MODIFIED ANALYTICAL METHODS FOR SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Abstract

Fractional partial differential equations (FPDEs) extend classical PDEs by incorporating fractional order derivatives, capturing complex phenomena in various fields such as physics, engineering, and finance. Traditional analytical methods often fall short in efficiently solving FPDEs due to their inherent complexity and non-local behavior. This paper presents modified analytical methods designed to address these challenges. By integrating fractional calculus with advanced techniques such as operational matrices and modified Laplace transforms, the proposed methods offer improved accuracy and computational efficiency. The paper demonstrates the efficacy of these approaches through a series of numerical examples and comparative analyses with existing methods. The results highlight significant advancements in the solution of FPDEs, offering a robust framework for future research and practical applications.