Analytical Solutions of Nonlinear Time Fractional Partial Differential Equations via Conformable Laplace Homotopy Perturbation Method

This paper presents a novel hybrid approach that combines the homotopy perturbation method (HPM) with the conformable Laplace transform (CLT) to derive the approximate analytical solutions for nonlinear fractional partial differential equations. The strength of this method lies in its seamless integration of HPM and CLT, providing a robust and systematic framework for tackling complex fractional models. Graphical results reveal a remarkable agreement between classical integer-order solutions and their fractional-order counterparts, underscoring the accuracy and reliability of the proposed technique. Additionally, the findings establish that the method is not only efficient but also highly adaptable for addressing a wide spectrum of nonlinear phenomena in mathematical physics and engineering.