Application of Intelligent Paradigm through Neural Networks for Numerical Solution of Multiorder Fractional Differential Equations

Table 1

Approximate solutions obtained by the proposed algorithm for different cases of multiorder fractional differential equations.

x	Example 1				Example 2	Example 3
	Case I	Case II	Case III	Case IV
0	0	0	0	0	0	2
0.5	0.342 638	0.314 465	0.289 938	0.268 587	0.041 666 67	1.875
1	2	2	2	2	0.333 333 33	1.5
1.5	5.815 061	6.021 178	6.244 705	6.487 114	1.125	0.875
2	12.594 79	13.278 03	14.062 87	14.964 4	2.666 666 67	0
2.5	23.132 03	24.641 87	26.455 39	28.633 64	5.208 333 33	−1.125
3	38.211 58	40.966 61	44.398 64	48.674 02	9	−2.5
3.5	58.613 01	63.094 17	68.851 28	76.247 64	14.291 666 7	−4.125
4	85.112 13	91.857 62	100.758 3	112.502 9	21.333 333 3	−6
4.5	118.481 9	128.083 1	141.054	158.577	30.375	−8.125
5	159.493 2	172.591 3	190.6632	215.5975	41.666 666 7	−10.5
5.5	208.915	226.198 3	250.5035	284.6834	55.458 333 3	−13.125
6	267.514 9	289.716 2	321.4856	366.9467	72	−16