Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks

Abstract

This study aims to employ artificial neural networks (ANNs) as a novel method for solving time fractional telegraph equations (TFTEs), which are typically addressed using the Caputo fractional derivative in scientific investigations. By integrating Chebyshev polynomials as a substitute for the traditional hidden layer, computational performance is enhanced, and the range of input patterns is broadened. A feed-forward neural network (NN) model, optimized using the adaptive moment estimation (Adam) technique, is utilized to refine network parameters and minimize errors. Additionally, the Taylor series is applied to the activation function, which removes any limitation on taking fractional derivatives during the minimization process. Several benchmark problems are selected to evaluate the proposed method, and their numerical solutions are obtained. The results demonstrate the method’s effectiveness and accuracy, as evidenced by the close agreement between the numerical solutions and analytical solutions. © 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.