The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations

Table 1

Numerical results of Example 4.1.

𝑥	𝑘= 1		𝑘 = 1/5		𝑘 = 0.005
	Analytical	Approx	Analytical	Approx	Analytical	Approx
	solution	solution	solution	solution	solution	solution
0	1	1	1	1	1	1
0.125	0.99437	0.993126	0.992747	0.992391	0.992212	0.992212
0.250	0.979919	0.974802	0.971922	0.970148	0.968995	0.968983
0.375	0.958424	0.944545	0.938558	0.933609	0.930733	0.930674
0.500	0.930957	0.904813	0.893615	0.883958	0.878038	0.877899
0.625	0.898335	0.857938	0.838087	0.822499	0.811743	0.811497
0.750	0.861241	0.805442	0.773025	0.750552	0.732892	0.732514
0.875	0.820277	0.748795	0.699540	0.669584	0.642719	0.642193
1	0.775989	0.688838	0.618798	0.580978	0.542633	0.541945