Uniqueness and Ulam–Hyers–Rassias stability results for sequential fractional pantograph q-differential equations

Houas, Mohamed; Martínez, Francisco; Samei, Mohammad Esmael; Kaabar, Mohammed K. A.

doi:10.1186/s13660-022-02828-7

Journal of Inequalities and Applications

Table 3 Numerical results of \(\nabla _{1}\), \(\nabla _{2}\), \(\Pi _{1}\), and \(\Pi _{2}\) for \(q = \frac{8}{9}\) in Example 5.1

From: Uniqueness and Ulam–Hyers–Rassias stability results for sequential fractional pantograph q-differential equations

n	\(q = \frac{8}{9}\)
n	\(\Gamma _{q}(\nu +1)\)	\(\Gamma _{q}(\nu -\sigma +1)\)	\(\Gamma _{q}(\nu -2\sigma +1)\)	\(\nabla _{1}\)	\(\nabla _{2}\)	\(\Pi _{1}\)	\(\Pi _{2}\)	Σ
1	21.16106	8.65603	14.61554	0.11280	0.00615	0.15435	0.11498	0.12166
2	17.64177	8.77836	19.44710	0.13530	0.00606	0.14941	0.08641	0.09307
3	15.46858	8.86537	23.57141	0.15431	0.00600	0.14652	0.07129	0.07794
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
34	8.40872	9.26182	52.74519	0.28387	0.00575	0.13693	0.03186	0.03860
35	8.39834	9.26262	52.82649	0.28422	0.00574	0.13692	0.03181	0.03855
36	8.38914	9.26333	52.89874	0.28453	0.00574	0.13690	0.03177	0.03851
37	8.38098	9.26396	52.96295	0.28481	0.00574	0.13689	0.03173	0.03847
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
56	8.32322	9.26844	53.42139	0.28679	0.00574	0.13681	0.03146	0.03820
57	8.32246	9.26850	53.42747	0.28681	0.00574	0.13680	0.03145	0.03820
58	8.32178	9.26855	53.43288	0.28684	0.00574	0.13680	0.03145	0.03820
59	8.32118	9.26860	53.43768	0.28686	0.00574	0.13680	0.03145	0.03819
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
65	8.31875	9.26879	53.45715	0.28694	0.00574	0.13680	0.03144	0.03818
66	8.31848	9.26881	53.45925	0.28695	0.00574	0.13680	0.03143	0.03818
67	8.31825	9.26882	53.46112	0.28696	0.00574	0.13680	0.03143	0.03818
68	8.31804	9.26884	53.46279	0.28697	0.00574	0.13680	0.03143	0.03818
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
73	8.31730	9.26890	53.46871	0.28699	0.00574	0.13680	0.03143	0.03818
74	8.31720	9.26891	53.46953	0.28700	0.00574	0.13680	0.03143
75	8.31711	9.26891	53.47026	0.28700	0.00574	0.13680	0.03143	0.03817
76	8.31703	9.26892	53.47091	0.28700	0.00574	0.13680	0.03143	0.03817
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
83	8.31666	9.26895	53.47382	0.28701	0.00574	0.13680	0.03143	0.03817
84	8.31663	9.26895	53.47408	0.28702	0.00574	0.13680	0.03143	0.03817
85	8.31661	9.26895	53.47430	0.28702	0.00574	0.13679	0.03143	0.03817
86	8.31658	9.26895	53.47450	0.28702	0.00574	0.13679	0.03143	0.03817

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