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

Table 6

Statistical analysis of performance measures including MSE, gradient, mu, number of iterations, and time taken by the system for obtaining the results of Example 4.

Performance measures	Case I		Case II		Case III		Case IV
	Hidden neurons	60	60	60	60	60	60	60	60
Training	8.67E-12	1.04E-11	1.64E-11	9.39E-13	3.88E-11	8.32E-13	3.83E-11	1.74E-12
Validation	1.37E-12	3.12E-12	1.48E-12	1.46E-12	3.12E-12	1.10E-12	4.99E-11	2.66E-12
Testing	8.52E-13	4.94E-13	1.06E-11	1.37E-12	8.76E-12	1.32E-12	4.29E-11	2.66E-12
Gradient	1.84E-07	3.49E-06	1.28E-05	1.43E-07	2.02E-06	4.23E-07	8.03E-07	3.33E-07
Mu	1.00E-13	1.00E-13	1.00E-13	1.00E-11	1.00E-12	1.00E-12	1.00E-11	1.00E-11
Epochs	1000	1000	502	1000	635	1000	1000	1000
Regression	1	1	1	1	1	1	1	1
Time (s)	6 s	5 s	2 s	5 s	3 s	5 s	5 s	5 s