Numerical Techniques for Solving Fractional Partial Differential Equations: A Comparative Study

Abstract

Fractional partial differential equations (FPDEs) have emerged as essential tools in modeling physical systems with memory and non-local properties. This paper investigates numerical methods for solving FPDEs, particularly the time-fractional diffusionand Burgers-type equations. We compare the Adomian Decomposition Method (ADM) and the Finite Difference Method (FDM) using the L1 scheme. Analytical and numer ical solutions are presented with detailed mathematical derivations, error comparisons, and insights into convergence and stability.