An enhanced Artificial Neural Network approach for solving nonlinear fractional-order differential equations

Abstract

This paper introduces a hybrid Chebyshev Collocation Method (CCM) and Artificial Neural Network (ANN) approach to address the computational challenges of nonlinear Caputo fractional differential equations. The purpose is to improve accuracy for static solutions by approximating the fractional derivative spatially. The methodology leverages CCM for spatial discretization and ANN for residual minimization, achieving low MSEs (e.g., $10^{-5}$) in three examples. The findings confirm improved convergence with increasing node count, with implications for efficient fractional PDE solvers. The novelty lies in the static CCM+ANN integration, offering a practical alternative to dynamic methods.