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

Table 5

Approximate solutions obtained by the proposed algorithm for different cases of the system of FDEs given in Example 4.

	Case I		Case II		Case III		Case IV
	0.0	0	0	0	0	0	0	0	0
0.5	0.420 448	0.566 502	0.353 553	0.664 67	0.314 98	0.752 288	0.267 943	0.913 678
1.0	1	1.133 003	1	1.329 34	1	1.504 575	1	1.827 355
1.5	1.660 023	1.699 505	1.837 117	1.994 011	1.965 556	2.256 863	2.160 595	2.741 033
2.0	2.378 414	2.266 006	2.828 427	2.658 681	3.174 802	3.009 151	3.732 132	3.654 71
2.5	3.143 584	2.832 508	3.952 847	3.323 351	4.605 039	3.761 439	5.702 772	4.568 388
3.0	3.948 222	3.399 009	5.196 152	3.988 021	6.240 251	4.513 726	8.063 626	5.482 065
3.5	4.787 238	3.965 511	6.547 9	4.652 691	8.068 264	5.266 014	10.807 6	6.395 743
4.0	5.656 854	4.532 012	8	5.317 362	10.079 37	6.018 302	13.928 81	7.309 42
4.5	6.554 139	5.098 514	9.545 942	5.982 032	12.265 56	6.770 59	17.422 23	8.223 098
5.0	7.476 744	5.665 015	11.180 34	6.646 702	14.620 09	7.522 877	21.283 5	9.136 775
5.5	8.422 739	6.231 517	12.898 64	7.311 372	17.137 12	8.275 165	25.508 75	10.050 45
6.0	9.390 507	6.798 019	14.696 94	7.976 042	19.811 56	9.027 453	30.094 52	10.964 13