On the generalized fractional snap boundary problems via G-Caputo operators: existence and stability analysis

Samei, Mohammad Esmael; Matar, Mohammed M.; Etemad, Sina; Rezapour, Shahram

doi:10.1186/s13662-021-03654-9

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Numerical values of \(\mathcal{O}_{j}\) and \(\Lambda _{j}\), \(j=2,3,4\), for \(\mathfrak{t} \in [1.1, 2.6]\) in Example 6.1 when \(\mathbb{G}_{2}=\mathfrak{t}\), \(\mathbb{G}_{3} = \ln \mathfrak{t}\), and \(\mathbb{G}_{4} = \sqrt{\mathfrak{t}}\)

From: On the generalized fractional snap boundary problems via G-Caputo operators: existence and stability analysis

t	\(\mathcal{O}_{1}\)	\(L\mathcal{O}_{1}<1\)	\(\mathcal{O}_{1}\)	\(\ell _{1} \geq \)
\(\mathbb{G}_{2}(\mathfrak{t}) = \mathfrak{t}\)
1.10	0.0000	0.0000	11.7700	11.7700
1.20	0.3282	0.0109	15.0025	15.2709
1.30	0.5418	0.0181	16.9019	17.3831
1.40	0.7766	0.0259	18.6975	19.4404
1.50	1.0389	0.0346	20.4797	21.5464
1.60	1.3307	0.0444	22.2789	23.7427
1.70	1.6525	0.0551	24.1088	26.0539
1.80	2.0046	0.0668	25.9761	28.4991
1.90	2.3869	0.0796	27.8846	31.0952
2.00	2.7993	0.0933	29.8361	33.8594
2.10	3.2416	0.1081	31.8319	36.8096
2.20	3.7137	0.1238	33.8722	39.9656
2.30	4.2154	0.1405	35.9573	43.3493
2.40	4.7465	0.1582	38.0871	46.9858
2.50	5.3068	0.1769	40.2614	50.9037
\(\mathbb{G}_{3}(\mathfrak{t}) = \ln \mathfrak{t}\)
1.10	0.0000	0.0000	11.7700	11.7700
1.20	0.3010	0.0100	14.7349	14.9780
1.30	0.4698	0.0157	16.2959	16.7025
1.40	0.6354	0.0212	17.6460	18.2281
1.50	0.8019	0.0267	18.8784	19.6511
1.60	0.9698	0.0323	20.0278	21.0062
1.70	1.1385	0.0380	21.1123	22.3103
1.80	1.3077	0.0436	22.1426	23.5737
1.90	1.4767	0.0492	23.1263	24.8029
2.00	1.6452	0.0548	24.0688	26.0026
2.10	1.8129	0.0604	24.9745	27.1763
2.20	1.9795	0.0660	25.8469	28.3269
2.30	2.1448	0.0715	26.6887	29.4566
2.40	2.3086	0.0770	27.5025	30.5673
2.50	2.4709	0.0824	28.2904	31.6606
\(\mathbb{G}_{4}(\mathfrak{t}) = \sqrt{\mathfrak{t}}\)
1.10	0.0000	0.0000	11.7700	11.7700
1.20	0.2130	0.0071	13.8243	13.9894
1.30	0.3101	0.0103	14.8256	15.0771
1.40	0.4003	0.0133	15.6800	16.0172
1.50	0.4890	0.0163	16.4605	16.8867
1.60	0.5779	0.0193	17.1943	17.7139
1.70	0.6678	0.0223	17.8948	18.5129
1.80	0.7589	0.0253	18.5698	19.2920
1.90	0.8512	0.0284	19.2245	20.0562
2.00	0.9449	0.0315	19.8622	20.8092
2.10	1.0398	0.0347	20.4856	21.5535
2.20	1.1360	0.0379	21.0964	22.2910
2.30	1.2333	0.0411	21.6961	23.0232
2.40	1.3318	0.0444	22.2859	23.7513
2.50	1.4314	0.0477	22.8668	24.4764

Back to article page