A Numerical Method for Solving Fractional Differential Equations by Using Neural Network

Table 2

(a) Comparison of results for the solution of Example for . (b) Comparison of results for the solution of Example for .

(a)

		Numerical solution				Accuracy
		GL	PSO	GA	NU	GL	PSO	GA	NU
	0.01				0.0101
	0.04	0.0401	0.0404	0.0396	0.0407
	0.09	0.0901	0.0907		0.0917
	0.16	0.1601	0.1604	0.1596	0.1621
	0.25	0.2501	0.2496		0.2505
	0.36	0.3602	0.3583	0.3573	0.3571
	0.49	0.4902	0.4869		0.4853
	0.64	0.6402	0.6362	0.6352	0.6397
	0.81	0.8102	0.8069		0.8186
	1	0.1001	0.1000	0.1004	0.1003

(b)

		Numerical solution			Accuracy
		GL	PSO	NU	GL	PSO	NU
	0.01	0.0107	0.0103	0.0092
	0.04	0.0413	0.0414	0.0377
	0.09	0.0918	0.0928	0.0875
	0.16	0.1622	0.1636	0.1592
	0.25	0.2527	0.2538	0.2511
	0.36	0.3631	0.3631	0.3609
	0.49	0.4934	0.4918	0.4884
	0.64	0.6438	0.6402	0.6373
	0.81	0.8141	0.8091	0.8106
	1	1.0044	0.9991	1.0020