Double Elzaki Transform Technique for Linear Fractional Partial Differential Equations

Abstract

This study presents a novel approach for obtaining analytical solutions to certain classes of linear partial differential equations (PDEs) of fractional order regarding Mittag-Leffler function according to initial and boundary conditions by employing a newly developed double integral transformation technique named Double Elzaki Transformation (DET). Fractional-order PDEs have gained significant attention due to their ability to accurately describe various complex phenomena in physics, engineering, and other applied sciences. The suggested transformation method broadens traditional integral transform techniques by introducing a double integral framework, improving its ability to handle fractional derivatives efficiently and systematically. The transformation converts the original fractional PDEs into algebraic equations within the transform domain, which are subsequently solved and inverted to yield series-form or exact solutions in the original domain. Several illustrative examples are provided to demonstrate the effectiveness and applicability of the method. The results indicate that the new DET is a powerful and reliable tool for solving linear fractional partial differential equations (LFPDEs), providing more accuracy and simplicity compared to existing methods.