id	sid	eid	entity	type
iajs-3665	1	1	338	CARDINAL
iajs-3665	1	2	2025	CARDINAL
iajs-3665	2	1	al-haitham	ORG
iajs-3665	2	2	university of baghdad	ORG
iajs-3665	3	1	4.0	CARDINAL
iajs-3665	3	2	oday al-shaher 1	PERSON
iajs-3665	3	3	m. mahmoudi 2	PERSON
iajs-3665	3	4	mohammed s. mechee	PERSON
iajs-3665	3	5	3* 1,2department	DATE
iajs-3665	3	6	university of qom	ORG
iajs-3665	3	7	qom	GPE
iajs-3665	3	8	iran 3information	ORG
iajs-3665	3	9	university of kufa	ORG
iajs-3665	3	10	najaf	GPE
iajs-3665	3	11	iraq	GPE
iajs-3665	4	1	3the	CARDINAL
iajs-3665	4	2	najaf	GPE
iajs-3665	4	3	najaf	GPE
iajs-3665	4	4	iraq	GPE
iajs-3665	5	1	9	CARDINAL
iajs-3665	5	2	1	CARDINAL
iajs-3665	5	3	2023	CARDINAL
iajs-3665	5	4	20	CARDINAL
iajs-3665	5	5	april 2025	DATE
iajs-3665	7	1	one	CARDINAL
iajs-3665	13	1	1	CARDINAL
iajs-3665	16	1	1	CARDINAL
iajs-3665	17	1	the twentieth century	DATE
iajs-3665	18	1	a https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/	TIME
iajs-3665	19	1	mailto:mohammeds.abed@uokufa.edu.iq	GPE
iajs-3665	20	1	2025	CARDINAL
iajs-3665	20	2	339	CARDINAL
iajs-3665	21	1	legendre	ORG
iajs-3665	22	1	foc	ORG
iajs-3665	23	1	foc	ORG
iajs-3665	23	2	2	CARDINAL
iajs-3665	24	1	riemann-liouville	ORG
iajs-3665	24	2	foc	ORG
iajs-3665	24	3	3	CARDINAL
iajs-3665	24	4	foc	ORG
iajs-3665	24	5	lagrange	GPE
iajs-3665	31	1	agrawa	ORG
iajs-3665	31	2	3	CARDINAL
iajs-3665	32	1	4,5	CARDINAL
iajs-3665	33	1	akbarian	PRODUCT
iajs-3665	33	2	6	CARDINAL
iajs-3665	34	1	bhrawy et al	PERSON
iajs-3665	35	1	7	CARDINAL
iajs-3665	36	1	second	ORDINAL
iajs-3665	36	2	torres	PERSON
iajs-3665	36	3	9	CARDINAL
iajs-3665	37	1	legendre	ORG
iajs-3665	38	1	ahmad	PERSON
iajs-3665	38	2	10	CARDINAL
iajs-3665	38	3	david et al	PERSON
iajs-3665	39	1	11	CARDINAL
iajs-3665	40	1	12-19	CARDINAL
iajs-3665	46	1	jeeves	PRODUCT
iajs-3665	47	1	2	CARDINAL
iajs-3665	48	1	ihjpas	PERSON
iajs-3665	49	1	2025	CARDINAL
iajs-3665	49	2	340 2.1	CARDINAL
iajs-3665	51	1	riemann-liouville	ORG
iajs-3665	51	2	∈	ORG
iajs-3665	52	1	2.1	CARDINAL
iajs-3665	53	1	riemann-liouville	ORG
iajs-3665	53	2	0	CARDINAL
iajs-3665	53	3	1	CARDINAL
iajs-3665	53	4	1	CARDINAL
iajs-3665	53	5	1	CARDINAL
iajs-3665	54	1	2	CARDINAL
iajs-3665	54	2	∈	ORG
iajs-3665	55	1	1	CARDINAL
iajs-3665	56	1	3	CARDINAL
iajs-3665	56	2	0	CARDINAL
iajs-3665	56	3	0	CARDINAL
iajs-3665	57	1	2.2	CARDINAL
iajs-3665	57	2	first	ORDINAL
iajs-3665	57	3	first	ORDINAL
iajs-3665	57	4	𝑢(𝜏	PERSON
iajs-3665	57	5	1	CARDINAL
iajs-3665	57	6	4	CARDINAL
iajs-3665	57	7	𝑢(0	PERSON
iajs-3665	58	1	5	CARDINAL
iajs-3665	58	2	2.2.1	CARDINAL
iajs-3665	58	3	second	ORDINAL
iajs-3665	59	1	second	ORDINAL
iajs-3665	60	1	𝜓(𝜏	ORG
iajs-3665	61	1	2	CARDINAL
iajs-3665	61	2	6	CARDINAL
iajs-3665	62	1	7	CARDINAL
iajs-3665	62	2	2.3	CARDINAL
iajs-3665	64	1	20	CARDINAL
iajs-3665	67	1	1,2	CARDINAL
iajs-3665	67	2	firstly	ORDINAL
iajs-3665	67	3	1 𝑚+1	CARDINAL
iajs-3665	70	1	2.3.1 cubic	QUANTITY
iajs-3665	70	2	20	CARDINAL
iajs-3665	70	3	ihjpas	PERSON
iajs-3665	71	1	2025	CARDINAL
iajs-3665	71	2	341 𝑠(ϛ	PERSON
iajs-3665	71	3	1 4	CARDINAL
iajs-3665	71	4	0	CARDINAL
iajs-3665	71	5	2 + ϛ)3	DATE
iajs-3665	71	6	2	CARDINAL
iajs-3665	74	1	2	CARDINAL
iajs-3665	74	2	4(1	CARDINAL
iajs-3665	75	1	ϛ)3	PRODUCT
iajs-3665	75	2	2	CARDINAL
iajs-3665	75	3	1 <	QUANTITY
iajs-3665	75	4	2	CARDINAL
iajs-3665	75	5	2	MONEY
iajs-3665	78	1	1	CARDINAL
iajs-3665	79	1	4𝑆	CARDINAL
iajs-3665	80	1	− 𝑆	PERSON
iajs-3665	80	2	1	CARDINAL
iajs-3665	82	1	2 ≤	MONEY
iajs-3665	82	2	− 𝑆	PERSON
iajs-3665	82	3	ϛ(𝑚 + 2)ħ	DATE
iajs-3665	82	4	1 + 𝑚)ħ ħ	QUANTITY
iajs-3665	82	5	4𝑆	CARDINAL
iajs-3665	82	6	2 + 𝑚)ħ ħ	QUANTITY
iajs-3665	82	7	1 + 𝑚 (	QUANTITY
iajs-3665	82	8	9	CARDINAL
iajs-3665	82	9	1	CARDINAL
iajs-3665	83	1	1	CARDINAL
iajs-3665	85	1	0	CARDINAL
iajs-3665	85	2	3 4 𝑥𝑘+1 1 4	DATE
iajs-3665	85	3	3 4	CARDINAL
iajs-3665	85	4	3 2	CARDINAL
iajs-3665	85	5	2.3.2	CARDINAL
iajs-3665	85	6	𝐽𝑥 ∝(𝑥	PERSON
iajs-3665	86	1	1 γ	CARDINAL
iajs-3665	86	2	0	CARDINAL
iajs-3665	86	3	3 2	DATE
iajs-3665	86	4	2	CARDINAL
iajs-3665	86	5	3 2	CARDINAL
iajs-3665	86	6	3 2	CARDINAL
iajs-3665	86	7	0	CARDINAL
iajs-3665	86	8	1 3 2	CARDINAL
iajs-3665	86	9	6𝑥3	CARDINAL
iajs-3665	86	10	1	CARDINAL
iajs-3665	86	11	2 0	DATE
iajs-3665	86	12	2	CARDINAL
iajs-3665	87	1	10	CARDINAL
iajs-3665	88	1	2025	CARDINAL
iajs-3665	88	2	342	CARDINAL
iajs-3665	89	1	1	CARDINAL
iajs-3665	90	1	3	CARDINAL
iajs-3665	90	2	3.1	CARDINAL
iajs-3665	91	1	second	ORDINAL
iajs-3665	93	1	𝑦(𝜁	PERSON
iajs-3665	94	1	11	CARDINAL
iajs-3665	94	2	𝑦(𝑥	ORG
iajs-3665	94	3	j = φi(xj	PERSON
iajs-3665	96	1	second	ORDINAL
iajs-3665	96	2	4	CARDINAL
iajs-3665	96	3	5	CARDINAL
iajs-3665	97	1	11	CARDINAL
iajs-3665	97	2	4	CARDINAL
iajs-3665	98	1	𝑖=1	GPE
iajs-3665	98	2	∑𝛼𝑖𝛷𝑖(𝜁𝑗	ORG
iajs-3665	98	3	∑𝛼𝑖𝛷𝑖	PERSON
iajs-3665	98	4	𝑖=1	GPE
iajs-3665	98	5	𝑖=1	GPE
iajs-3665	98	6	𝑖=1	GPE
iajs-3665	98	7	0	CARDINAL
iajs-3665	98	8	1	CARDINAL
iajs-3665	99	1	2	CARDINAL
iajs-3665	99	2	12	CARDINAL
iajs-3665	100	1	⃗	ORG
iajs-3665	100	2	𝛷𝑘⃗⃗ ⃗⃗ ⃗⃗	ORG
iajs-3665	100	3	1,2	CARDINAL
iajs-3665	103	1	2025	CARDINAL
iajs-3665	103	2	343 3.1.1	CARDINAL
iajs-3665	104	1	6	CARDINAL
iajs-3665	104	2	7	CARDINAL
iajs-3665	108	1	1	CARDINAL
iajs-3665	109	1	1	CARDINAL
iajs-3665	109	2	ii	PERSON
iajs-3665	109	3	6	CARDINAL
iajs-3665	109	4	7	CARDINAL
iajs-3665	109	5	11	CARDINAL
iajs-3665	109	6	integer n	ORG
iajs-3665	109	7	0,1,2	CARDINAL
iajs-3665	112	1	𝑡2	GPE
iajs-3665	112	2	13	CARDINAL
iajs-3665	114	1	13	CARDINAL
iajs-3665	114	2	1,2	CARDINAL
iajs-3665	114	3	vi	PERSON
iajs-3665	114	4	13	CARDINAL
iajs-3665	114	5	6	CARDINAL
iajs-3665	114	6	1,2	CARDINAL
iajs-3665	115	1	3.2	CARDINAL
iajs-3665	116	1	foc	ORG
iajs-3665	117	1	𝑥(𝜍	GPE
iajs-3665	117	2	𝑢(𝜍	ORG
iajs-3665	118	1	𝑥(𝜍	GPE
iajs-3665	118	2	𝑢(𝜍	ORG
iajs-3665	119	1	𝜍0	ORG
iajs-3665	119	2	14	CARDINAL
iajs-3665	121	1	𝜀(𝜍)𝑥(𝜍	TIME
iajs-3665	123	1	0 ≤	MONEY
iajs-3665	123	2	15	CARDINAL
iajs-3665	123	3	𝜍0	ORG
iajs-3665	123	4	16	CARDINAL
iajs-3665	123	5	𝑥(𝜍	PERSON
iajs-3665	123	6	𝑢(𝜍	ORG
iajs-3665	123	7	𝑥(𝜍	PERSON
iajs-3665	123	8	𝑢(𝜍	ORG
iajs-3665	124	1	𝑥(𝜍	PERSON
iajs-3665	124	2	𝑢(𝜍	ORG
iajs-3665	124	3	𝑥(𝜍	GPE
iajs-3665	124	4	𝑢(𝜍	ORG
iajs-3665	125	1	17	CARDINAL
iajs-3665	125	2	𝜍0	ORG
iajs-3665	125	3	18	CARDINAL
iajs-3665	126	1	𝑥(𝜍	GPE
iajs-3665	126	2	𝑢(𝜍	ORG
iajs-3665	126	3	𝑒(𝜍	DATE
iajs-3665	126	4	𝑓(𝜍	PERSON
iajs-3665	126	5	𝑔(𝜍	ORG
iajs-3665	127	1	hooke	ORG
iajs-3665	127	2	jeeves	PRODUCT
iajs-3665	128	1	3.3	CARDINAL
iajs-3665	129	1	foc	ORG
iajs-3665	130	1	foc	ORG
iajs-3665	131	1	two	CARDINAL
iajs-3665	131	2		CARDINAL
iajs-3665	132	1	2025	CARDINAL
iajs-3665	132	2	344 1	DATE
iajs-3665	132	3	foc	ORG
iajs-3665	132	4	11	CARDINAL
iajs-3665	132	5	foc	ORG
iajs-3665	132	6	𝑥(𝑡	ORG
iajs-3665	132	7	1	CARDINAL
iajs-3665	135	1	19	CARDINAL
iajs-3665	135	2	000	CARDINAL
iajs-3665	136	1	2	CARDINAL
iajs-3665	136	2	15	CARDINAL
iajs-3665	136	3	u(t	ORG
iajs-3665	136	4	u(t	ORG
iajs-3665	137	1	3	CARDINAL
iajs-3665	137	2	x(t	PERSON
iajs-3665	137	3	u(t	ORG
iajs-3665	137	4	14	CARDINAL
iajs-3665	138	1	4	CARDINAL
iajs-3665	138	2	14	CARDINAL
iajs-3665	139	1		CARDINAL
iajs-3665	139	2	1	CARDINAL
iajs-3665	139	3	1-4	CARDINAL
iajs-3665	140	1	2	CARDINAL
iajs-3665	140	2	14	CARDINAL
iajs-3665	140	3	hooke-jeeves	ORG
iajs-3665	141	1	3.4	CARDINAL
iajs-3665	142	1	4	CARDINAL
iajs-3665	143	1	two	CARDINAL
iajs-3665	143	2	foc	ORG
iajs-3665	143	3	u(t	ORG
iajs-3665	143	4	foc	ORG
iajs-3665	145	1	1	CARDINAL
iajs-3665	145	2	𝑥(𝜎	PERSON
iajs-3665	146	1	2 1	CARDINAL
iajs-3665	146	2	20	CARDINAL
iajs-3665	148	1	0 ≤	MONEY
iajs-3665	148	2	21	CARDINAL
iajs-3665	148	3	the bcs 𝑥(0	ORG
iajs-3665	148	4	1	CARDINAL
iajs-3665	149	1	+ 1	DATE
iajs-3665	149	2	22	CARDINAL
iajs-3665	151	1	19	CARDINAL
iajs-3665	153	1	19	CARDINAL
iajs-3665	153	2	21	CARDINAL
iajs-3665	153	3	𝑇.	NORP
iajs-3665	153	4	2-(a	CARDINAL
iajs-3665	154	1	2	CARDINAL
iajs-3665	155	1	𝑥(𝜎),𝑢(𝜎),𝑇	CARDINAL
iajs-3665	155	2	𝑥(𝜎	PERSON
iajs-3665	155	3	𝑥(𝜎),𝑢(𝜎),𝑇	CARDINAL
iajs-3665	155	4	− 2𝑥(𝜎	PERSON
iajs-3665	155	5	2	CARDINAL
iajs-3665	155	6	23	CARDINAL
iajs-3665	155	7	2025	CARDINAL
iajs-3665	155	8	345	CARDINAL
iajs-3665	156	1	1	CARDINAL
iajs-3665	156	2	24	CARDINAL
iajs-3665	156	3	0	CARDINAL
iajs-3665	156	4	25	CARDINAL
iajs-3665	157	1	𝜎(−𝜎 + 1	DATE
iajs-3665	157	2	2 + 2𝜎	QUANTITY
iajs-3665	158	1	11	CARDINAL
iajs-3665	159	1	19	CARDINAL
iajs-3665	159	2	23	CARDINAL
iajs-3665	159	3	0.997	CARDINAL
iajs-3665	160	1	2-(b	CARDINAL
iajs-3665	161	1	3	CARDINAL
iajs-3665	162	1	12	CARDINAL
iajs-3665	162	2	𝑥(𝜎),𝑢(𝜎),𝑇	CARDINAL
iajs-3665	162	3	𝑥(𝜎	PERSON
iajs-3665	162	4	𝑥(𝜎),𝑢(𝜎),𝑇	CARDINAL
iajs-3665	162	5	2	CARDINAL
iajs-3665	162	6	26	CARDINAL
iajs-3665	162	7	27	CARDINAL
iajs-3665	162	8	bcs 𝑥(0	ORG
iajs-3665	162	9	0	CARDINAL
iajs-3665	162	10	1 .	CARDINAL
iajs-3665	163	1	28	CARDINAL
iajs-3665	163	2	𝑥(𝜏	DATE
iajs-3665	163	3	19	CARDINAL
iajs-3665	163	4	28	CARDINAL
iajs-3665	164	1	2-(c	CARDINAL
iajs-3665	164	2	19	CARDINAL
iajs-3665	164	3	26	CARDINAL
iajs-3665	165	1	2	CARDINAL
iajs-3665	166	1	1	CARDINAL
iajs-3665	166	2	2	CARDINAL
iajs-3665	166	3	3	CARDINAL
iajs-3665	167	1	2025	CARDINAL
iajs-3665	167	2	346 5	DATE
iajs-3665	167	3	a)1	PRODUCT
iajs-3665	167	4	2	CARDINAL
iajs-3665	167	5	3	CARDINAL
iajs-3665	167	6	2	CARDINAL
iajs-3665	171	1	6	CARDINAL
iajs-3665	171	2	two	CARDINAL
iajs-3665	172	1	the fractionalorder systems	ORG
iajs-3665	174	1	three	CARDINAL
iajs-3665	174	2	two	CARDINAL
iajs-3665	175	1	al-haitham	ORG
iajs-3665	178	1	1	CARDINAL
iajs-3665	179	1	dover	GPE
iajs-3665	179	2	2012	DATE
iajs-3665	180	1	2	CARDINAL
iajs-3665	180	2	ezz-eldien ss	ORG
iajs-3665	180	3	doha	GPE
iajs-3665	180	4	abdelkawy ma	PERSON
iajs-3665	182	1	2017;90(1):123044	ORG
iajs-3665	183	1	3	CARDINAL
iajs-3665	183	2	agrawal op	PERSON
iajs-3665	185	1	j vib	PERSON
iajs-3665	186	1	2008;14(9-10):1291	CARDINAL
iajs-3665	187	1	4	CARDINAL
iajs-3665	187	2	sweilam nh	ORG
iajs-3665	187	3	al-ajami	ORG
iajs-3665	187	4	hoppe rh	PERSON
iajs-3665	188	1	sci world j. 2013;2013:306237	ORG
iajs-3665	189	1	5	CARDINAL
iajs-3665	189	2	bhrawy	PERSON
iajs-3665	189	3	doha e	GPE
iajs-3665	190	1	ezz-eldien s	ORG
iajs-3665	190	2	abdelkawy m.	PERSON
iajs-3665	192	1	2015;15(23):1-15	CARDINAL
iajs-3665	193	1	6	CARDINAL
iajs-3665	194	1	akbarian	ORG
iajs-3665	194	2	keyanpour m.	PERSON
iajs-3665	196	1	2013;8(2):582-97	CARDINAL
iajs-3665	197	1	7	CARDINAL
iajs-3665	197	2	bhrawy	PERSON
iajs-3665	197	3	doha e	GPE
iajs-3665	197	4	machado jt	PERSON
iajs-3665	197	5	ezz-eldien s.	ORG
iajs-3665	198	1	asian	NORP
iajs-3665	199	1	2015;17(6):2389	CARDINAL
iajs-3665	203	1	2025	CARDINAL
iajs-3665	203	2	347 8	DATE
iajs-3665	204	1	el-sayed	NORP
iajs-3665	205	1	second	ORDINAL
iajs-3665	207	1	2015;73:141-7	DATE
iajs-3665	207	2	almeida r	PERSON
iajs-3665	210	1	2015;80(4):1811-6	CARDINAL
iajs-3665	211	1	10	CARDINAL
iajs-3665	212	1	ahmad wm	PERSON
iajs-3665	212	2	el-khazali r. fractional-order	ORG
iajs-3665	214	1	2007;33(4):1367-75	CARDINAL
iajs-3665	216	1	david sa	PERSON
iajs-3665	218	1	ensino fis	PERSON
iajs-3665	219	1	2011;33(4):4302	CARDINAL
iajs-3665	220	1	12	CARDINAL
iajs-3665	223	1	2023;15(3):624	CARDINAL
iajs-3665	224	1	13	CARDINAL
iajs-3665	224	2	podlubny i. fractional differential	ORG
iajs-3665	225	1	1999	DATE
iajs-3665	226	1	14	CARDINAL
iajs-3665	227	1	srivastava hm	PERSON
iajs-3665	227	2	trujillo jj	PERSON
iajs-3665	228	1	2006	DATE
iajs-3665	229	1	15	CARDINAL
iajs-3665	230	1	diethelm k.	PERSON
iajs-3665	232	1	2010	DATE
iajs-3665	233	1	http://doi.org/10.1007/978-3-642-14574-2 16	ORG
iajs-3665	234	1	mainardi f. fractional calculus	ORG
iajs-3665	235	1	imperial college press	ORG
iajs-3665	235	2	2010	DATE
iajs-3665	236	1	17	DATE
iajs-3665	237	1	machado jt	PERSON
iajs-3665	237	2	kiryakova	PERSON
iajs-3665	237	3	mainardi f.	PERSON
iajs-3665	238	1	sci numer	ORG
iajs-3665	239	1	2011;16(3):1140	CARDINAL
iajs-3665	239	2	18	CARDINAL
iajs-3665	241	1	2010	DATE
iajs-3665	242	1	19	CARDINAL
iajs-3665	242	2	agrawal op	PERSON
iajs-3665	242	3	machado jt	PERSON
iajs-3665	243	1	2007	DATE
iajs-3665	244	1	http://doi.org/10.1007/978-1-4020-6042-7 20	ORG
iajs-3665	246	1	diethelm k	PERSON
iajs-3665	246	2	scalas e	GPE
iajs-3665	246	3	trujillo jj	PERSON
iajs-3665	247	1	2012	DATE
iajs-3665	252	1	http://doi.org/10.1007/978-3-642-14574-2	GPE