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

Boundary Value Problems

Table 10 Some numerical results of \(M(\alpha , b)\) in equation (33) in Example 3 for \(q=\frac{1}{7}, \frac{1}{2}, \frac{8}{9}\). Note that \((a) = m_{0}\), \((b) = 0.02 \times M(\alpha , b)\), and \((c) =2.02 \times M(\alpha , b)\)

n	\(q =\frac{1}{7}\)			\(q =\frac{1}{2}\)			\(q =\frac{8}{9}\)
n	(a)	(b)	(c)	(a)	(b)	(c)	(a)	(b)	(c)
1	0.9738	0.281	28.3846	1.0314	0.2123	21.4385	2.1001	0.1181	11.9271
2	0.9717	0.2818	28.463	0.9796	0.2319	23.4183	1.7825	0.134	13.5364
3	0.9714	0.2819	28.4743	0.9561	0.2419	24.4275	1.5838	0.1468	14.823
4	0.9714	0.2819	28.4759	0.9448	0.2469	24.9369	1.4475	0.1572	15.8798
5	0.9714	0.2819	28.4761	0.9393	0.2494	25.1928	1.3484	0.166	16.764
6	0.9714	0.2819	28.4761	0.9365	0.2507	25.3211	1.2733	0.1734	17.5126
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
19	0.9714	0.2819	28.4761	0.9338	0.252	25.4494	0.9646	0.2141	21.6253
20	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.958	0.2152	21.739
21	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9522	0.2162	21.8398
22	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.947	0.2171	21.9289
23	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9426	0.2179	22.0079
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
103	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9086	0.2306	23.2886
104	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9086	0.2306	23.2886
105	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9086	0.2306	23.2886
106	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9086	0.2306	23.2886
107	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9086	0.2306	23.2888
108	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9086	0.2306	23.2888
109	0.9714	0.2819	28.4761	0.9338	0.252	25.4496	0.9085	0.2306	23.2888