Numerical Techniques for Solving Linear Fractional Partial Differential Equations

Abstract

Fractional partial differential equations appear in many fields, such as physics, finance, fluid mechanics, engineering, and biology. In this study, we focus on finding numerical solutions for linear fractional partial differential equations. We use the Homotopy Perturbation Method (HPM) to develop an approximate solution. The goal of this study is to show that HPM is an efficient and reliable method for solving these equations. The fractional derivative is defined in the Caputo sense. The improved algorithm provides solutions as a series that quickly converges and is easy to compute. The results agree well with previous studies, confirming that this method is accurate, efficient, and simple to apply.