Research Article
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 |
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