Explicit iteration and unbounded solutions for fractional q–difference equations with boundary conditions on an infinite interval

Journal of Inequalities and Applications

Table 4 Numerical results of Λ, ∇ and μ for \(\mathrm{q} = \frac{1}{7}\) in Example 4.2

n	\(\Gamma _{\mathrm{q}}(\varsigma )\)	\(\Gamma _{\mathrm{q}}(\nu )\)	\(\Gamma _{\mathrm{q}}(\varsigma -\nu )\)	Λ	∇	\(\mu > \nabla \mathfrak{p}( \mu ) \int _{0}^{\infty } \uppsi (\xi ) \,\mathrm{d}_{\mathrm{q}} \xi \)
	\(\mathrm{q} = \frac{1}{2}\) and calculated μ = 0.1
1	2.6975	2.1251	−2.7521	3.8027	0.2630	0.1>0.0047
2	2.4776	2.0057	−3.5667	2.9254	0.3418	0.1>0.0061
3	2.3791	1.9515	−3.9922	2.5995	0.3847	0.1>0.0069
4	2.3324	1.9256	−4.2092	2.4564	0.4071	0.1>0.0073
5	2.3096	1.9130	−4.3188	2.3891	0.4186	0.1>0.0075
6	2.2984	1.9067	−4.3739	2.3565	0.4244	0.1>0.0076
7	2.2928	1.9036	−4.4015	2.3404	0.4273	0.1>0.0077
8	2.2900	1.9020	−4.4153	2.3324	0.4287	0.1>0.0077
9	2.2886	1.9013	−4.4222	2.3284	0.4295	0.1>0.0077
10	2.2879	1.9009	−4.4257	2.3264	0.4298	0.1>0.0077
11	2.2876	1.9007	−4.4274	2.3254	0.4300	0.1>0.0077
12	2.2874	1.9006	−4.4283	2.3249	0.4301	0.1>0.0077
13	2.2873	1.9005	−4.4287	2.3247	0.4302	0.1>0.0077
14	2.2873	1.9005	−4.4289	2.3246	0.4302	0.1>0.0077