Neural network method for fractional-order partial differential equations

Abstract

In this paper, neural network method is first proposed to solve the fractional-order partial differential equations. The neural network based on the sine and the cosine functions is established on the sample points which are evenly distributed in the solution area. In view of the fractional heat conduction equation and the fractional wave equation, the training error function is established, and the related algorithm for the initial boundary value problem of the above equations is given. Then, the learning rate of the neural network is analyzed. Finally, several numerical examples are given to verify the effectiveness of solving the fractional-order partial differential equations by the present method.