Research Article

Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

Table 2

Numerical values when = 0.50, 0.75, and 1.0 for (61).

FVIM2D-FLFsFVIM2D-FLFsFVIM2D-FLFsExact

0.250.250.12422501 0.12225461 0.09230374 0.09224583 0.06250058 0.062500 0.062500
0.500.24845002 0.24450922 0.18460748 0.18449165 0.12500117 0.125000 0.125000
0.750.37267504 0.36676383 0.27691122 0.27673748 0.18750175 0.187500 0.187500
1.000.49690005 0.48901844 0.36921496 0.36898331 0.25000234 0.250000 0.250000

0.500.250.18377520 0.16584130 0.15148283 0.14985508 0.12507592 0.125000 0.125000
0.500.36755040 0.33168259 0.30296566 0.29971016 0.25015184 0.2500000.250000
0.750.55132559 0.49752389 0.45444848 0.44956524 0.37522776 0.375000 0.375000
1.000.73510079 0.66336518 0.60593131 0.59942032 0.50030368 0.500000 0.500000

0.750.250.27227270 0.20678964 0.21407798 0.20119503 0.18881843 0.187500 0.187500
0.500.54454540 0.41357929 0.42815596 0.40239005 0.37763687 0.375000 0.375000
0.750.81681810 0.62036893 0.64223394 0.60358508 0.56645530 0.562500 0.562500
1.001.08909080 0.82715857 0.85631192 0.80478011 0.75527373 0.750000 0.750000