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

Journal of Inequalities and Applications

Table 3 Numerical results of \(M_{1}\), \(M_{2}\), and \(p= M_{1}+ \frac{M_{2}}{(1-\zeta )\Gamma _{q}(1- \zeta )} \) for \(q = \frac{1}{5}\), \(\frac{1}{2}\), \(\frac{7}{8}\) in Example 4.2

n	\(q = \frac{ 1}{ 5}\)			\(q = \frac{ 1}{ 2}\)			\(q = \frac{7}{8}\)
n	\(M_{1}\)	\(M_{2}\)	p	\(M_{1}\)	\(M_{2}\)	p	\(M_{1}\)	\(M_{2}\)	p
1	0.5809	0.5452	1.5070	0.4399	0.4099	1.1219	0.1773	0.1759	0.6224
2	0.5892	0.5453	1.5075	0.4773	0.4219	1.1421	0.2244	0.2199	0.7104
3	0.5909	0.5453	1.5075	0.4943	0.4237	1.1455	0.2607	0.2518	0.7677
4	0.5912	0.5453	1.5075	0.5026	0.4240	1.1465	0.2894	0.2750	0.8067
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
9	0.5913	0.5453	1.5075	0.5107	0.4240	1.1473	0.3722	0.3243	0.8834
10	0.5913	0.5453	1.5075	0.5108	0.4240	1.1473	0.3817	0.3276	0.8884
11	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.3899	0.3299	0.8921
12	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.3969	0.3316	0.8949
13	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4029	0.3327	0.8970
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
40	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4435	0.3353	0.9071
41	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4437	0.3353	0.9072
42	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4438	0.3353	0.9072
43	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4439	0.3353	0.9072
44	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4440	0.3353	0.9072
45	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4441	0.3353	0.9073
46	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4442	0.3353	0.9073
47	0.5913	0.5453	1.5075	0.5109	0.4240	1.1474	0.4442	0.3353	0.9073