Research Article
Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
Table 3
Numerical values when
= 0.750, 0.875, and 1.000 for (
63).
| | | | | | FVIM | 2D-FLFs | FVIM | 2D-FLFs | FVIM | Exact |
| 0.25 | 0.25 | 0.26622298 | 0.26622021 | 0.26593959 | 0.26594005 | 0.26578827 | 0.26578827 | 0.50 | 0.56489190 | 0.56488083 | 0.56375836 | 0.56376020 | 0.56315308 | 0.56315308 | 0.75 | 0.89600678 | 0.89598187 | 0.89345630 | 0.89346046 | 0.89209443 | 0.89209443 | 1.00 | 1.25956762 | 1.25952332 | 1.25503343 | 1.25504082 | 1.25261232 | 1.25261232 |
| 0.50 | 0.25 | 0.28474208 | 0.28474415 | 0.28340402 | 0.28340659 | 0.28256846 | 0.28256846 | 0.50 | 0.63896831 | 0.63897662 | 0.63361610 | 0.63362636 | 0.63027383 | 0.63027383 | 0.75 | 1.06267869 | 1.06269739 | 1.05063622 | 1.05065931 | 1.04311611 | 1.04311611 | 1.00 | 1.55587323 | 1.55590647 | 1.53446439 | 1.53450544 | 1.52109530 | 1.52109531 |
| 0.75 | 0.25 | 0.30690489 | 0.30690747 | 0.30361709 | 0.30361656 | 0.30139478 | 0.30139480 | 0.50 | 0.72761955 | 0.72762986 | 0.71446834 | 0.71446625 | 0.70557913 | 0.70557918 | 0.75 | 1.26214400 | 1.26216719 | 1.23255378 | 1.23254905 | 1.21255304 | 1.21255316 | 1.00 | 1.91047821 | 1.91051944 | 1.85787338 | 1.85786498 | 1.82231652 | 1.82231673 |
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