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

n	\(\mathcal{I}_{q}^{\alpha }[m_{2}] (t)\)			\(\mathcal{I}_{q}^{\alpha +1} [m_{2}] (1)\)	\(\mathcal{I}_{q}^{\alpha -1} [m_{2}] (s)\)
n	t = 0	t = 1	sup	\(\mathcal{I}_{q}^{\alpha +1} [m_{2}] (1)\)	s = 1	s = a	s = b
\(q = \frac{1}{8}\)
1	0	0.0005	0.0005	0.0005	0.0006	0.0001	0.0004
2	0	0.0005	0.0005	0.0005	0.0006	0.0001	0.0004
3	0	0.0005	0.0005	0.0005	0.0006	0.0001	0.0004
\(q = \frac{1}{2}\)
1	0	0.0003	0.0003	0.0002	0.0005	0.0001	0.0003
2	0	0.0003	0.0003	0.0002	0.0005	0.0001	0.0003
3	0	0.0003	0.0003	0.0002	0.0005	0.0001	0.0003
\(q = \frac{6}{7}\)
1	0	0.0001	0.0001	0	0.0003	0	0.0002
2	0	0.0001	0.0001	0	0.0004	0	0.0002
3	0	0.0001	0.0001	0	0.0004	0.0001	0.0003
4	0	0.0001	0.0001	0	0.0004	0.0001	0.0003
5	0	0.0002	0.0002	0	0.0004	0.0001	0.0003
6	0	0.0002	0.0002	0.0001	0.0005	0.0001	0.0003
7	0	0.0002	0.0002	0.0001	0.0005	0.0001	0.0003
8	0	0.0002	0.0002	0.0001	0.0005	0.0001	0.0003