Existence and uniqueness of solutions for multi-term fractional q-integro-differential equations via quantum calculus

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 Some numerical results for calculation of \(\varGamma_{q}(\alpha )\), \(\varGamma_{q}(\alpha-1)\), A, M and K in Theorem 5 with \(q=\frac{1}{3}\) and \(m=40\)

n	\(\varGamma_{q}(\alpha)\)	\(\varGamma_{q}(\alpha-1)\)	\(A_{0}\)	\(\ell ^{*}\)	\(K_{0}\)
1	1.054210	1.106942	6.752182	0.065737	0.174695
2	0.996499	1.137694	6.991433	0.102154	0.271472
3	0.970276	1.152228	7.125250	0.118079	0.313793
4	0.957751	1.159303	7.195379	0.123517	0.328243
5	0.951628	1.162796	7.231213	0.125129	0.332527
6	0.948600	1.164531	7.249318	0.125570	0.33370
7	0.947094	1.165395	7.258417	0.125686	0.334007
8	0.946343	1.165827	7.262978	0.125715	0.334086
9	0.945968	1.166043	7.265261	0.125723	0.334105
10	0.945781	1.166150	7.266403	0.125725	0.334111
11	0.945687	1.166204	7.266975	0.125725	0.334112
12	0.945641	1.166231	7.267261	0.125725	0.334112
13	0.945617	1.166245	7.267403	0.125725	0.334112
14	0.945606	1.166251	7.267475	0.125725	0.334112
15	0.945600	1.166255	7.267511	0.125725	0.334112
16	0.945597	1.166256	7.267528	0.125725	0.334112
17	0.945595	1.166257	7.267537	0.125725	0.334112
18	0.945595	1.166258	7.267542	0.125725	0.334112
19	0.945594	1.166258	7.267544	0.125725	0.334112
20	0.945594	1.166258	7.267545	0.125725	0.334112
21	0.945594	1.166258	7.267546	0.125725	0.334112
22	0.945594	1.166258	7.267546	0.125725	0.334112
23	0.945594	1.166258	7.267546	0.125725	0.334112
24	0.945594	1.166258	7.267546	0.125725	0.334112