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

Journal of Inequalities and Applications

Table 5 Numerical results of Λ, ∇ and μ for \(\mathrm{q} = \frac{8}{9}\) in Example 4.2

n	\(\Gamma _{\mathrm{q}}(\varsigma )\)	\(\Gamma _{\mathrm{q}}(\nu )\)	\(\Gamma _{\mathrm{q}}(\varsigma -\nu )\)	Λ	∇	\(\mu > \nabla \mathfrak{p}( \mu ) \int _{0}^{\infty } \uppsi (\xi ) \,\mathrm{d}_{\mathrm{q}} \xi \)
	\(\mathrm{q} = \frac{8}{9}\) and calculated μ = 0.1
1	55.9818	21.9886	−3.1623	95.6034	0.0105	0.1>0.0000
2	41.2031	18.2245	−5.4122	57.5855	0.0174	0.1>0.0000
3	32.8940	15.9102	−7.6526	41.6420	0.0240	0.1>0.0000
4	27.6527	14.3446	−9.8069	32.9949	0.0303	0.1>0.0000
5	24.0881	13.2182	−11.8371	27.6229	0.0362	0.1>0.0000
6	21.5322	12.3725	−13.7253	23.9933	0.0417	0.1>0.0001
7	19.6267	11.7174	−15.4655	21.3974	0.0467	0.1>0.0001
8	18.1631	11.1978	−17.0587	19.4632	0.0514	0.1>0.0001
⋮	⋮	⋮	⋮	⋮	⋮	⋮
79	11.0024	8.3731	−31.1770	10.6630	0.0938	0.1>0.0001
80	11.0023	8.3731	−31.1774	10.6629	0.0938	0.1>0.0001
81	11.0022	8.3730	−31.1777	10.6627	0.0938	0.1>0.0001
82	11.0021	8.3730	−31.1780	10.6626	0.0938	0.1>0.0001
83	11.0020	8.3729	−31.1783	10.6625	0.0938	0.1>0.0001
84	11.0019	8.3729	−31.1786	10.6624	0.0938	0.1>0.0001
85	11.0019	8.3729	−31.1788	10.6624	0.0938	0.1>0.0001
86	11.0018	8.3729	−31.1790	10.6623	0.0938	0.1>0.0001
87	11.0017	8.3728	−31.1792	10.6622	0.0938	0.1>0.0001
88	11.0017	8.3728	−31.1793	10.6622	0.0938	0.1>0.0001
89	11.0016	8.3728	−31.1794	10.6621	0.0938	0.1>0.0001
90	11.0016	8.3728	−31.1796	10.6621	0.0938	0.1>0.0001