Neural Network Method For Solving Fractional Diffusion Equations

In this paper, neural networks based on Legendre polynomials are established to solve space and time fractional diffusion equations. The error functions containing adjustable parameters (the weights) for the training sets are constructed. The range of learning rate is analyzed to ensure that the error decreases with respect to training times. Several nu-merical examples including numerical results and graphs are illustrated. The results show that more training can achieve high precision. (c) 2020 Elsevier Inc. All rights reserved.