An Artificial Neural Network Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation

In this paper, the solution of the fractional partial differential-difference Toda Lattice Equation by Artificial Neural Networks is examined.According to the method, we approximate the unknown values un = u(., tn) of the desired function by the artificial neural networks.As an application we demonstrate the capabilities of this method for identification of various values of order of fractional derivative .Thereafter, the artificial neural networks algorithm is used in order to identify the unknown values un.Comparing the results with the finite difference solution, the algorithm can identify the function u(x, t) better than the other method.