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 10 Some numerical results for calculation of \(M_{0}\), \(M(1)\), \(M(b)\), \(M(t)\), and \(\Delta < 1\) in Example 2 for \(q=\frac{1}{8}, \frac{1}{2}, \frac{6}{7}\)

n	\(M_{0}\)	M(1)	M(b)	M(t)	Δ
\(q =\frac{1}{8}\)
1	0.0343	0.0391	0.0357	0.0349	0.5855
2	0.0343	0.0391	0.0357	0.0349	0.5859
3	0.0343	0.0391	0.0357	0.0349	0.5859
4	0.0343	0.0391	0.0357	0.0349	0.5859
\(q =\frac{1}{2}\)
1	0.0167	0.0299	0.0373	0.018	0.5275
2	0.0179	0.0311	0.0368	0.0193	0.5426
3	0.0183	0.0314	0.0368	0.0197	0.5504
4	0.0184	0.0315	0.0367	0.0198	0.5542
5	0.0184	0.0315	0.0367	0.0198	0.5561
6	0.0184	0.0315	0.0367	0.0198	0.5571
7	0.0184	0.0315	0.0367	0.0198	0.5576
8	0.0184	0.0315	0.0367	0.0198	0.5578
9	0.0184	0.0315	0.0367	0.0198	0.5579
10	0.0184	0.0315	0.0367	0.0198	0.5580
11	0.0184	0.0315	0.0367	0.0198	0.5580
12	0.0184	0.0315	0.0367	0.0198	0.5580
\(q =\frac{6}{7}\)
1	0.0029	0.0144	0.0434	0.0036	0.4067
2	0.0045	0.018	0.0407	0.0054	0.4166
3	0.0058	0.0206	0.0394	0.0069	0.4317
⋮	⋮	⋮	⋮	⋮	⋮
13	0.0107	0.0267	0.0375	0.0122	0.5218
14	0.0108	0.0268	0.0374	0.0122	0.5253
15	0.0108	0.0268	0.0374	0.0123	0.5283
16	0.0109	0.0269	0.0374	0.0123	0.5308
17	0.0109	0.0269	0.0374	0.0124	0.533
18	0.0109	0.0269	0.0374	0.0124	0.5348
19	0.0109	0.0269	0.0374	0.0124	0.5364
20	0.011	0.0269	0.0374	0.0124	0.5378
21	0.011	0.0269	0.0374	0.0124	0.5389
22	0.011	0.027	0.0374	0.0125	0.5399
23	0.011	0.027	0.0374	0.0125	0.5408
24	0.011	0.027	0.0374	0.0125	0.5415
⋮	⋮	⋮	⋮	⋮	⋮
53	0.011	0.027	0.0374	0.0125	0.5457
54	0.011	0.027	0.0374	0.0125	0.5458
55	0.011	0.027	0.0374	0.0125	0.5458