Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

Table 1

Numerical results of Example 11 for 𝑚=9 in comparison to [16].

𝑥	𝛼=0.50		𝛼=0.75		𝛼=1.00
	Reference [16]	Ours	Reference [16]	Ours	Reference [16]	Ours	Exact
0.1	0.330159	0.330108	0.190108	0.190101	0.099667	0.099668	0.099668
0.2	0.436737	0.436839	0.309886	0.309976	0.197358	0.197375	0.197375
0.3	0.504842	0.504889	0.404552	0.404615	0.291289	0.291313	0.291313
0.4	0.553802	0.553782	0.481638	0.481632	0.379946	0.379949	0.379949
0.5	0.591265	0.591195	0.545178	0.545090	0.462172	0.462117	0.462117
0.6	0.621026	0.621014	0.597790	0.597783	0.537048	0.537050	0.53705
0.7	0.645480	0.645485	0.641801	0.641820	0.604338	0.604368	0.604368
0.8	0.666016	0.666020	0.678835	0.678850	0.664009	0.664037	0.664037
0.9	0.683560	0.683554	0.710182	0.710175	0.716300	0.716298	0.716298