On the existence of solutions for a multi-singular pointwise defined fractional q-integro-differential equation

Boundary Value Problems

Table 5 Some numerical results of \(m_{0}\) in equation (27) in Example 1 for \(q=\frac{1}{7}, \frac{1}{2}, \frac{8}{9}\)

n	\(q =\frac{1}{7}\)			\(q =\frac{1}{2}\)			\(q =\frac{8}{9}\)
n	\(\varGamma _{q}(\beta _{2} +1)\)	\(\varGamma _{q}( 2 -\beta _{1})\)	\(m_{0}\)	\(\varGamma _{q}(\beta _{2} +1)\)	\(\varGamma _{q}( 2 -\beta _{1})\)	\(m_{0}\)	\(\varGamma _{q}(\beta _{2} +1)\)	\(\varGamma _{q}( 2 -\beta _{1})\)	\(m_{0}\)
1	0.9661	0.9656	0.9656	0.9965	0.9772	0.9772	1.6936	1.389	1.389
2	0.9644	0.9642	0.9642	0.9565	0.9493	0.9493	1.4923	1.2733	1.2733
3	0.9641	0.964	0.964	0.9382	0.9364	0.9364	1.3628	1.1967	1.1967
4	0.9641	0.964	0.964	0.9294	0.9302	0.9294	1.2721	1.1419	1.1419
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
10	0.9641	0.964	0.964	0.921	0.9243	0.921	1.031	0.9905	0.9905
11	0.9641	0.964	0.964	0.9209	0.9242	0.9209	1.0124	0.9783	0.9783
12	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.9967	0.9681	0.9681
13	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.9833	0.9593	0.9593
14	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.9719	0.9517	0.9517
15	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.962	0.9452	0.9452
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
67	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.8928	0.8988	0.8928
68	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.8928	0.8988	0.8928
69	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.8928	0.8988	0.8928
70	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.8927	0.8988	0.8927
71	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.8927	0.8988	0.8927
72	0.9641	0.964	0.964	0.9209	0.9242	0.9209	0.8927	0.8988	0.8927