Application of Intelligent Paradigm through Neural Networks for Numerical Solution of Multiorder Fractional Differential Equations

Table 2

Statistical analysis of performance measures including MSE, gradient, mu, number of iterations, and time taken by the system for calculating the results of Examples 1, 2, and 3.

Example	Case	Hidden neurons	Mean square error			Gradient	Mu	Epochs	Regression	Time (s)
			Training	Validation	Testing
1	I	60	7.50E-11	1.08E-10	1.06E-10	1.00E-07	1.00E-10	1000	1	5
	II	60	5.84E-11	8.57E-11	1.13E-10	1.00E-07	1.00E-10	1000	1	5
	III	60	7.64E-11	9.79E-11	1.15E-10	5.82E-04	1.00E-10	1000	1	5
	IV	60	1.26E-10	1.75E-10	1.66E-10	1.40E-04	1.00E-09	1000	1	5
2		60	5.18E-14	1.12E-13	1.61E-13	1.24E-08	1.00E-13	890	1	2
3		60	5.52E-12	1.58E-13	2.53E-12	1.51E-06	1.00E-10	1000	1	5