Solutions of two fractional q-integro-differential equations under sum and integral boundary value conditions on a time scale

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 7 Some numerical results of \(\mathcal{I}_{q}^{\alpha } [m_{1}] (t)\), \(\mathcal{I}_{q}^{\alpha -1} [m_{1}] (1)\), \(\mathcal{I}_{q}^{\alpha -2} [m_{1}] (b)\), and \(\mathcal{I}_{q}^{\alpha -\zeta } [m_{1}] (t)\) in Example 2 for \(t \in \overline{J}\) and \(q=\frac{1}{8}, \frac{1}{2}, \frac{6}{7}\)

n	\(\sup \mathcal{I}_{q}^{\alpha } [m_{1}] (t)\)	\(\sup \mathcal{I}_{q}^{\alpha -1} [m_{1}] (1)\)	\(\sup \mathcal{I}_{q}^{\alpha -2} [m_{1}] (b)\)	\(\sup \mathcal{I}_{q}^{\alpha -\zeta } [m_{1}] (t)\)
\(q = \frac{1}{8} \)
1	0.0104	0.0116	0.0116	0.0106
2	0.0106	0.0118	0.0115	0.0108
3	0.0106	0.0118	0.0115	0.0108
4	0.0106	0.0118	0.0115	0.0108
\(q = \frac{1}{2} \)
1	0.0058	0.0095	0.0119	0.0062
2	0.0073	0.011	0.0113	0.0077
3	0.0081	0.0118	0.011	0.0086
4	0.0085	0.0121	0.0109	0.009
5	0.0087	0.0123	0.0108	0.0092
6	0.0088	0.0124	0.0108	0.0093
7	0.0089	0.0125	0.0108	0.0094
8	0.0089	0.0125	0.0107	0.0094
9	0.0089	0.0125	0.0107	0.0094
10	0.0089	0.0125	0.0107	0.0095
11	0.0089	0.0125	0.0107	0.0095
\(q = \frac{6}{7} \)
1	0.0009	0.0041	0.0147	0.001
2	0.0014	0.0055	0.0134	0.0017
3	0.002	0.0066	0.0126	0.0024
⋮	⋮	⋮	⋮	⋮
22	0.0074	0.0126	0.0105	0.0081
23	0.0075	0.0126	0.0104	0.0082
24	0.0075	0.0127	0.0104	0.0082
25	0.0076	0.0127	0.0104	0.0083
26	0.0076	0.0127	0.0104	0.0083
27	0.0077	0.0128	0.0104	0.0084
28	0.0077	0.0128	0.0104	0.0084
29	0.0077	0.0128	0.0104	0.0084
30	0.0077	0.0128	0.0104	0.0084
31	0.0077	0.0128	0.0104	0.0085
32	0.0078	0.0129	0.0104	0.0085