An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks

This study aims to develop a new strategy for solving partial differential equations with fractional derivatives (FPDEs) using artificial neural networks (ANNs). Numerical solutions to FPDEs are obtained through the Hermite wavelet neural network (HWNN) model. The Caputo fractional derivative is consistently applied throughout the research to address fractional-order partial differential problems. To enhance computational efficiency and expand the input pattern, the hidden layer is removed. A neural network (NN) model featuring a feed-forward architecture and error-back propagation without supervision is employed to optimize network parameters and minimize errors. Numerical illustrations are presented to demonstrate the effectiveness of this approach in preserving computational efficiency while solving FPDEs.

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