New semi-analytical solutions of the time-fractional Fokker–Planck equation by the neural network method

Abstract

This paper suggests a neural network method for solving the time-fractional Fokker–Planck equation. An energy function is constructed by means of initial–boundary value conditions. The Caputo derivative is approximated by L1 numerical scheme and an unconstrained discretization minimization problem is presented. Gradient descent algorithm is adopted for neural network training. Semi-analytical solutions are obtained where two numerical examples demonstrate the method’s efficiency.