The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach

Journal of Inequalities and Applications

Table 6 Numerical results of \(\int _{0}^{1} (1- q \xi )^{ (\sigma -3)} \mu ( \xi ) \varrho _{q}( \xi ) \,\mathrm{d}_{q}\xi \) for \(\sigma =\frac{18}{7}\) in Assumption (A2) and for \(q = \frac{1}{5}\), \(\frac{1}{2}\), \(\frac{7}{8}\) in Example 4.3

n	\(0<\int _{0}^{1} (1- q \xi )^{ (\sigma -3)} \mu ( \xi ) \varrho _{q}(\xi ) \,\mathrm{d}_{q}\xi < 1\)
n	\(q = \frac{ 1}{ 5}\)	\(q = \frac{ 1}{ 2}\)	\(q = \frac{7}{8}\)
1	0.28515	0.31485	0.00482
2	0.34871	0.47839	0.01824
3	0.36161	0.57866	0.04195
4	0.36420	0.63251	0.07572
5	0.36472	0.66022	0.11804
6	0.36482	0.67425	0.16674
7	0.36484	0.68130	0.21946
8	0.36485	0.68484	0.25289
9	0.36485	0.68661	0.28682
10	0.36485	0.68750	0.31984
11	0.36485	0.68794	0.35125
⋮	⋮	⋮	⋮
15	0.36485	0.68836	0.45528
16	0.36485	0.68837	0.47565
17	0.36485	0.68838	0.49394
18	0.36485	0.68838	0.51030
19	0.36485	0.68838	0.52486
⋮	⋮	⋮	⋮
77	0.36485	0.68838	0.63313
78	0.36485	0.68838	0.63314
79	0.36485	0.68838	0.63314
80	0.36485	0.68838	0.63315
81	0.36485	0.68838	0.63315
82	0.36485	0.68838	0.63315
83	0.36485	0.68838	0.63316
84	0.36485	0.68838	0.63316
85	0.36485	0.68838	0.63316