Numerical Methods for Fractional Differential Equations Using Physics Informed Neural Networks

This paper investigates the numerical solution of fractional differential equations involving the Erdelyi-Kober fractional operator, which play a pivotal role in modeling memory-dependent and anomalous dynamic processes in applied mathematics, physics, and engineering, including anomalous diffusion, viscoelasticity, and heterogeneous heat conduction. We introduce a novel neural network-based framework that integrates Physics-Informed Neural Networks with the Theory of Functional Connections and