Existence, uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Numerical results of \(\vartheta _{j}\) for \(j=1,2, 3,4\) and ϑ, in Example 1

n	τ	\(\vartheta _{j}\)				ϑ
n	τ	\(\vartheta _{1}\)	\(\vartheta _{2}\)	\(\vartheta _{3}\)	\(\vartheta _{4}\)	ϑ
1	1.00	0.0000	0.0220	0.2236	0.0000	−0.0049
2	1.05	0.0658	0.0220	0.2236	0.0876	0.0008
3	1.10	0.1268	0.0220	0.2236	0.1699	0.0166
4	1.15	0.1845	0.0220	0.2236	0.2483	0.0409
5	1.20	0.2394	0.0220	0.2236	0.3230	0.0724
6	1.25	0.2918	0.0220	0.2236	0.3945	0.1102
7	1.30	0.3420	0.0220	0.2236	0.4631	0.1535
8	1.35	0.3902	0.0220	0.2236	0.5290	0.2015
9	1.40	0.4364	0.0220	0.2236	0.5925	0.2537
10	1.45	0.4810	0.0220	0.2236	0.6536	0.3095
11	1.50	0.5240	0.0220	0.2236	0.7126	0.3685
12	1.55	0.5655	0.0220	0.2236	0.7696	0.4303
13	1.60	0.6056	0.0220	0.2236	0.8248	0.4946
14	1.65	0.6444	0.0220	0.2236	0.8783	0.5610
15	1.70	0.6820	0.0220	0.2236	0.9301	0.6294
16	1.75	0.7185	0.0220	0.2236	0.9804	0.6995
17	1.80	0.7540	0.0220	0.2236	1.0292	0.7711
18	1.85	0.7884	0.0220	0.2236	1.0767	0.8439
19	1.90	0.8219	0.0220	0.2236	1.1229	0.9179
20	1.95	0.8544	0.0220	0.2236	1.1679	0.9930
21	2.00	0.8862	0.0220	0.2236	1.2117	1.0689