))κ−1ℏ′	ADJ
ejpam-5697	486	6	(	(	PUNCT
ejpam-5697	486	7	ζ	ζ	NOUN
ejpam-5697	486	8	)	)	PUNCT
ejpam-5697	486	9	(	(	PUNCT
ejpam-5697	486	10	ℏ(ζ)−	ℏ(ζ)−	PROPN
ejpam-5697	486	11	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-5697	486	12	)	)	PUNCT
ejpam-5697	486	13	)	)	PUNCT
ejpam-5697	486	14	κn	κn	NOUN
ejpam-5697	486	15	dζdϑ	dζdϑ	NOUN
ejpam-5697	486	16	=	=	PUNCT
ejpam-5697	486	17	∫	∫	PROPN
ejpam-5697	486	18	ξ	ξ	SYM
ejpam-5697	486	19	0	0	NUM
ejpam-5697	486	20	peκ,1	peκ,1	NOUN
ejpam-5697	486	21	(	(	PUNCT
ejpam-5697	486	22	−	−	PROPN
ejpam-5697	486	23	ωδ	ωδ	X
ejpam-5697	486	24	(	(	PUNCT
ejpam-5697	486	25	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	486	26	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	486	27	)	)	PUNCT
ejpam-5697	486	28	)	)	PUNCT
ejpam-5697	486	29	κ	κ	X
ejpam-5697	486	30	)	)	PUNCT
ejpam-5697	486	31	g′(ζ)dζ	g′(ζ)dζ	PROPN
ejpam-5697	486	32	+	+	CCONJ
ejpam-5697	486	33	δ	δ	PROPN
ejpam-5697	486	34	ln	ln	ADJ
ejpam-5697	486	35	p	p	X
ejpam-5697	486	36	(	(	PUNCT
ejpam-5697	486	37	1−δ)γ(κ	1−δ)γ(κ	NUM
ejpam-5697	486	38	)	)	PUNCT
ejpam-5697	486	39	∑∞	∑∞	NOUN
ejpam-5697	486	40	n=0	n=0	NUM
ejpam-5697	486	41	(	(	PUNCT
ejpam-5697	486	42	−ωδ	−ωδ	X
ejpam-5697	486	43	ln	ln	ADJ
ejpam-5697	486	44	p)n	p)n	NOUN
ejpam-5697	486	45	γ(κn+1	γ(κn+1	X
ejpam-5697	486	46	)	)	PUNCT
ejpam-5697	487	1	×	×	NOUN
ejpam-5697	487	2	∫	∫	PROPN
ejpam-5697	487	3	ξ	ξ	SYM
ejpam-5697	487	4	0	0	NUM
ejpam-5697	487	5	g	g	PROPN
ejpam-5697	487	6	′(ϑ	′(ϑ	NOUN
ejpam-5697	487	7	)	)	PUNCT
ejpam-5697	487	8	(	(	PUNCT
ejpam-5697	487	9	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	487	10	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-5697	487	11	)	)	PUNCT
ejpam-5697	487	12	)	)	PUNCT
ejpam-5697	488	1	κ(n+1)−1	κ(n+1)−1	NOUN
ejpam-5697	488	2	∫	∫	X
ejpam-5697	488	3	ξ	ξ	X
ejpam-5697	488	4	z	z	PROPN
ejpam-5697	488	5	(	(	PUNCT
ejpam-5697	488	6	ℏ(ξ)−ℏ(ζ	ℏ(ξ)−ℏ(ζ	NOUN
ejpam-5697	488	7	)	)	PUNCT
ejpam-5697	488	8	(	(	PUNCT
ejpam-5697	488	9	ℏ(ξ)−ℏ(ϑ	ℏ(ξ)−ℏ(ϑ	NOUN
ejpam-5697	488	10	)	)	PUNCT
ejpam-5697	488	11	)	)	PUNCT
ejpam-5697	488	12	)	)	PUNCT
ejpam-5697	489	1	κ−1	κ−1	PROPN
ejpam-5697	489	2	(	(	PUNCT
ejpam-5697	489	3	ℏ(ζ)−ℏ(ϑ	ℏ(ζ)−ℏ(ϑ	NOUN
ejpam-5697	489	4	)	)	PUNCT
ejpam-5697	489	5	(	(	PUNCT
ejpam-5697	489	6	ℏ(ξ)−ℏ(ϑ	ℏ(ξ)−ℏ(ϑ	NOUN
ejpam-5697	489	7	)	)	PUNCT
ejpam-5697	489	8	)	)	PUNCT
ejpam-5697	489	9	)	)	PUNCT
ejpam-5697	489	10	κn	κn	NOUN
ejpam-5697	489	11	ℏ′	ℏ′	X
ejpam-5697	489	12	(	(	PUNCT
ejpam-5697	489	13	ζ)dζdϑ	ζ)dζdϑ	NOUN
ejpam-5697	489	14	=	=	SYM
ejpam-5697	489	15	∫	∫	PROPN
ejpam-5697	489	16	ξ	ξ	SYM
ejpam-5697	489	17	0	0	NUM
ejpam-5697	489	18	peκ,1	peκ,1	NOUN
ejpam-5697	489	19	(	(	PUNCT
ejpam-5697	489	20	−	−	PROPN
ejpam-5697	489	21	ωδ	ωδ	X
ejpam-5697	489	22	(	(	PUNCT
ejpam-5697	489	23	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	489	24	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	489	25	)	)	PUNCT
ejpam-5697	489	26	)	)	PUNCT
ejpam-5697	489	27	κ	κ	X
ejpam-5697	489	28	)	)	PUNCT
ejpam-5697	489	29	g′(ζ)dζ	g′(ζ)dζ	PROPN
ejpam-5697	489	30	+	+	CCONJ
ejpam-5697	489	31	δ	δ	PROPN
ejpam-5697	489	32	ln	ln	ADJ
ejpam-5697	489	33	p	p	X
ejpam-5697	489	34	(	(	PUNCT
ejpam-5697	489	35	1−δ)γ(κ	1−δ)γ(κ	NUM
ejpam-5697	489	36	)	)	PUNCT
ejpam-5697	489	37	∑∞	∑∞	NOUN
ejpam-5697	489	38	n=0	n=0	NUM
ejpam-5697	489	39	(	(	PUNCT
ejpam-5697	489	40	−ωδ	−ωδ	NOUN
ejpam-5697	489	41	)	)	PUNCT
ejpam-5697	489	42	n	n	X
ejpam-5697	489	43	γ(κn+1	γ(κn+1	ADV
ejpam-5697	489	44	)	)	PUNCT
ejpam-5697	489	45	×b(κn+	×b(κn+	ADP
ejpam-5697	489	46	1	1	NUM
ejpam-5697	489	47	,	,	PUNCT
ejpam-5697	489	48	κ	κ	NOUN
ejpam-5697	489	49	)	)	PUNCT
ejpam-5697	489	50	∫	∫	PROPN
ejpam-5697	490	1	ξ	ξ	SYM
ejpam-5697	490	2	0	0	NUM
ejpam-5697	490	3	g	g	PROPN
ejpam-5697	490	4	′(ϑ	′(ϑ	NOUN
ejpam-5697	490	5	)	)	PUNCT
ejpam-5697	490	6	(	(	PUNCT
ejpam-5697	490	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	490	8	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-5697	490	9	)	)	PUNCT
ejpam-5697	490	10	)	)	PUNCT
ejpam-5697	490	11	κ(n+1	κ(n+1	NUM
ejpam-5697	490	12	)	)	PUNCT
ejpam-5697	490	13	dϑ	dϑ	NOUN
ejpam-5697	491	1	=	=	PUNCT
ejpam-5697	491	2	∫	∫	PROPN
ejpam-5697	491	3	ξ	ξ	SYM
ejpam-5697	491	4	0	0	NUM
ejpam-5697	491	5	peκ,1	peκ,1	NOUN
ejpam-5697	491	6	(	(	PUNCT
ejpam-5697	491	7	−	−	PROPN
ejpam-5697	491	8	ωδ	ωδ	X
ejpam-5697	491	9	(	(	PUNCT
ejpam-5697	491	10	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	491	11	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	491	12	)	)	PUNCT
ejpam-5697	491	13	)	)	PUNCT
ejpam-5697	491	14	κ	κ	X
ejpam-5697	491	15	)	)	PUNCT
ejpam-5697	491	16	g′(ζ)dζ	g′(ζ)dζ	NOUN
ejpam-5697	491	17	+	+	PUNCT
ejpam-5697	491	18	ωδ	ωδ	INTJ
ejpam-5697	491	19	ln	ln	ADJ
ejpam-5697	491	20	p	p	PROPN
ejpam-5697	491	21	γ(κ	γ(κ	PROPN
ejpam-5697	491	22	)	)	PUNCT
ejpam-5697	491	23	∑∞	∑∞	NOUN
ejpam-5697	491	24	n=0	n=0	PRON
ejpam-5697	491	25	(	(	PUNCT
ejpam-5697	491	26	−ωδ	−ωδ	X
ejpam-5697	491	27	ln	ln	ADJ
ejpam-5697	491	28	p)n	p)n	NOUN
ejpam-5697	491	29	γ(κn+1	γ(κn+1	NOUN
ejpam-5697	491	30	)	)	PUNCT
ejpam-5697	491	31	×γ(κn+1)γ(κ	×γ(κn+1)γ(κ	X
ejpam-5697	491	32	)	)	PUNCT
ejpam-5697	491	33	γ(κ(n+1)+1	γ(κ(n+1)+1	NOUN
ejpam-5697	491	34	)	)	PUNCT
ejpam-5697	491	35	∫	∫	PROPN
ejpam-5697	492	1	ξ	ξ	SYM
ejpam-5697	492	2	0	0	NUM
ejpam-5697	492	3	g	g	PROPN
ejpam-5697	492	4	′(ϑ	′(ϑ	NOUN
ejpam-5697	492	5	)	)	PUNCT
ejpam-5697	492	6	(	(	PUNCT
ejpam-5697	492	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	492	8	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-5697	492	9	)	)	PUNCT
ejpam-5697	492	10	)	)	PUNCT
ejpam-5697	492	11	κ(n+1	κ(n+1	NUM
ejpam-5697	492	12	)	)	PUNCT
ejpam-5697	492	13	dϑ	dϑ	NOUN
ejpam-5697	493	1	=	=	PUNCT
ejpam-5697	493	2	∫	∫	PROPN
ejpam-5697	493	3	ξ	ξ	SYM
ejpam-5697	493	4	0	0	NUM
ejpam-5697	493	5	peκ,1	peκ,1	NOUN
ejpam-5697	493	6	(	(	PUNCT
ejpam-5697	493	7	−	−	PROPN
ejpam-5697	493	8	ωδ	ωδ	X
ejpam-5697	493	9	(	(	PUNCT
ejpam-5697	493	10	ℏ(ξ)−	ℏ(ξ)−	PROPN
ejpam-5697	493	11	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	493	12	)	)	PUNCT
ejpam-5697	493	13	)	)	PUNCT
ejpam-5697	493	14	κ	κ	X
ejpam-5697	493	15	)	)	PUNCT
ejpam-5697	493	16	g′(ζ)dζ	g′(ζ)dζ	NOUN
ejpam-5697	493	17	−	−	NOUN
ejpam-5697	493	18	∑∞	∑∞	NOUN
ejpam-5697	493	19	n=0	n=0	NUM
ejpam-5697	493	20	(	(	PUNCT
ejpam-5697	493	21	−ωδ	−ωδ	NOUN
ejpam-5697	493	22	ln	ln	PROPN
ejpam-5697	493	23	p)n+1	p)n+1	PROPN
ejpam-5697	493	24	γ(κ(n+1)+1	γ(κ(n+1)+1	PROPN
ejpam-5697	493	25	)	)	PUNCT
ejpam-5697	493	26	×	×	NOUN
ejpam-5697	493	27	∫	∫	PROPN
ejpam-5697	494	1	ξ	ξ	SYM
ejpam-5697	494	2	0	0	NUM
ejpam-5697	494	3	g	g	PROPN
ejpam-5697	494	4	′(ϑ	′(ϑ	NOUN
ejpam-5697	494	5	)	)	PUNCT
ejpam-5697	494	6	(	(	PUNCT
ejpam-5697	494	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	494	8	ℏ(ϑ	ℏ(ϑ	PROPN
ejpam-5697	494	9	)	)	PUNCT
ejpam-5697	494	10	)	)	PUNCT
ejpam-5697	494	11	κ(n+1	κ(n+1	NUM
ejpam-5697	494	12	)	)	PUNCT
ejpam-5697	494	13	dϑ	dϑ	NOUN
ejpam-5697	494	14	=	=	PUNCT
ejpam-5697	494	15	∑∞	∑∞	NOUN
ejpam-5697	494	16	n=0	n=0	PRON
ejpam-5697	494	17	(	(	PUNCT
ejpam-5697	494	18	−ωδ	−ωδ	X
ejpam-5697	494	19	ln	ln	ADJ
ejpam-5697	494	20	p)n	p)n	NOUN
ejpam-5697	494	21	γ(κn+1	γ(κn+1	PUNCT
ejpam-5697	494	22	)	)	PUNCT
ejpam-5697	494	23	∫	∫	PROPN
ejpam-5697	495	1	ξ	ξ	SYM
ejpam-5697	495	2	0	0	NUM
ejpam-5697	495	3	g	g	PROPN
ejpam-5697	495	4	′(ζ	′(ζ	NOUN
ejpam-5697	495	5	)	)	PUNCT
ejpam-5697	495	6	(	(	PUNCT
ejpam-5697	495	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	495	8	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	495	9	)	)	PUNCT
ejpam-5697	495	10	)	)	PUNCT
ejpam-5697	495	11	κn	κn	NOUN
ejpam-5697	495	12	dζ	dζ	PROPN
ejpam-5697	495	13	−	−	PROPN
ejpam-5697	495	14	∑∞	∑∞	NOUN
ejpam-5697	495	15	n=0	n=0	NUM
ejpam-5697	495	16	(	(	PUNCT
ejpam-5697	495	17	−ωδ	−ωδ	NOUN
ejpam-5697	495	18	ln	ln	PROPN
ejpam-5697	495	19	p)n+1	p)n+1	PROPN
ejpam-5697	495	20	γ(κ(n+1)+1	γ(κ(n+1)+1	PROPN
ejpam-5697	495	21	)	)	PUNCT
ejpam-5697	495	22	∫	∫	PROPN
ejpam-5697	496	1	ξ	ξ	SYM
ejpam-5697	496	2	0	0	NUM
ejpam-5697	496	3	g	g	PROPN
ejpam-5697	496	4	′(ζ	′(ζ	NOUN
ejpam-5697	496	5	)	)	PUNCT
ejpam-5697	496	6	(	(	PUNCT
ejpam-5697	496	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	496	8	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	496	9	)	)	PUNCT
ejpam-5697	496	10	)	)	PUNCT
ejpam-5697	496	11	κ(n+1	κ(n+1	NUM
ejpam-5697	496	12	)	)	PUNCT
ejpam-5697	497	1	dζ	dζ	PROPN
ejpam-5697	497	2	=	=	PUNCT
ejpam-5697	497	3	∑∞	∑∞	NOUN
ejpam-5697	497	4	n=0	n=0	NUM
ejpam-5697	497	5	(	(	PUNCT
ejpam-5697	497	6	−ωδ	−ωδ	X
ejpam-5697	497	7	ln	ln	ADJ
ejpam-5697	497	8	p)n	p)n	NOUN
ejpam-5697	497	9	γ(κn+1	γ(κn+1	PUNCT
ejpam-5697	497	10	)	)	PUNCT
ejpam-5697	497	11	∫	∫	PROPN
ejpam-5697	498	1	ξ	ξ	SYM
ejpam-5697	498	2	0	0	NUM
ejpam-5697	498	3	g	g	PROPN
ejpam-5697	498	4	′(ζ	′(ζ	NOUN
ejpam-5697	498	5	)	)	PUNCT
ejpam-5697	498	6	(	(	PUNCT
ejpam-5697	498	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	498	8	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	498	9	)	)	PUNCT
ejpam-5697	498	10	)	)	PUNCT
ejpam-5697	498	11	κn	κn	NOUN
ejpam-5697	498	12	dζ	dζ	PROPN
ejpam-5697	498	13	−	−	PROPN
ejpam-5697	498	14	∑∞	∑∞	NOUN
ejpam-5697	498	15	n=1	n=1	PROPN
ejpam-5697	498	16	(	(	PUNCT
ejpam-5697	498	17	−ωδ	−ωδ	X
ejpam-5697	498	18	ln	ln	ADJ
ejpam-5697	498	19	p)n	p)n	NOUN
ejpam-5697	498	20	γ(κn+1	γ(κn+1	PUNCT
ejpam-5697	498	21	)	)	PUNCT
ejpam-5697	498	22	∫	∫	PROPN
ejpam-5697	499	1	ξ	ξ	SYM
ejpam-5697	499	2	0	0	NUM
ejpam-5697	499	3	g	g	PROPN
ejpam-5697	499	4	′(ζ	′(ζ	NOUN
ejpam-5697	499	5	)	)	PUNCT
ejpam-5697	499	6	(	(	PUNCT
ejpam-5697	499	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	499	8	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	499	9	)	)	PUNCT
ejpam-5697	499	10	)	)	PUNCT
ejpam-5697	500	1	κn	κn	NOUN
ejpam-5697	500	2	dζ	dζ	PROPN
ejpam-5697	500	3	=	=	SYM
ejpam-5697	500	4	∫	∫	PROPN
ejpam-5697	500	5	ξ	ξ	SYM
ejpam-5697	500	6	0	0	NUM
ejpam-5697	500	7	g	g	NOUN
ejpam-5697	500	8	′(ζ)dζ	′(ζ)dζ	PROPN
ejpam-5697	500	9	+	+	NOUN
ejpam-5697	500	10	∑∞	∑∞	NOUN
ejpam-5697	500	11	n=1	n=1	PROPN
ejpam-5697	500	12	(	(	PUNCT
ejpam-5697	500	13	−ωδ	−ωδ	X
ejpam-5697	500	14	ln	ln	ADJ
ejpam-5697	500	15	p)n	p)n	NOUN
ejpam-5697	500	16	γ(κn+1	γ(κn+1	PUNCT
ejpam-5697	500	17	)	)	PUNCT
ejpam-5697	500	18	∫	∫	PROPN
ejpam-5697	501	1	ξ	ξ	SYM
ejpam-5697	501	2	0	0	NUM
ejpam-5697	501	3	g	g	PROPN
ejpam-5697	501	4	′(ζ	′(ζ	NOUN
ejpam-5697	501	5	)	)	PUNCT
ejpam-5697	501	6	(	(	PUNCT
ejpam-5697	501	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	501	8	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	501	9	)	)	PUNCT
ejpam-5697	501	10	)	)	PUNCT
ejpam-5697	501	11	κn	κn	NOUN
ejpam-5697	501	12	dζ	dζ	PROPN
ejpam-5697	501	13	−	−	PROPN
ejpam-5697	501	14	∑∞	∑∞	NOUN
ejpam-5697	501	15	n=1	n=1	PROPN
ejpam-5697	501	16	(	(	PUNCT
ejpam-5697	501	17	−ωδ	−ωδ	NOUN
ejpam-5697	501	18	ln	ln	ADJ
ejpam-5697	501	19	p)n	p)n	NOUN
ejpam-5697	501	20	γ(κ(n)+1	γ(κ(n)+1	NOUN
ejpam-5697	501	21	)	)	PUNCT
ejpam-5697	502	1	∫	∫	PROPN
ejpam-5697	503	1	ξ	ξ	SYM
ejpam-5697	503	2	0	0	NUM
ejpam-5697	503	3	g	g	PROPN
ejpam-5697	503	4	′(ζ	′(ζ	NOUN
ejpam-5697	503	5	)	)	PUNCT
ejpam-5697	503	6	(	(	PUNCT
ejpam-5697	503	7	ℏ(ξ)−	ℏ(ξ)−	NOUN
ejpam-5697	503	8	ℏ(ζ	ℏ(ζ	PROPN
ejpam-5697	503	9	)	)	PUNCT
ejpam-5697	503	10	)	)	PUNCT
ejpam-5697	504	1	κn	κn	NOUN
ejpam-5697	504	2	dζ	dζ	PROPN
ejpam-5697	504	3	=	=	SYM
ejpam-5697	504	4	∫	∫	PROPN
ejpam-5697	504	5	ξ	ξ	SYM
ejpam-5697	504	6	0	0	NUM
ejpam-5697	504	7	g	g	NOUN
ejpam-5697	504	8	′(ζ)dζ	′(ζ)dζ	PROPN
ejpam-5697	504	9	=	=	PROPN
ejpam-5697	504	10	g(ξ)−	g(ξ)−	PROPN
ejpam-5697	504	11	g(0	g(0	PROPN
ejpam-5697	504	12	)	)	PUNCT
ejpam-5697	504	13	.	.	PUNCT
ejpam-5697	505	1	hence	hence	ADV
ejpam-5697	505	2	the	the	DET
ejpam-5697	505	3	result	result	NOUN
ejpam-5697	505	4	is	be	AUX
ejpam-5697	505	5	completed	complete	VERB
ejpam-5697	505	6	.	.	PUNCT
ejpam-5697	506	1	5	5	X
ejpam-5697	506	2	.	.	X
ejpam-5697	506	3	conclusion	conclusion	NOUN
ejpam-5697	506	4	in	in	ADP
ejpam-5697	506	5	this	this	DET
ejpam-5697	506	6	paper	paper	NOUN
ejpam-5697	506	7	,	,	PUNCT
ejpam-5697	506	8	the	the	DET
ejpam-5697	506	9	generalization	generalization	NOUN
ejpam-5697	506	10	of	of	ADP
ejpam-5697	506	11	power	power	NOUN
ejpam-5697	506	12	fractional	fractional	ADJ
ejpam-5697	506	13	integral	integral	ADJ
ejpam-5697	506	14	and	and	CCONJ
ejpam-5697	506	15	derivative	derivative	ADJ
ejpam-5697	506	16	operators	operator	NOUN
ejpam-5697	506	17	in	in	ADP
ejpam-5697	506	18	both	both	CCONJ
ejpam-5697	506	19	the	the	DET
ejpam-5697	506	20	caputo	caputo	PROPN
ejpam-5697	506	21	and	and	CCONJ
ejpam-5697	506	22	r	r	NOUN
ejpam-5697	506	23	-	-	PUNCT
ejpam-5697	506	24	l	l	NOUN
ejpam-5697	506	25	sense	sense	NOUN
ejpam-5697	506	26	are	be	AUX
ejpam-5697	506	27	presented	present	VERB
ejpam-5697	506	28	.	.	PUNCT
ejpam-5697	507	1	these	these	DET
ejpam-5697	507	2	new	new	ADJ
ejpam-5697	507	3	operators	operator	NOUN
ejpam-5697	507	4	allowed	allow	VERB
ejpam-5697	507	5	us	we	PRON
ejpam-5697	507	6	to	to	PART
ejpam-5697	507	7	solve	solve	VERB
ejpam-5697	507	8	differential	differential	ADJ
ejpam-5697	507	9	equations	equation	NOUN
ejpam-5697	507	10	,	,	PUNCT
ejpam-5697	507	11	and	and	CCONJ
ejpam-5697	507	12	we	we	PRON
ejpam-5697	507	13	investigated	investigate	VERB
ejpam-5697	507	14	their	their	PRON
ejpam-5697	507	15	solutions	solution	NOUN
ejpam-5697	507	16	using	use	VERB
ejpam-5697	507	17	the	the	DET
ejpam-5697	507	18	generalized	generalized	ADJ
ejpam-5697	507	19	laplace	laplace	NOUN
ejpam-5697	507	20	transform	transform	NOUN
ejpam-5697	507	21	.	.	PUNCT
ejpam-5697	508	1	it	it	PRON
ejpam-5697	508	2	is	be	AUX
ejpam-5697	508	3	shown	show	VERB
ejpam-5697	508	4	that	that	SCONJ
ejpam-5697	508	5	the	the	DET
ejpam-5697	508	6	defined	define	VERB
ejpam-5697	508	7	operators	operator	NOUN
ejpam-5697	508	8	in	in	ADP
ejpam-5697	508	9	xp	xp	INTJ
ejpam-5697	508	10	have	have	VERB
ejpam-5697	508	11	norm	norm	NOUN
ejpam-5697	508	12	and	and	CCONJ
ejpam-5697	508	13	are	be	AUX
ejpam-5697	508	14	bounded	bound	VERB
ejpam-5697	508	15	.	.	PUNCT
ejpam-5697	509	1	we	we	PRON
ejpam-5697	509	2	evaluate	evaluate	VERB
ejpam-5697	509	3	the	the	DET
ejpam-5697	509	4	laplace	laplace	NOUN
ejpam-5697	509	5	transform	transform	NOUN
ejpam-5697	509	6	of	of	ADP
ejpam-5697	509	7	both	both	DET
ejpam-5697	509	8	fos	fos	VERB
ejpam-5697	509	9	.	.	PUNCT
ejpam-5697	510	1	the	the	DET
ejpam-5697	510	2	inverse	inverse	ADJ
ejpam-5697	510	3	property	property	NOUN
ejpam-5697	510	4	of	of	ADP
ejpam-5697	510	5	the	the	DET
ejpam-5697	510	6	operators	operator	NOUN
ejpam-5697	510	7	gauhar	gauhar	VERB
ejpam-5697	510	8	rahman	rahman	PROPN
ejpam-5697	510	9	et	et	PROPN
ejpam-5697	510	10	al	al	PROPN
ejpam-5697	510	11	.	.	PUNCT
ejpam-5697	510	12	/	/	SYM
ejpam-5697	510	13	eur	eur	PROPN
ejpam-5697	510	14	.	.	PUNCT
ejpam-5697	511	1	j.	j.	PROPN
ejpam-5697	511	2	pure	pure	PROPN
ejpam-5697	511	3	appl	appl	PROPN
ejpam-5697	511	4	.	.	PROPN
ejpam-5697	511	5	math	math	PROPN
ejpam-5697	511	6	,	,	PUNCT
ejpam-5697	511	7	18	18	NUM
ejpam-5697	511	8	(	(	PUNCT
ejpam-5697	511	9	1	1	NUM
ejpam-5697	511	10	)	)	PUNCT
ejpam-5697	511	11	(	(	PUNCT
ejpam-5697	511	12	2025	2025	NUM
ejpam-5697	511	13	)	)	PUNCT
ejpam-5697	511	14	,	,	PUNCT
ejpam-5697	511	15	5697	5697	NUM
ejpam-5697	511	16	24	24	NUM
ejpam-5697	511	17	of	of	ADP
ejpam-5697	511	18	26	26	NUM
ejpam-5697	511	19	is	be	AUX
ejpam-5697	511	20	presented	present	VERB
ejpam-5697	511	21	under	under	ADP
ejpam-5697	511	22	certain	certain	ADJ
ejpam-5697	511	23	condition	condition	NOUN
ejpam-5697	511	24	g(0	g(0	NOUN
ejpam-5697	511	25	)	)	PUNCT
ejpam-5697	511	26	=	=	SYM
ejpam-5697	512	1	0	0	X
ejpam-5697	512	2	.	.	PUNCT
ejpam-5697	512	3	additionally	additionally	ADV
ejpam-5697	512	4	,	,	PUNCT
ejpam-5697	512	5	we	we	PRON
ejpam-5697	512	6	presented	present	VERB
ejpam-5697	512	7	some	some	DET
ejpam-5697	512	8	examples	example	NOUN
ejpam-5697	512	9	both	both	CCONJ
ejpam-5697	512	10	analytically	analytically	ADV
ejpam-5697	512	11	and	and	CCONJ
ejpam-5697	512	12	graphically	graphically	ADV
ejpam-5697	512	13	.	.	PUNCT
ejpam-5697	513	1	this	this	DET
ejpam-5697	513	2	behavior	behavior	NOUN
ejpam-5697	513	3	demonstrates	demonstrate	VERB
ejpam-5697	513	4	the	the	DET
ejpam-5697	513	5	boundedness	boundedness	NOUN
ejpam-5697	513	6	and	and	CCONJ
ejpam-5697	513	7	convergence	convergence	NOUN
ejpam-5697	513	8	of	of	ADP
ejpam-5697	513	9	the	the	DET
ejpam-5697	513	10	solution	solution	NOUN
ejpam-5697	513	11	.	.	PUNCT
ejpam-5697	514	1	the	the	DET
ejpam-5697	514	2	graphical	graphical	ADJ
ejpam-5697	514	3	representations	representation	NOUN
ejpam-5697	514	4	are	be	AUX
ejpam-5697	514	5	given	give	VERB
ejpam-5697	514	6	in	in	ADP
ejpam-5697	514	7	both	both	PRON
ejpam-5697	514	8	two	two	NUM
ejpam-5697	514	9	and	and	CCONJ
ejpam-5697	514	10	three	three	NUM
ejpam-5697	514	11	dimensions	dimension	NOUN
ejpam-5697	514	12	.	.	PUNCT
ejpam-5697	515	1	the	the	DET
ejpam-5697	515	2	operators	operator	NOUN
ejpam-5697	515	3	presented	present	VERB
ejpam-5697	515	4	in	in	ADP
ejpam-5697	515	5	this	this	DET
ejpam-5697	515	6	paper	paper	NOUN
ejpam-5697	515	7	are	be	AUX
ejpam-5697	515	8	more	more	ADV
ejpam-5697	515	9	general	general	ADJ
ejpam-5697	515	10	than	than	ADP
ejpam-5697	515	11	the	the	DET
ejpam-5697	515	12	existing	exist	VERB
ejpam-5697	515	13	operators	operator	NOUN
ejpam-5697	515	14	cited	cite	VERB
ejpam-5697	515	15	in	in	ADP
ejpam-5697	515	16	literature	literature	NOUN
ejpam-5697	515	17	.	.	PUNCT
ejpam-5697	516	1	acknowledgements	acknowledgement	VERB
ejpam-5697	516	2	the	the	DET
ejpam-5697	516	3	authors	author	NOUN
ejpam-5697	516	4	,	,	PUNCT
ejpam-5697	516	5	t.	t.	NOUN
ejpam-5697	516	6	abdeljawad	abdeljawad	PROPN
ejpam-5697	516	7	and	and	CCONJ
ejpam-5697	516	8	aiman	aiman	PROPN
ejpam-5697	516	9	mukheimer	mukheimer	PROPN
ejpam-5697	516	10	,	,	PUNCT
ejpam-5697	516	11	would	would	AUX
ejpam-5697	516	12	like	like	VERB
ejpam-5697	516	13	to	to	PART
ejpam-5697	516	14	thank	thank	VERB
ejpam-5697	516	15	prince	prince	PROPN
ejpam-5697	516	16	sultan	sultan	PROPN
ejpam-5697	516	17	university	university	PROPN
ejpam-5697	516	18	for	for	ADP
ejpam-5697	516	19	the	the	DET
ejpam-5697	516	20	support	support	NOUN
ejpam-5697	516	21	through	through	ADP
ejpam-5697	516	22	tas	tas	PROPN
ejpam-5697	516	23	research	research	NOUN
ejpam-5697	516	24	lab	lab	NOUN
ejpam-5697	516	25	.	.	PUNCT
ejpam-5697	517	1	authors	author	NOUN
ejpam-5697	517	2	’	'	PUNCT
ejpam-5697	517	3	contributions	contribution	NOUN
ejpam-5697	517	4	all	all	DET
ejpam-5697	517	5	authors	author	NOUN
ejpam-5697	517	6	contributed	contribute	VERB
ejpam-5697	517	7	equally	equally	ADV
ejpam-5697	517	8	to	to	ADP
ejpam-5697	517	9	the	the	DET
ejpam-5697	517	10	writing	writing	NOUN
ejpam-5697	517	11	of	of	ADP
ejpam-5697	517	12	this	this	DET
ejpam-5697	517	13	paper	paper	NOUN
ejpam-5697	517	14	.	.	PUNCT
ejpam-5697	518	1	all	all	DET
ejpam-5697	518	2	authors	author	NOUN
ejpam-5697	518	3	read	read	VERB
ejpam-5697	518	4	and	and	CCONJ
ejpam-5697	518	5	approved	approve	VERB
ejpam-5697	518	6	the	the	DET
ejpam-5697	518	7	final	final	ADJ
ejpam-5697	518	8	manuscript	manuscript	NOUN
ejpam-5697	518	9	.	.	PUNCT
ejpam-5697	519	1	competing	compete	VERB
ejpam-5697	519	2	interests	interest	NOUN
ejpam-5697	519	3	the	the	DET
ejpam-5697	519	4	authors	author	NOUN
ejpam-5697	519	5	declare	declare	VERB
ejpam-5697	519	6	that	that	SCONJ
ejpam-5697	519	7	they	they	PRON
ejpam-5697	519	8	have	have	VERB
ejpam-5697	519	9	no	no	DET
ejpam-5697	519	10	competing	compete	VERB
ejpam-5697	519	11	interests	interest	NOUN
ejpam-5697	519	12	.	.	PUNCT
ejpam-5697	520	1	references	reference	NOUN
ejpam-5697	520	2	[	[	X
ejpam-5697	520	3	1	1	NUM
ejpam-5697	520	4	]	]	X
ejpam-5697	520	5	n.	n.	PROPN
ejpam-5697	520	6	h.	h.	PROPN
ejpam-5697	520	7	abel	abel	PROPN
ejpam-5697	520	8	.	.	PUNCT
ejpam-5697	521	1	solution	solution	NOUN
ejpam-5697	521	2	de	de	X
ejpam-5697	521	3	quelques	quelques	X
ejpam-5697	521	4	problemes	probleme	NOUN
ejpam-5697	521	5	l’aide	l’aide	PROPN
ejpam-5697	521	6	d’integrales	d’integrale	VERB
ejpam-5697	521	7	definies	definie	NOUN
ejpam-5697	521	8	.	.	PUNCT
ejpam-5697	521	9	1823	1823	NUM
ejpam-5697	521	10	.	.	PUNCT
ejpam-5697	522	1	[	[	X
ejpam-5697	522	2	2	2	NUM
ejpam-5697	522	3	]	]	PUNCT
ejpam-5697	522	4	a.	a.	NOUN
ejpam-5697	522	5	atangana	atangana	PROPN
ejpam-5697	522	6	and	and	CCONJ
ejpam-5697	522	7	d.	d.	PROPN
ejpam-5697	522	8	baleanu	baleanu	PROPN
ejpam-5697	522	9	.	.	PUNCT
ejpam-5697	523	1	new	new	ADJ
ejpam-5697	523	2	fractional	fractional	ADJ
ejpam-5697	523	3	derivatives	derivative	NOUN
ejpam-5697	523	4	with	with	ADP
ejpam-5697	523	5	non	non	ADJ
ejpam-5697	523	6	-	-	ADJ
ejpam-5697	523	7	local	local	ADJ
ejpam-5697	523	8	and	and	CCONJ
ejpam-5697	523	9	nonsingular	nonsingular	ADJ
ejpam-5697	523	10	kernel	kernel	PROPN
ejpam-5697	523	11	,	,	PUNCT
ejpam-5697	523	12	theory	theory	NOUN
ejpam-5697	523	13	and	and	CCONJ
ejpam-5697	523	14	application	application	NOUN
ejpam-5697	523	15	to	to	PART
ejpam-5697	523	16	heat	heat	NOUN
ejpam-5697	523	17	transfer	transfer	NOUN
ejpam-5697	523	18	model	model	NOUN
ejpam-5697	523	19	.	.	PUNCT
ejpam-5697	524	1	therm	therm	PROPN
ejpam-5697	524	2	.	.	PUNCT
ejpam-5697	525	1	sci	sci	PROPN
ejpam-5697	525	2	.	.	PROPN
ejpam-5697	525	3	,	,	PUNCT
ejpam-5697	525	4	20:763	20:763	NUM
ejpam-5697	525	5	–	–	PUNCT
ejpam-5697	525	6	769	769	NUM
ejpam-5697	525	7	,	,	PUNCT
ejpam-5697	525	8	2016	2016	NUM
ejpam-5697	525	9	.	.	PUNCT
ejpam-5697	526	1	[	[	X
ejpam-5697	526	2	3	3	X
ejpam-5697	526	3	]	]	X
ejpam-5697	526	4	d.	d.	PROPN
ejpam-5697	526	5	baleanu	baleanu	PROPN
ejpam-5697	526	6	,	,	PUNCT
ejpam-5697	526	7	k.	k.	PROPN
ejpam-5697	526	8	diethelm	diethelm	PROPN
ejpam-5697	526	9	,	,	PUNCT
ejpam-5697	526	10	e.	e.	PROPN
ejpam-5697	526	11	scalas	scalas	PROPN
ejpam-5697	526	12	,	,	PUNCT
ejpam-5697	526	13	and	and	CCONJ
ejpam-5697	526	14	j.	j.	PROPN
ejpam-5697	526	15	j.	j.	PROPN
ejpam-5697	526	16	trujillo	trujillo	PROPN
ejpam-5697	526	17	.	.	PUNCT
ejpam-5697	526	18	fractional	fractional	ADJ
ejpam-5697	526	19	calculus	calculus	NOUN
ejpam-5697	526	20	:	:	PUNCT
ejpam-5697	526	21	models	model	NOUN
ejpam-5697	526	22	and	and	CCONJ
ejpam-5697	526	23	numerical	numerical	ADJ
ejpam-5697	526	24	methods	method	NOUN
ejpam-5697	526	25	.	.	PUNCT
ejpam-5697	527	1	series	series	PROPN
ejpam-5697	527	2	on	on	ADP
ejpam-5697	527	3	complexity	complexity	NOUN
ejpam-5697	527	4	,	,	PUNCT
ejpam-5697	527	5	nonlinearity	nonlinearity	NOUN
ejpam-5697	527	6	and	and	CCONJ
ejpam-5697	527	7	chaos	chaos	NOUN
ejpam-5697	527	8	,	,	PUNCT
ejpam-5697	527	9	world	world	NOUN
ejpam-5697	527	10	scientific	scientific	NOUN
ejpam-5697	527	11	,	,	PUNCT
ejpam-5697	527	12	university	university	PROPN
ejpam-5697	527	13	edwardsville	edwardsville	PROPN
ejpam-5697	527	14	usa	usa	PROPN
ejpam-5697	527	15	,	,	PUNCT
ejpam-5697	527	16	2012	2012	NUM
ejpam-5697	527	17	.	.	PUNCT
ejpam-5697	528	1	[	[	X
ejpam-5697	528	2	4	4	X
ejpam-5697	528	3	]	]	PUNCT
ejpam-5697	528	4	m.	m.	NOUN
ejpam-5697	528	5	caputo	caputo	PROPN
ejpam-5697	528	6	and	and	CCONJ
ejpam-5697	528	7	m.	m.	PROPN
ejpam-5697	528	8	fabrizio	fabrizio	PROPN
ejpam-5697	528	9	.	.	PUNCT
ejpam-5697	529	1	a	a	DET
ejpam-5697	529	2	new	new	ADJ
ejpam-5697	529	3	definition	definition	NOUN
ejpam-5697	529	4	of	of	ADP
ejpam-5697	529	5	fractional	fractional	ADJ
ejpam-5697	529	6	derivative	derivative	NOUN
ejpam-5697	529	7	without	without	ADP
ejpam-5697	529	8	singular	singular	ADJ
ejpam-5697	529	9	kernel	kernel	PROPN
ejpam-5697	529	10	.	.	PUNCT
ejpam-5697	530	1	prog	prog	PROPN
ejpam-5697	530	2	.	.	PUNCT
ejpam-5697	531	1	frac	frac	PROPN
ejpam-5697	531	2	.	.	PROPN
ejpam-5697	532	1	differ	differ	VERB
ejpam-5697	532	2	.	.	PUNCT
ejpam-5697	533	1	appl	appl	PROPN
ejpam-5697	533	2	.	.	PROPN
ejpam-5697	533	3	,	,	PUNCT
ejpam-5697	533	4	2:73–85	2:73–85	NUM
ejpam-5697	533	5	,	,	PUNCT
ejpam-5697	533	6	2015	2015	NUM
ejpam-5697	533	7	.	.	PUNCT
ejpam-5697	534	1	[	[	X
ejpam-5697	534	2	5	5	NUM
ejpam-5697	534	3	]	]	PUNCT
ejpam-5697	534	4	m.	m.	NOUN
ejpam-5697	534	5	farman	farman	PROPN
ejpam-5697	534	6	,	,	PUNCT
ejpam-5697	534	7	s.	s.	PROPN
ejpam-5697	534	8	jamil	jamil	PROPN
ejpam-5697	534	9	,	,	PUNCT
ejpam-5697	534	10	m.	m.	PROPN
ejpam-5697	534	11	b.	b.	PROPN
ejpam-5697	534	12	riaz	riaz	PROPN
ejpam-5697	534	13	,	,	PUNCT
ejpam-5697	534	14	m.	m.	PROPN
ejpam-5697	534	15	azeem	azeem	PROPN
ejpam-5697	534	16	,	,	PUNCT
ejpam-5697	534	17	and	and	CCONJ
ejpam-5697	534	18	m.	m.	NOUN
ejpam-5697	534	19	u.	u.	PROPN
ejpam-5697	534	20	saleem	saleem	PROPN
ejpam-5697	534	21	.	.	PUNCT
ejpam-5697	535	1	numerical	numerical	ADJ
ejpam-5697	535	2	and	and	CCONJ
ejpam-5697	535	3	quantitative	quantitative	ADJ
ejpam-5697	535	4	analysis	analysis	NOUN
ejpam-5697	535	5	of	of	ADP
ejpam-5697	535	6	hiv	hiv	PROPN
ejpam-5697	535	7	/	/	SYM
ejpam-5697	535	8	aids	aids	PROPN
ejpam-5697	535	9	model	model	NOUN
ejpam-5697	535	10	with	with	ADP
ejpam-5697	535	11	modified	modify	VERB
ejpam-5697	535	12	atangana	atangana	PROPN
ejpam-5697	535	13	-	-	PUNCT
ejpam-5697	535	14	baleanu	baleanu	PROPN
ejpam-5697	535	15	in	in	ADP
ejpam-5697	535	16	caputo	caputo	PROPN
ejpam-5697	535	17	sense	sense	PROPN
ejpam-5697	535	18	derivative	derivative	PROPN
ejpam-5697	535	19	.	.	PUNCT
ejpam-5697	536	1	alexandria	alexandria	PROPN
ejpam-5697	536	2	engineering	engineering	PROPN
ejpam-5697	536	3	journal	journal	PROPN
ejpam-5697	536	4	,	,	PUNCT
ejpam-5697	536	5	66:31–42	66:31–42	NUM
ejpam-5697	536	6	,	,	PUNCT
ejpam-5697	536	7	2023	2023	NUM
ejpam-5697	536	8	.	.	PUNCT
ejpam-5697	537	1	[	[	X
ejpam-5697	537	2	6	6	NUM
ejpam-5697	537	3	]	]	X
ejpam-5697	537	4	o.	o.	PROPN
ejpam-5697	537	5	l.	l.	PROPN
ejpam-5697	537	6	hölder	hölder	PROPN
ejpam-5697	537	7	.	.	PUNCT
ejpam-5697	538	1	ueber	ueber	PROPN
ejpam-5697	538	2	einen	einen	PROPN
ejpam-5697	538	3	mittelwertsatz	mittelwertsatz	PROPN
ejpam-5697	538	4	.	.	PUNCT
ejpam-5697	539	1	nachrichten	nachrichten	PROPN
ejpam-5697	539	2	von	von	PROPN
ejpam-5697	539	3	der	der	PROPN
ejpam-5697	539	4	königl	königl	PROPN
ejpam-5697	539	5	gesellschaft	gesellschaft	PROPN
ejpam-5697	539	6	der	der	NOUN
ejpam-5697	539	7	wissenschaften	wissenschaften	AUX
ejpam-5697	539	8	und	und	VERB
ejpam-5697	539	9	der	der	ADJ
ejpam-5697	539	10	georg	georg	NOUN
ejpam-5697	539	11	-	-	PUNCT
ejpam-5697	539	12	augusts	august	NOUN
ejpam-5697	539	13	-	-	PUNCT
ejpam-5697	539	14	universität	universität	ADJ
ejpam-5697	539	15	zu	zu	PROPN
ejpam-5697	539	16	göttingen	göttingen	PROPN
ejpam-5697	539	17	,	,	PUNCT
ejpam-5697	539	18	band	band	NOUN
ejpam-5697	539	19	(	(	PUNCT
ejpam-5697	539	20	in	in	ADP
ejpam-5697	539	21	german	german	NOUN
ejpam-5697	539	22	)	)	PUNCT
ejpam-5697	539	23	,	,	PUNCT
ejpam-5697	539	24	2:38–47	2:38–47	PROPN
ejpam-5697	539	25	,	,	PUNCT
ejpam-5697	539	26	1889	1889	NUM
ejpam-5697	539	27	.	.	PUNCT
ejpam-5697	540	1	[	[	X
ejpam-5697	540	2	7	7	X
ejpam-5697	540	3	]	]	X
ejpam-5697	540	4	w.	w.	PROPN
ejpam-5697	540	5	h.	h.	PROPN
ejpam-5697	540	6	huang	huang	PROPN
ejpam-5697	540	7	,	,	PUNCT
ejpam-5697	540	8	m.	m.	PROPN
ejpam-5697	540	9	samraiz	samraiz	PROPN
ejpam-5697	540	10	,	,	PUNCT
ejpam-5697	540	11	a.	a.	PROPN
ejpam-5697	540	12	mehmood	mehmood	PROPN
ejpam-5697	540	13	,	,	PUNCT
ejpam-5697	540	14	d.	d.	PROPN
ejpam-5697	540	15	baleanu	baleanu	PROPN
ejpam-5697	540	16	,	,	PUNCT
ejpam-5697	540	17	g.	g.	PROPN
ejpam-5697	540	18	rahman	rahman	PROPN
ejpam-5697	540	19	,	,	PUNCT
ejpam-5697	540	20	and	and	CCONJ
ejpam-5697	540	21	s.	s.	PROPN
ejpam-5697	540	22	naheed	naheed	PROPN
ejpam-5697	540	23	.	.	PUNCT
ejpam-5697	541	1	modified	modify	VERB
ejpam-5697	541	2	atangana	atangana	PROPN
ejpam-5697	541	3	-	-	PUNCT
ejpam-5697	541	4	baleanu	baleanu	ADJ
ejpam-5697	541	5	fractional	fractional	ADJ
ejpam-5697	541	6	operators	operator	NOUN
ejpam-5697	541	7	involving	involve	VERB
ejpam-5697	541	8	generalized	generalize	VERB
ejpam-5697	541	9	mittag	mittag	ADJ
ejpam-5697	541	10	-	-	PUNCT
ejpam-5697	541	11	leffler	leffler	NOUN
ejpam-5697	541	12	function	function	NOUN
ejpam-5697	541	13	.	.	PUNCT
ejpam-5697	542	1	alexandria	alexandria	PROPN
ejpam-5697	542	2	engineering	engineering	PROPN
ejpam-5697	542	3	journal	journal	PROPN
ejpam-5697	542	4	,	,	PUNCT
ejpam-5697	542	5	75:639–648	75:639–648	PROPN
ejpam-5697	542	6	,	,	PUNCT
ejpam-5697	542	7	2023	2023	NUM
ejpam-5697	542	8	.	.	PUNCT
ejpam-5697	543	1	[	[	X
ejpam-5697	543	2	8	8	NUM
ejpam-5697	543	3	]	]	X
ejpam-5697	543	4	f.	f.	PROPN
ejpam-5697	543	5	jarad	jarad	PROPN
ejpam-5697	543	6	and	and	CCONJ
ejpam-5697	543	7	t.	t.	PROPN
ejpam-5697	543	8	abdeljawad	abdeljawad	NOUN
ejpam-5697	543	9	.	.	PUNCT
ejpam-5697	544	1	generalized	generalize	VERB
ejpam-5697	544	2	fractional	fractional	ADJ
ejpam-5697	544	3	derivatives	derivative	NOUN
ejpam-5697	544	4	and	and	CCONJ
ejpam-5697	544	5	laplace	laplace	NOUN
ejpam-5697	544	6	transform	transform	NOUN
ejpam-5697	544	7	.	.	PUNCT
ejpam-5697	545	1	aims	aim	VERB
ejpam-5697	545	2	mathematics	mathematic	NOUN
ejpam-5697	545	3	,	,	PUNCT
ejpam-5697	545	4	130:709–722	130:709–722	NUM
ejpam-5697	545	5	,	,	PUNCT
ejpam-5697	545	6	2020	2020	NUM
ejpam-5697	545	7	.	.	PUNCT
ejpam-5697	546	1	gauhar	gauhar	PROPN
ejpam-5697	546	2	rahman	rahman	PROPN
ejpam-5697	546	3	et	et	PROPN
ejpam-5697	546	4	al	al	PROPN
ejpam-5697	546	5	.	.	PUNCT
ejpam-5697	546	6	/	/	SYM
ejpam-5697	546	7	eur	eur	PROPN
ejpam-5697	546	8	.	.	PUNCT
ejpam-5697	547	1	j.	j.	PROPN
ejpam-5697	547	2	pure	pure	PROPN
ejpam-5697	547	3	appl	appl	PROPN
ejpam-5697	547	4	.	.	PROPN
ejpam-5697	547	5	math	math	PROPN
ejpam-5697	547	6	,	,	PUNCT
ejpam-5697	547	7	18	18	NUM
ejpam-5697	547	8	(	(	PUNCT
ejpam-5697	547	9	1	1	NUM
ejpam-5697	547	10	)	)	PUNCT
ejpam-5697	547	11	(	(	PUNCT
ejpam-5697	547	12	2025	2025	NUM
ejpam-5697	547	13	)	)	PUNCT
ejpam-5697	547	14	,	,	PUNCT
ejpam-5697	547	15	5697	5697	NUM
ejpam-5697	547	16	25	25	NUM
ejpam-5697	547	17	of	of	ADP
ejpam-5697	547	18	26	26	NUM
ejpam-5697	548	1	[	[	X
ejpam-5697	548	2	9	9	NUM
ejpam-5697	548	3	]	]	PUNCT
ejpam-5697	548	4	a.	a.	NOUN
ejpam-5697	548	5	a.	a.	NOUN
ejpam-5697	548	6	kilbas	kilbas	PROPN
ejpam-5697	548	7	,	,	PUNCT
ejpam-5697	548	8	h.	h.	PROPN
ejpam-5697	548	9	m.	m.	PROPN
ejpam-5697	548	10	srivastava	srivastava	PROPN
ejpam-5697	548	11	,	,	PUNCT
ejpam-5697	548	12	and	and	CCONJ
ejpam-5697	548	13	j.	j.	PROPN
ejpam-5697	548	14	j.	j.	PROPN
ejpam-5697	548	15	trujillo	trujillo	PROPN
ejpam-5697	548	16	.	.	PUNCT
ejpam-5697	548	17	theory	theory	NOUN
ejpam-5697	548	18	and	and	CCONJ
ejpam-5697	548	19	applications	application	NOUN
ejpam-5697	548	20	of	of	ADP
ejpam-5697	548	21	fractional	fractional	ADJ
ejpam-5697	548	22	differential	differential	ADJ
ejpam-5697	548	23	equations	equation	NOUN
ejpam-5697	548	24	.	.	PUNCT
ejpam-5697	549	1	elsevier	elsevier	NOUN
ejpam-5697	549	2	,	,	PUNCT
ejpam-5697	549	3	north	north	PROPN
ejpam-5697	549	4	-	-	PUNCT
ejpam-5697	549	5	holland	holland	PROPN
ejpam-5697	549	6	mathematics	mathematics	PROPN
ejpam-5697	549	7	studies	study	NOUN
ejpam-5697	549	8	,	,	PUNCT
ejpam-5697	549	9	new	new	PROPN
ejpam-5697	549	10	york	york	PROPN
ejpam-5697	549	11	,	,	PUNCT
ejpam-5697	549	12	london	london	PROPN
ejpam-5697	549	13	,	,	PUNCT
ejpam-5697	549	14	2006	2006	NUM
ejpam-5697	549	15	.	.	PUNCT
ejpam-5697	550	1	[	[	X
ejpam-5697	550	2	10	10	NUM
ejpam-5697	550	3	]	]	X
ejpam-5697	550	4	j.	j.	PROPN
ejpam-5697	550	5	losada	losada	PROPN
ejpam-5697	550	6	and	and	CCONJ
ejpam-5697	550	7	j.	j.	PROPN
ejpam-5697	550	8	j.	j.	PROPN
ejpam-5697	550	9	nieto	nieto	PROPN
ejpam-5697	550	10	.	.	PUNCT
ejpam-5697	551	1	properties	property	NOUN
ejpam-5697	551	2	of	of	ADP
ejpam-5697	551	3	a	a	DET
ejpam-5697	551	4	new	new	ADJ
ejpam-5697	551	5	fractional	fractional	ADJ
ejpam-5697	551	6	derivative	derivative	NOUN
ejpam-5697	551	7	without	without	ADP
ejpam-5697	551	8	singular	singular	ADJ
ejpam-5697	551	9	kernel	kernel	PROPN
ejpam-5697	551	10	.	.	PUNCT
ejpam-5697	552	1	prog	prog	PROPN
ejpam-5697	552	2	.	.	PUNCT
ejpam-5697	553	1	frac	frac	PROPN
ejpam-5697	553	2	.	.	PROPN
ejpam-5697	554	1	differ	differ	VERB
ejpam-5697	554	2	.	.	PUNCT
ejpam-5697	555	1	appl	appl	PROPN
ejpam-5697	555	2	.	.	PROPN
ejpam-5697	555	3	,	,	PUNCT
ejpam-5697	555	4	1:87–92	1:87–92	NUM
ejpam-5697	555	5	,	,	PUNCT
ejpam-5697	555	6	2015	2015	NUM
ejpam-5697	555	7	.	.	PUNCT
ejpam-5697	556	1	[	[	X
ejpam-5697	556	2	11	11	NUM
ejpam-5697	556	3	]	]	X
ejpam-5697	556	4	e.	e.	PROPN
ejpam-5697	556	5	m.	m.	PROPN
ejpam-5697	556	6	lotfi	lotfi	PROPN
ejpam-5697	556	7	,	,	PUNCT
ejpam-5697	556	8	h.	h.	PROPN
ejpam-5697	556	9	zine	zine	PROPN
ejpam-5697	556	10	,	,	PUNCT
ejpam-5697	556	11	d.	d.	PROPN
ejpam-5697	556	12	f.	f.	PROPN
ejpam-5697	556	13	m.	m.	PROPN
ejpam-5697	556	14	torres	torres	PROPN
ejpam-5697	556	15	,	,	PUNCT
ejpam-5697	556	16	and	and	CCONJ
ejpam-5697	556	17	n.	n.	PROPN
ejpam-5697	556	18	yousfi	yousfi	PROPN
ejpam-5697	556	19	.	.	PUNCT
ejpam-5697	557	1	the	the	DET
ejpam-5697	557	2	power	power	NOUN
ejpam-5697	557	3	fractional	fractional	ADJ
ejpam-5697	557	4	calculus	calculus	NOUN
ejpam-5697	557	5	:	:	PUNCT
ejpam-5697	557	6	first	first	ADJ
ejpam-5697	557	7	definitions	definition	NOUN
ejpam-5697	557	8	and	and	CCONJ
ejpam-5697	557	9	properties	property	NOUN
ejpam-5697	557	10	with	with	ADP
ejpam-5697	557	11	applications	application	NOUN
ejpam-5697	557	12	to	to	ADP
ejpam-5697	557	13	power	power	NOUN
ejpam-5697	557	14	fractional	fractional	ADJ
ejpam-5697	557	15	differential	differential	NOUN
ejpam-5697	557	16	equations	equation	NOUN
ejpam-5697	557	17	.	.	PUNCT
ejpam-5697	558	1	mathematics	mathematic	NOUN
ejpam-5697	558	2	,	,	PUNCT
ejpam-5697	558	3	10:35994	10:35994	NUM
ejpam-5697	558	4	,	,	PUNCT
ejpam-5697	558	5	2022	2022	NUM
ejpam-5697	558	6	.	.	PUNCT
ejpam-5697	559	1	[	[	X
ejpam-5697	559	2	12	12	NUM
ejpam-5697	559	3	]	]	PUNCT
ejpam-5697	559	4	f.	f.	PROPN
ejpam-5697	559	5	mainardi	mainardi	PROPN
ejpam-5697	559	6	.	.	PUNCT
ejpam-5697	560	1	fractional	fractional	ADJ
ejpam-5697	560	2	calculus	calculus	NOUN
ejpam-5697	560	3	and	and	CCONJ
ejpam-5697	560	4	waves	wave	NOUN
ejpam-5697	560	5	in	in	ADP
ejpam-5697	560	6	linear	linear	PROPN
ejpam-5697	560	7	viscoelasticity	viscoelasticity	NOUN
ejpam-5697	560	8	:	:	PUNCT
ejpam-5697	560	9	an	an	DET
ejpam-5697	560	10	introduction	introduction	NOUN
ejpam-5697	560	11	to	to	ADP
ejpam-5697	560	12	mathematical	mathematical	ADJ
ejpam-5697	560	13	models	model	NOUN
ejpam-5697	560	14	.	.	PUNCT
ejpam-5697	561	1	world	world	NOUN
ejpam-5697	561	2	scientific	scientific	ADJ
ejpam-5697	561	3	publishing	publishing	NOUN
ejpam-5697	561	4	company	company	NOUN
ejpam-5697	561	5	,	,	PUNCT
ejpam-5697	561	6	london	london	PROPN
ejpam-5697	561	7	,	,	PUNCT
ejpam-5697	561	8	2010	2010	NUM
ejpam-5697	561	9	.	.	PUNCT
ejpam-5697	562	1	[	[	X
ejpam-5697	562	2	13	13	NUM
ejpam-5697	562	3	]	]	PUNCT
ejpam-5697	562	4	k.	k.	PROPN
ejpam-5697	562	5	s.	s.	PROPN
ejpam-5697	562	6	miller	miller	PROPN
ejpam-5697	562	7	and	and	CCONJ
ejpam-5697	562	8	b.	b.	PROPN
ejpam-5697	562	9	ross	ross	PROPN
ejpam-5697	562	10	.	.	PUNCT
ejpam-5697	563	1	an	an	DET
ejpam-5697	563	2	introduction	introduction	NOUN
ejpam-5697	563	3	to	to	ADP
ejpam-5697	563	4	the	the	DET
ejpam-5697	563	5	fractional	fractional	ADJ
ejpam-5697	563	6	calculus	calculus	NOUN
ejpam-5697	563	7	and	and	CCONJ
ejpam-5697	563	8	fractional	fractional	ADJ
ejpam-5697	563	9	differential	differential	ADJ
ejpam-5697	563	10	equations	equation	NOUN
ejpam-5697	563	11	.	.	PUNCT
ejpam-5697	564	1	wiley	wiley	PROPN
ejpam-5697	564	2	,	,	PUNCT
ejpam-5697	564	3	new	new	PROPN
ejpam-5697	564	4	york	york	PROPN
ejpam-5697	564	5	,	,	PUNCT
ejpam-5697	564	6	1993	1993	NUM
ejpam-5697	564	7	.	.	PUNCT
ejpam-5697	565	1	[	[	X
ejpam-5697	565	2	14	14	NUM
ejpam-5697	565	3	]	]	PUNCT
ejpam-5697	565	4	p.	p.	NOUN
ejpam-5697	565	5	o.	o.	PROPN
ejpam-5697	566	1	mohammad	mohammad	PROPN
ejpam-5697	566	2	,	,	PUNCT
ejpam-5697	566	3	h.	h.	PROPN
ejpam-5697	566	4	m.	m.	PROPN
ejpam-5697	566	5	srivastava	srivastava	PROPN
ejpam-5697	566	6	,	,	PUNCT
ejpam-5697	566	7	d.	d.	PROPN
ejpam-5697	566	8	baleanu	baleanu	PROPN
ejpam-5697	566	9	,	,	PUNCT
ejpam-5697	566	10	and	and	CCONJ
ejpam-5697	566	11	k.	k.	PROPN
ejpam-5697	566	12	m.	m.	PROPN
ejpam-5697	566	13	abualnaja	abualnaja	PROPN
ejpam-5697	566	14	.	.	PUNCT
ejpam-5697	567	1	modified	modify	VERB
ejpam-5697	567	2	fractional	fractional	ADJ
ejpam-5697	567	3	difference	difference	NOUN
ejpam-5697	567	4	operators	operator	NOUN
ejpam-5697	567	5	defined	define	VERB
ejpam-5697	567	6	using	use	VERB
ejpam-5697	567	7	m	m	PROPN
ejpam-5697	567	8	-	-	PUNCT
ejpam-5697	567	9	l	l	NOUN
ejpam-5697	567	10	kernels	kernel	NOUN
ejpam-5697	567	11	.	.	PUNCT
ejpam-5697	568	1	symmetry	symmetry	PROPN
ejpam-5697	568	2	,	,	PUNCT
ejpam-5697	568	3	14:1519	14:1519	NUM
ejpam-5697	568	4	,	,	PUNCT
ejpam-5697	568	5	2022	2022	NUM
ejpam-5697	568	6	.	.	PUNCT
ejpam-5697	569	1	[	[	X
ejpam-5697	569	2	15	15	NUM
ejpam-5697	569	3	]	]	PUNCT
ejpam-5697	569	4	k.	k.	PROPN
ejpam-5697	569	5	s.	s.	PROPN
ejpam-5697	569	6	nisar	nisar	PROPN
ejpam-5697	569	7	,	,	PUNCT
ejpam-5697	569	8	g.	g.	PROPN
ejpam-5697	569	9	rahman	rahman	PROPN
ejpam-5697	569	10	,	,	PUNCT
ejpam-5697	569	11	d.	d.	PROPN
ejpam-5697	569	12	baleanu	baleanu	PROPN
ejpam-5697	569	13	,	,	PUNCT
ejpam-5697	569	14	s.	s.	PROPN
ejpam-5697	569	15	mubeen	mubeen	PROPN
ejpam-5697	569	16	,	,	PUNCT
ejpam-5697	569	17	and	and	CCONJ
ejpam-5697	569	18	m.	m.	PROPN
ejpam-5697	569	19	arshad	arshad	PROPN
ejpam-5697	569	20	.	.	PUNCT
ejpam-5697	570	1	the	the	DET
ejpam-5697	570	2	(	(	PUNCT
ejpam-5697	570	3	k	k	NOUN
ejpam-5697	570	4	,	,	PUNCT
ejpam-5697	570	5	s)-fractional	s)-fractional	ADJ
ejpam-5697	570	6	calculus	calculus	NOUN
ejpam-5697	570	7	of	of	ADP
ejpam-5697	570	8	k	k	ADJ
ejpam-5697	570	9	-	-	ADJ
ejpam-5697	570	10	mittag	mittag	ADJ
ejpam-5697	570	11	-	-	PUNCT
ejpam-5697	570	12	leffler	leffler	NOUN
ejpam-5697	570	13	function	function	NOUN
ejpam-5697	570	14	.	.	PUNCT
ejpam-5697	571	1	adv	adv	PROPN
ejpam-5697	571	2	.	.	PUNCT
ejpam-5697	571	3	difference	difference	PROPN
ejpam-5697	571	4	equ	equ	PROPN
ejpam-5697	571	5	.	.	PROPN
ejpam-5697	571	6	,	,	PUNCT
ejpam-5697	571	7	2017:115210	2017:115210	NUM
ejpam-5697	571	8	,	,	PUNCT
ejpam-5697	571	9	2017	2017	NUM
ejpam-5697	571	10	.	.	PUNCT
ejpam-5697	572	1	[	[	X
ejpam-5697	572	2	16	16	NUM
ejpam-5697	572	3	]	]	PUNCT
ejpam-5697	572	4	k.	k.	PROPN
ejpam-5697	572	5	b.	b.	PROPN
ejpam-5697	572	6	oldham	oldham	PROPN
ejpam-5697	572	7	and	and	CCONJ
ejpam-5697	572	8	j.	j.	PROPN
ejpam-5697	572	9	spanier	spanier	PROPN
ejpam-5697	572	10	.	.	PUNCT
ejpam-5697	573	1	the	the	DET
ejpam-5697	573	2	fractional	fractional	ADJ
ejpam-5697	573	3	calculus	calculus	NOUN
ejpam-5697	573	4	.	.	PUNCT
ejpam-5697	574	1	academic	academic	ADJ
ejpam-5697	574	2	press	press	NOUN
ejpam-5697	574	3	,	,	PUNCT
ejpam-5697	574	4	new	new	PROPN
ejpam-5697	574	5	york	york	PROPN
ejpam-5697	574	6	,	,	PUNCT
ejpam-5697	574	7	1974	1974	NUM
ejpam-5697	574	8	.	.	PUNCT
ejpam-5697	575	1	[	[	X
ejpam-5697	575	2	17	17	NUM
ejpam-5697	575	3	]	]	PUNCT
ejpam-5697	575	4	s.	s.	PROPN
ejpam-5697	575	5	k.	k.	PROPN
ejpam-5697	575	6	panda	panda	PROPN
ejpam-5697	575	7	.	.	PUNCT
ejpam-5697	576	1	applying	apply	VERB
ejpam-5697	576	2	fixed	fix	VERB
ejpam-5697	576	3	point	point	NOUN
ejpam-5697	576	4	methods	method	NOUN
ejpam-5697	576	5	and	and	CCONJ
ejpam-5697	576	6	fractional	fractional	ADJ
ejpam-5697	576	7	operators	operator	NOUN
ejpam-5697	576	8	in	in	ADP
ejpam-5697	576	9	the	the	DET
ejpam-5697	576	10	modelling	modelling	NOUN
ejpam-5697	576	11	of	of	ADP
ejpam-5697	576	12	novel	novel	ADJ
ejpam-5697	576	13	coronavirus	coronavirus	NOUN
ejpam-5697	576	14	2019	2019	NUM
ejpam-5697	576	15	-	-	PUNCT
ejpam-5697	576	16	ncov	ncov	NOUN
ejpam-5697	576	17	/	/	SYM
ejpam-5697	576	18	sars	sar	NOUN
ejpam-5697	576	19	-	-	PUNCT
ejpam-5697	576	20	cov-2	cov-2	NOUN
ejpam-5697	576	21	.	.	PUNCT
ejpam-5697	577	1	results	results	PROPN
ejpam-5697	577	2	phy	phy	PROPN
ejpam-5697	577	3	.	.	PROPN
ejpam-5697	577	4	,	,	PUNCT
ejpam-5697	577	5	9:103433	9:103433	NUM
ejpam-5697	577	6	,	,	PUNCT
ejpam-5697	577	7	2020	2020	NUM
ejpam-5697	577	8	.	.	PUNCT
ejpam-5697	578	1	[	[	X
ejpam-5697	578	2	18	18	NUM
ejpam-5697	578	3	]	]	PUNCT
ejpam-5697	578	4	s.	s.	PROPN
ejpam-5697	578	5	k.	k.	PROPN
ejpam-5697	578	6	panda	panda	PROPN
ejpam-5697	578	7	,	,	PUNCT
ejpam-5697	578	8	t.	t.	NOUN
ejpam-5697	578	9	abdeljawad	abdeljawad	NOUN
ejpam-5697	578	10	,	,	PUNCT
ejpam-5697	578	11	and	and	CCONJ
ejpam-5697	578	12	c.	c.	PROPN
ejpam-5697	578	13	ravichandran	ravichandran	NOUN
ejpam-5697	578	14	.	.	PUNCT
ejpam-5697	579	1	a	a	DET
ejpam-5697	579	2	complex	complex	ADJ
ejpam-5697	579	3	valued	value	VERB
ejpam-5697	579	4	approach	approach	NOUN
ejpam-5697	579	5	to	to	ADP
ejpam-5697	579	6	the	the	DET
ejpam-5697	579	7	solution	solution	NOUN
ejpam-5697	579	8	of	of	ADP
ejpam-5697	579	9	riemann	riemann	PROPN
ejpam-5697	579	10	-	-	PUNCT
ejpam-5697	579	11	liouville	liouville	NOUN
ejpam-5697	579	12	integral	integral	ADJ
ejpam-5697	579	13	,	,	PUNCT
ejpam-5697	579	14	atangana	atangana	PROPN
ejpam-5697	579	15	-	-	PUNCT
ejpam-5697	579	16	baleanu	baleanu	ADJ
ejpam-5697	579	17	integral	integral	ADJ
ejpam-5697	579	18	operator	operator	NOUN
ejpam-5697	579	19	and	and	CCONJ
ejpam-5697	579	20	non	non	ADJ
ejpam-5697	579	21	-	-	ADJ
ejpam-5697	579	22	linear	linear	ADJ
ejpam-5697	579	23	telegraph	telegraph	NOUN
ejpam-5697	579	24	equation	equation	NOUN
ejpam-5697	579	25	via	via	ADP
ejpam-5697	579	26	fixed	fix	VERB
ejpam-5697	579	27	point	point	NOUN
ejpam-5697	579	28	method	method	NOUN
ejpam-5697	579	29	.	.	PUNCT
ejpam-5697	580	1	chaos	chaos	NOUN
ejpam-5697	580	2	,	,	PUNCT
ejpam-5697	580	3	solitons	soliton	NOUN
ejpam-5697	580	4	and	and	CCONJ
ejpam-5697	580	5	fractals	fractal	NOUN
ejpam-5697	580	6	,	,	PUNCT
ejpam-5697	580	7	130:109439	130:109439	NUM
ejpam-5697	580	8	,	,	PUNCT
ejpam-5697	580	9	2020	2020	NUM
ejpam-5697	580	10	.	.	PUNCT
ejpam-5697	581	1	[	[	X
ejpam-5697	581	2	19	19	NUM
ejpam-5697	581	3	]	]	PUNCT
ejpam-5697	581	4	s.	s.	PROPN
ejpam-5697	581	5	k.	k.	PROPN
ejpam-5697	581	6	panda	panda	PROPN
ejpam-5697	581	7	,	,	PUNCT
ejpam-5697	581	8	t.	t.	NOUN
ejpam-5697	581	9	abdeljawad	abdeljawad	NOUN
ejpam-5697	581	10	,	,	PUNCT
ejpam-5697	581	11	and	and	CCONJ
ejpam-5697	581	12	c.	c.	PROPN
ejpam-5697	581	13	ravichandran	ravichandran	NOUN
ejpam-5697	581	14	.	.	PUNCT
ejpam-5697	582	1	a	a	DET
ejpam-5697	582	2	novel	novel	ADJ
ejpam-5697	582	3	fixed	fix	VERB
ejpam-5697	582	4	point	point	NOUN
ejpam-5697	582	5	approach	approach	NOUN
ejpam-5697	582	6	to	to	ADP
ejpam-5697	582	7	atangana	atangana	PROPN
ejpam-5697	582	8	-	-	PUNCT
ejpam-5697	582	9	baleanu	baleanu	ADJ
ejpam-5697	582	10	fractional	fractional	ADJ
ejpam-5697	582	11	and	and	CCONJ
ejpam-5697	582	12	lp	lp	ADJ
ejpam-5697	582	13	-	-	PUNCT
ejpam-5697	582	14	fradholm	fradholm	ADJ
ejpam-5697	582	15	integral	integral	ADJ
ejpam-5697	582	16	equation	equation	NOUN
ejpam-5697	582	17	.	.	PUNCT
ejpam-5697	583	1	alexandria	alexandria	PROPN
ejpam-5697	583	2	engineering	engineering	PROPN
ejpam-5697	583	3	journal	journal	PROPN
ejpam-5697	583	4	,	,	PUNCT
ejpam-5697	583	5	59:1959–1970	59:1959–1970	NUM
ejpam-5697	583	6	,	,	PUNCT
ejpam-5697	583	7	2020	2020	NUM
ejpam-5697	583	8	.	.	PUNCT
ejpam-5697	584	1	[	[	X
ejpam-5697	584	2	20	20	NUM
ejpam-5697	584	3	]	]	PUNCT
ejpam-5697	584	4	s.	s.	PROPN
ejpam-5697	584	5	k.	k.	PROPN
ejpam-5697	584	6	panda	panda	PROPN
ejpam-5697	584	7	,	,	PUNCT
ejpam-5697	584	8	c.	c.	NOUN
ejpam-5697	584	9	ravichandran	ravichandran	NOUN
ejpam-5697	584	10	,	,	PUNCT
ejpam-5697	584	11	and	and	CCONJ
ejpam-5697	584	12	b.	b.	PROPN
ejpam-5697	584	13	hazrika	hazrika	PROPN
ejpam-5697	584	14	.	.	PROPN
ejpam-5697	585	1	result	result	VERB
ejpam-5697	585	2	on	on	ADP
ejpam-5697	585	3	system	system	NOUN
ejpam-5697	585	4	of	of	ADP
ejpam-5697	585	5	a	a	DET
ejpam-5697	585	6	-	-	PUNCT
ejpam-5697	585	7	b	b	NOUN
ejpam-5697	585	8	fractional	fractional	ADJ
ejpam-5697	585	9	order	order	NOUN
ejpam-5697	585	10	willis	willis	PROPN
ejpam-5697	585	11	aneurysm	aneurysm	PROPN
ejpam-5697	585	12	and	and	CCONJ
ejpam-5697	585	13	nonlinear	nonlinear	ADJ
ejpam-5697	585	14	singular	singular	NOUN
ejpam-5697	585	15	perturbed	perturb	VERB
ejpam-5697	585	16	boundary	boundary	ADJ
ejpam-5697	585	17	value	value	NOUN
ejpam-5697	585	18	problems	problem	NOUN
ejpam-5697	585	19	.	.	PUNCT
ejpam-5697	586	1	chaos	chaos	NOUN
ejpam-5697	586	2	,	,	PUNCT
ejpam-5697	586	3	solitons	soliton	NOUN
ejpam-5697	586	4	and	and	CCONJ
ejpam-5697	586	5	fractals	fractal	NOUN
ejpam-5697	586	6	,	,	PUNCT
ejpam-5697	586	7	2020	2020	NUM
ejpam-5697	586	8	.	.	PUNCT
ejpam-5697	587	1	[	[	X
ejpam-5697	587	2	21	21	NUM
ejpam-5697	587	3	]	]	X
ejpam-5697	587	4	i.	i.	NOUN
ejpam-5697	587	5	podlubny	podlubny	PROPN
ejpam-5697	587	6	.	.	PUNCT
ejpam-5697	588	1	fractional	fractional	ADJ
ejpam-5697	588	2	differential	differential	ADJ
ejpam-5697	588	3	equations	equation	NOUN
ejpam-5697	588	4	.	.	PUNCT
ejpam-5697	589	1	academic	academic	ADJ
ejpam-5697	589	2	press	press	NOUN
ejpam-5697	589	3	,	,	PUNCT
ejpam-5697	589	4	san	san	PROPN
ejpam-5697	589	5	diego	diego	PROPN
ejpam-5697	589	6	,	,	PUNCT
ejpam-5697	589	7	1999	1999	NUM
ejpam-5697	589	8	.	.	PUNCT
ejpam-5697	590	1	[	[	X
ejpam-5697	590	2	22	22	NUM
ejpam-5697	590	3	]	]	PUNCT
ejpam-5697	590	4	m.	m.	NOUN
ejpam-5697	590	5	a.	a.	NOUN
ejpam-5697	590	6	refai	refai	PROPN
ejpam-5697	590	7	.	.	PUNCT
ejpam-5697	591	1	on	on	ADP
ejpam-5697	591	2	weighted	weight	VERB
ejpam-5697	591	3	atangana	atangana	PROPN
ejpam-5697	591	4	baleanu	baleanu	PROPN
ejpam-5697	591	5	fractional	fractional	ADJ
ejpam-5697	591	6	derivative	derivative	ADJ
ejpam-5697	591	7	operator	operator	NOUN
ejpam-5697	591	8	.	.	PUNCT
ejpam-5697	592	1	alexandria	alexandria	PROPN
ejpam-5697	592	2	engineering	engineering	PROPN
ejpam-5697	592	3	journal	journal	PROPN
ejpam-5697	592	4	,	,	PUNCT
ejpam-5697	592	5	2020:3	2020:3	NUM
ejpam-5697	592	6	,	,	PUNCT
ejpam-5697	592	7	2020	2020	NUM
ejpam-5697	592	8	.	.	PUNCT
ejpam-5697	593	1	[	[	X
ejpam-5697	593	2	23	23	NUM
ejpam-5697	593	3	]	]	PUNCT
ejpam-5697	593	4	m.	m.	NOUN
ejpam-5697	593	5	a.	a.	NOUN
ejpam-5697	593	6	refai	refai	PROPN
ejpam-5697	593	7	and	and	CCONJ
ejpam-5697	593	8	d.	d.	PROPN
ejpam-5697	593	9	baleanu	baleanu	PROPN
ejpam-5697	593	10	.	.	PUNCT
ejpam-5697	594	1	on	on	ADP
ejpam-5697	594	2	an	an	DET
ejpam-5697	594	3	extension	extension	NOUN
ejpam-5697	594	4	of	of	ADP
ejpam-5697	594	5	the	the	DET
ejpam-5697	594	6	operator	operator	NOUN
ejpam-5697	594	7	with	with	ADP
ejpam-5697	594	8	m	m	NOUN
ejpam-5697	594	9	-	-	ADJ
ejpam-5697	594	10	l	l	NOUN
ejpam-5697	594	11	function	function	NOUN
ejpam-5697	594	12	.	.	PUNCT
ejpam-5697	595	1	fractals	fractal	NOUN
ejpam-5697	595	2	,	,	PUNCT
ejpam-5697	595	3	30:2240129	30:2240129	NUM
ejpam-5697	595	4	,	,	PUNCT
ejpam-5697	595	5	2022	2022	NUM
ejpam-5697	595	6	.	.	PUNCT
ejpam-5697	596	1	[	[	X
ejpam-5697	596	2	24	24	NUM
ejpam-5697	596	3	]	]	X
ejpam-5697	596	4	s.	s.	PROPN
ejpam-5697	596	5	g.	g.	PROPN
ejpam-5697	596	6	samko	samko	PROPN
ejpam-5697	596	7	,	,	PUNCT
ejpam-5697	596	8	a.	a.	NOUN
ejpam-5697	596	9	a.	a.	NOUN
ejpam-5697	596	10	kilbas	kilbas	PROPN
ejpam-5697	596	11	,	,	PUNCT
ejpam-5697	596	12	and	and	CCONJ
ejpam-5697	596	13	o.	o.	PROPN
ejpam-5697	596	14	i.	i.	PROPN
ejpam-5697	596	15	marichev	marichev	PROPN
ejpam-5697	596	16	.	.	PUNCT
ejpam-5697	597	1	fractional	fractional	ADJ
ejpam-5697	597	2	integrals	integral	NOUN
ejpam-5697	597	3	and	and	CCONJ
ejpam-5697	597	4	derivatives	derivative	NOUN
ejpam-5697	597	5	,	,	PUNCT
ejpam-5697	597	6	theory	theory	NOUN
ejpam-5697	597	7	and	and	CCONJ
ejpam-5697	597	8	applications	application	NOUN
ejpam-5697	597	9	.	.	PUNCT
ejpam-5697	598	1	gordon	gordon	PROPN
ejpam-5697	598	2	and	and	CCONJ
ejpam-5697	598	3	breach	breach	PROPN
ejpam-5697	598	4	,	,	PUNCT
ejpam-5697	598	5	amsterdam	amsterdam	PROPN
ejpam-5697	598	6	,	,	PUNCT
ejpam-5697	598	7	1993	1993	NUM
ejpam-5697	598	8	.	.	PUNCT
ejpam-5697	599	1	[	[	X
ejpam-5697	599	2	25	25	NUM
ejpam-5697	599	3	]	]	PUNCT
ejpam-5697	599	4	m.	m.	NOUN
ejpam-5697	599	5	samraiz	samraiz	PROPN
ejpam-5697	599	6	,	,	PUNCT
ejpam-5697	599	7	a.	a.	PROPN
ejpam-5697	599	8	mehmood	mehmood	PROPN
ejpam-5697	599	9	,	,	PUNCT
ejpam-5697	599	10	s.	s.	PROPN
ejpam-5697	599	11	iqbal	iqbal	PROPN
ejpam-5697	599	12	,	,	PUNCT
ejpam-5697	599	13	s.	s.	PROPN
ejpam-5697	599	14	naheed	naheed	PROPN
ejpam-5697	599	15	,	,	PUNCT
ejpam-5697	599	16	g.	g.	PROPN
ejpam-5697	599	17	rahman	rahman	PROPN
ejpam-5697	599	18	,	,	PUNCT
ejpam-5697	599	19	and	and	CCONJ
ejpam-5697	599	20	y.	y.	PROPN
ejpam-5697	599	21	m.	m.	PROPN
ejpam-5697	599	22	chu	chu	PROPN
ejpam-5697	599	23	.	.	PROPN
ejpam-5697	599	24	generalized	generalize	VERB
ejpam-5697	599	25	fractional	fractional	ADJ
ejpam-5697	599	26	operator	operator	NOUN
ejpam-5697	599	27	with	with	ADP
ejpam-5697	599	28	applications	application	NOUN
ejpam-5697	599	29	in	in	ADP
ejpam-5697	599	30	mathematical	mathematical	ADJ
ejpam-5697	599	31	physics	physics	NOUN
ejpam-5697	599	32	.	.	PUNCT
ejpam-5697	600	1	chaos	chaos	NOUN
ejpam-5697	600	2	soliton	soliton	NOUN
ejpam-5697	600	3	and	and	CCONJ
ejpam-5697	600	4	fractals	fractal	NOUN
ejpam-5697	600	5	,	,	PUNCT
ejpam-5697	600	6	165:112830	165:112830	NUM
ejpam-5697	600	7	,	,	PUNCT
ejpam-5697	600	8	2022	2022	NUM
ejpam-5697	600	9	.	.	PUNCT
ejpam-5697	601	1	[	[	X
ejpam-5697	601	2	26	26	NUM
ejpam-5697	601	3	]	]	PUNCT
ejpam-5697	601	4	m.	m.	NOUN
ejpam-5697	601	5	samraiz	samraiz	PROPN
ejpam-5697	601	6	,	,	PUNCT
ejpam-5697	601	7	a.	a.	PROPN
ejpam-5697	601	8	mehmood	mehmood	PROPN
ejpam-5697	601	9	,	,	PUNCT
ejpam-5697	601	10	s.	s.	PROPN
ejpam-5697	601	11	naheed	naheed	PROPN
ejpam-5697	601	12	,	,	PUNCT
ejpam-5697	601	13	g.	g.	PROPN
ejpam-5697	601	14	rehman	rehman	PROPN
ejpam-5697	601	15	,	,	PUNCT
ejpam-5697	601	16	a.	a.	NOUN
ejpam-5697	601	17	kashuri	kashuri	PROPN
ejpam-5697	601	18	,	,	PUNCT
ejpam-5697	601	19	and	and	CCONJ
ejpam-5697	601	20	k.	k.	X
ejpam-5697	601	21	nonlaopon	nonlaopon	NOUN
ejpam-5697	601	22	.	.	PUNCT
ejpam-5697	602	1	on	on	ADP
ejpam-5697	602	2	novel	novel	ADJ
ejpam-5697	602	3	fractional	fractional	ADJ
ejpam-5697	602	4	operators	operator	NOUN
ejpam-5697	602	5	involving	involve	VERB
ejpam-5697	602	6	the	the	DET
ejpam-5697	602	7	multivariate	multivariate	NOUN
ejpam-5697	602	8	m	m	NOUN
ejpam-5697	602	9	-	-	ADJ
ejpam-5697	602	10	l	l	NOUN
ejpam-5697	602	11	function	function	NOUN
ejpam-5697	602	12	.	.	PUNCT
ejpam-5697	603	1	mathematics	mathematic	NOUN
ejpam-5697	603	2	,	,	PUNCT
ejpam-5697	603	3	10:3991	10:3991	NUM
ejpam-5697	603	4	,	,	PUNCT
ejpam-5697	603	5	2022	2022	NUM
ejpam-5697	603	6	.	.	PUNCT
ejpam-5697	604	1	gauhar	gauhar	PROPN
ejpam-5697	604	2	rahman	rahman	PROPN
ejpam-5697	604	3	et	et	PROPN
ejpam-5697	604	4	al	al	PROPN
ejpam-5697	604	5	.	.	PUNCT
ejpam-5697	604	6	/	/	SYM
ejpam-5697	604	7	eur	eur	PROPN
ejpam-5697	604	8	.	.	PUNCT
ejpam-5697	605	1	j.	j.	PROPN
ejpam-5697	605	2	pure	pure	PROPN
ejpam-5697	605	3	appl	appl	PROPN
ejpam-5697	605	4	.	.	PROPN
ejpam-5697	605	5	math	math	PROPN
ejpam-5697	605	6	,	,	PUNCT
ejpam-5697	605	7	18	18	NUM
ejpam-5697	605	8	(	(	PUNCT
ejpam-5697	605	9	1	1	NUM
ejpam-5697	605	10	)	)	PUNCT
ejpam-5697	605	11	(	(	PUNCT
ejpam-5697	605	12	2025	2025	NUM
ejpam-5697	605	13	)	)	PUNCT
ejpam-5697	605	14	,	,	PUNCT
ejpam-5697	605	15	5697	5697	NUM
ejpam-5697	605	16	26	26	NUM
ejpam-5697	605	17	of	of	ADP
ejpam-5697	605	18	26	26	NUM
ejpam-5697	605	19	[	[	SYM
ejpam-5697	605	20	27	27	NUM
ejpam-5697	605	21	]	]	PUNCT
ejpam-5697	605	22	m.	m.	NOUN
ejpam-5697	605	23	samraiz	samraiz	PROPN
ejpam-5697	605	24	,	,	PUNCT
ejpam-5697	605	25	z.	z.	PROPN
ejpam-5697	605	26	perveen	perveen	PROPN
ejpam-5697	605	27	,	,	PUNCT
ejpam-5697	605	28	t.	t.	PROPN
ejpam-5697	605	29	abdeljawad	abdeljawad	PROPN
ejpam-5697	605	30	,	,	PUNCT
ejpam-5697	605	31	s.	s.	PROPN
ejpam-5697	605	32	iqbal	iqbal	PROPN
ejpam-5697	605	33	,	,	PUNCT
ejpam-5697	605	34	and	and	CCONJ
ejpam-5697	605	35	s.	s.	PROPN
ejpam-5697	605	36	naheed	naheed	PROPN
ejpam-5697	605	37	.	.	PUNCT
ejpam-5697	606	1	on	on	ADP
ejpam-5697	606	2	certain	certain	ADJ
ejpam-5697	606	3	fractional	fractional	ADJ
ejpam-5697	606	4	calculus	calculus	NOUN
ejpam-5697	606	5	operators	operator	NOUN
ejpam-5697	606	6	and	and	CCONJ
ejpam-5697	606	7	their	their	PRON
ejpam-5697	606	8	applications	application	NOUN
ejpam-5697	606	9	in	in	ADP
ejpam-5697	606	10	mathematical	mathematical	ADJ
ejpam-5697	606	11	physics	physics	NOUN
ejpam-5697	606	12	.	.	PUNCT
ejpam-5697	607	1	phys	phy	NOUN
ejpam-5697	607	2	.	.	PUNCT
ejpam-5697	608	1	scripta	scripta	PROPN
ejpam-5697	608	2	,	,	PUNCT
ejpam-5697	608	3	95:115210	95:115210	NUM
ejpam-5697	608	4	,	,	PUNCT
ejpam-5697	608	5	2020	2020	NUM
ejpam-5697	608	6	.	.	PUNCT
ejpam-5697	609	1	[	[	X
ejpam-5697	609	2	28	28	NUM
ejpam-5697	609	3	]	]	X
ejpam-5697	609	4	m.	m.	NOUN
ejpam-5697	609	5	samraiz	samraiz	PROPN
ejpam-5697	609	6	,	,	PUNCT
ejpam-5697	609	7	z.	z.	PROPN
ejpam-5697	609	8	perveen	perveen	PROPN
ejpam-5697	609	9	,	,	PUNCT
ejpam-5697	609	10	g.	g.	PROPN
ejpam-5697	609	11	rahman	rahman	PROPN
ejpam-5697	609	12	,	,	PUNCT
ejpam-5697	609	13	k.	k.	PROPN
ejpam-5697	609	14	s.	s.	PROPN
ejpam-5697	609	15	nisar	nisar	PROPN
ejpam-5697	609	16	,	,	PUNCT
ejpam-5697	609	17	and	and	CCONJ
ejpam-5697	609	18	d.	d.	PROPN
ejpam-5697	609	19	kumar	kumar	PROPN
ejpam-5697	609	20	.	.	PUNCT
ejpam-5697	610	1	on	on	ADP
ejpam-5697	610	2	(	(	PUNCT
ejpam-5697	610	3	k	k	NOUN
ejpam-5697	610	4	,	,	PUNCT
ejpam-5697	610	5	s)-hilferprabhakar	s)-hilferprabhakar	ADJ
ejpam-5697	610	6	fractional	fractional	ADJ
ejpam-5697	610	7	derivative	derivative	NOUN
ejpam-5697	610	8	with	with	ADP
ejpam-5697	610	9	applications	application	NOUN
ejpam-5697	610	10	in	in	ADP
ejpam-5697	610	11	mathematical	mathematical	ADJ
ejpam-5697	610	12	physics	physics	NOUN
ejpam-5697	610	13	.	.	PUNCT
ejpam-5697	611	1	front	front	NOUN
ejpam-5697	611	2	.	.	PUNCT
ejpam-5697	612	1	phys	phy	NOUN
ejpam-5697	612	2	.	.	PUNCT
ejpam-5697	612	3	,	,	PUNCT
ejpam-5697	612	4	8	8	NUM
ejpam-5697	612	5	,	,	PUNCT
ejpam-5697	612	6	2020	2020	NUM
ejpam-5697	612	7	.	.	PUNCT
ejpam-5697	613	1	[	[	X
ejpam-5697	613	2	29	29	NUM
ejpam-5697	613	3	]	]	PUNCT
ejpam-5697	613	4	s.	s.	PROPN
ejpam-5697	613	5	wu	wu	PROPN
ejpam-5697	613	6	,	,	PUNCT
ejpam-5697	613	7	m.	m.	NOUN
ejpam-5697	613	8	samraiz	samraiz	PROPN
ejpam-5697	613	9	,	,	PUNCT
ejpam-5697	613	10	a.	a.	PROPN
ejpam-5697	613	11	mehmood	mehmood	PROPN
ejpam-5697	613	12	,	,	PUNCT
ejpam-5697	613	13	f.	f.	PROPN
ejpam-5697	613	14	jarad	jarad	PROPN
ejpam-5697	613	15	,	,	PUNCT
ejpam-5697	613	16	and	and	CCONJ
ejpam-5697	613	17	s.	s.	PROPN
ejpam-5697	613	18	naheed	naheed	PROPN
ejpam-5697	613	19	.	.	PUNCT
ejpam-5697	614	1	some	some	DET
ejpam-5697	614	2	symmetric	symmetric	ADJ
ejpam-5697	614	3	properties	property	NOUN
ejpam-5697	614	4	and	and	CCONJ
ejpam-5697	614	5	applications	application	NOUN
ejpam-5697	614	6	of	of	ADP
ejpam-5697	614	7	weighted	weight	VERB
ejpam-5697	614	8	fractional	fractional	ADJ
ejpam-5697	614	9	integral	integral	ADJ
ejpam-5697	614	10	operator	operator	NOUN
ejpam-5697	614	11	.	.	PUNCT
ejpam-5697	615	1	fractals	fractal	NOUN
ejpam-5697	615	2	,	,	PUNCT
ejpam-5697	615	3	8:1–9	8:1–9	NUM
ejpam-5697	615	4	,	,	PUNCT
ejpam-5697	615	5	2020	2020	NUM
ejpam-5697	615	6	.	.	PUNCT
ejpam-5697	616	1	[	[	X
ejpam-5697	616	2	30	30	NUM
ejpam-5697	616	3	]	]	X
ejpam-5697	616	4	s.	s.	PROPN
ejpam-5697	616	5	wu	wu	PROPN
ejpam-5697	616	6	,	,	PUNCT
ejpam-5697	616	7	m.	m.	NOUN
ejpam-5697	616	8	samraiz	samraiz	PROPN
ejpam-5697	616	9	,	,	PUNCT
ejpam-5697	616	10	z.	z.	PROPN
ejpam-5697	616	11	perveen	perveen	PROPN
ejpam-5697	616	12	,	,	PUNCT
ejpam-5697	616	13	s.	s.	PROPN
ejpam-5697	616	14	iqbal	iqbal	PROPN
ejpam-5697	616	15	,	,	PUNCT
ejpam-5697	616	16	and	and	CCONJ
ejpam-5697	616	17	a.	a.	NOUN
ejpam-5697	616	18	hussian	hussian	PROPN
ejpam-5697	616	19	.	.	PUNCT
ejpam-5697	617	1	on	on	ADP
ejpam-5697	617	2	weighted	weight	VERB
ejpam-5697	617	3	k	k	ADJ
ejpam-5697	617	4	-	-	ADJ
ejpam-5697	617	5	fractional	fractional	ADJ
ejpam-5697	617	6	operator	operator	NOUN
ejpam-5697	617	7	with	with	ADP
ejpam-5697	617	8	application	application	NOUN
ejpam-5697	617	9	in	in	ADP
ejpam-5697	617	10	mathematical	mathematical	ADJ
ejpam-5697	617	11	physics	physic	NOUN
ejpam-5697	617	12	.	.	PUNCT
ejpam-5697	617	13	fractals	fractal	NOUN
ejpam-5697	617	14	,	,	PUNCT
ejpam-5697	617	15	29:2150084	29:2150084	NUM
ejpam-5697	617	16	,	,	PUNCT
ejpam-5697	617	17	2021	2021	NUM
ejpam-5697	617	18	.	.	PUNCT
ejpam-5697	618	1	[	[	X
ejpam-5697	618	2	31	31	NUM
ejpam-5697	618	3	]	]	PUNCT
ejpam-5697	618	4	x.	x.	PROPN
ejpam-5697	618	5	j.	j.	PROPN
ejpam-5697	618	6	yang	yang	PROPN
ejpam-5697	618	7	,	,	PUNCT
ejpam-5697	618	8	h.	h.	PROPN
ejpam-5697	618	9	m.	m.	PROPN
ejpam-5697	618	10	srivastava	srivastava	PROPN
ejpam-5697	618	11	,	,	PUNCT
ejpam-5697	618	12	and	and	CCONJ
ejpam-5697	618	13	j.	j.	PROPN
ejpam-5697	618	14	a.	a.	PROPN
ejpam-5697	618	15	t.	t.	PROPN
ejpam-5697	618	16	machado	machado	PROPN
ejpam-5697	618	17	.	.	PUNCT
ejpam-5697	619	1	a	a	DET
ejpam-5697	619	2	new	new	ADJ
ejpam-5697	619	3	fractional	fractional	ADJ
ejpam-5697	619	4	derivative	derivative	NOUN
ejpam-5697	619	5	without	without	ADP
ejpam-5697	619	6	a	a	DET
ejpam-5697	619	7	singular	singular	ADJ
ejpam-5697	619	8	kernel	kernel	NOUN
ejpam-5697	619	9	:	:	PUNCT
ejpam-5697	619	10	application	application	NOUN
ejpam-5697	619	11	to	to	ADP
ejpam-5697	619	12	the	the	DET
ejpam-5697	619	13	modeling	modeling	NOUN
ejpam-5697	619	14	of	of	ADP
ejpam-5697	619	15	the	the	DET
ejpam-5697	619	16	steady	steady	ADJ
ejpam-5697	619	17	heat	heat	NOUN
ejpam-5697	619	18	flow	flow	NOUN
ejpam-5697	619	19	.	.	PUNCT
ejpam-5697	620	1	therm	therm	PROPN
ejpam-5697	620	2	.	.	PUNCT
ejpam-5697	621	1	sci	sci	PROPN
ejpam-5697	621	2	.	.	PROPN
ejpam-5697	621	3	,	,	PUNCT
ejpam-5697	621	4	20:753–756	20:753–756	PROPN
ejpam-5697	621	5	,	,	PUNCT
ejpam-5697	621	6	2016	2016	NUM
ejpam-5697	621	7	.	.	PUNCT
ejpam-5697	622	1	[	[	X
ejpam-5697	622	2	32	32	NUM
ejpam-5697	622	3	]	]	PUNCT
ejpam-5697	622	4	d.	d.	PROPN
ejpam-5697	622	5	zwillinger	zwillinger	PROPN
ejpam-5697	622	6	and	and	CCONJ
ejpam-5697	622	7	a.	a.	PROPN
ejpam-5697	622	8	jeffrey	jeffrey	PROPN
ejpam-5697	622	9	.	.	PUNCT
ejpam-5697	623	1	table	table	NOUN
ejpam-5697	623	2	of	of	ADP
ejpam-5697	623	3	integrals	integral	NOUN
ejpam-5697	623	4	,	,	PUNCT
ejpam-5697	623	5	series	series	NOUN
ejpam-5697	623	6	,	,	PUNCT
ejpam-5697	623	7	and	and	CCONJ
ejpam-5697	623	8	products	product	NOUN
ejpam-5697	623	9	.	.	PUNCT
ejpam-5697	624	1	elsevier	elsevier	NOUN
ejpam-5697	624	2	,	,	PUNCT
ejpam-5697	624	3	nonlinearity	nonlinearity	NOUN
ejpam-5697	624	4	and	and	CCONJ
ejpam-5697	624	5	chaos	chaos	NOUN
ejpam-5697	624	6	,	,	PUNCT
ejpam-5697	624	7	world	world	NOUN
ejpam-5697	624	8	scientific	scientific	ADJ
ejpam-5697	624	9	,	,	PUNCT
ejpam-5697	624	10	2007	2007	NUM
ejpam-5697	624	11	.	.	PUNCT