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

Table 3

Numerical values when 𝛽 = 0.750, 0.875, and 1.000 for (63).

𝑡	𝑥	𝛽=0.750		𝛽=0.875		𝛽=1.000
		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