An Innovative Approach to Solve Linear Mixed Partial Fractional Differential Equations Containing More Than Two Independent Variables

Abstract

This work introduces the Laplace Substitution Method (LSM) for solving linear mixed partial fractional differential equations involving more than two independent variables. The method transforms such complex equations into ordinary fractional differential equations by employing an analytical approach that combines repeated substitution with the Laplace transform of fractional derivatives. LSM stands out as a highly effective, practical, and robust tool for addressing these types of problems. Furthermore, its implementation is relatively straightforward. This study is expected to facilitate the analysis of linear mixed partial fractional differential equations, which frequently arise in various fields of research and technological innovation. To validate the proposed method, illustrative examples are provided. The method's effectiveness and numerical stability are further assessed through graphical analysis.