Analytical Investigation of 2D Bratu-Type Fractional Differential Equations via HPTM

In this study, the two-dimensional fractional Bratu-type differential equation is introduced and thoroughly investigated utilizing the homotopy perturbation transformation approach. The analysis is conducted in the framework of Caputo fractional derivatives. Existence and uniqueness of the solution to the proposed 2D fractional Bratu-type model are established under appropriate conditions, ensuring the well-posed ness of the problem. Several illustrative examples are provided to demonstrate the application of the method to the 2D fractional Bratu-type differential equation. The results, presented graphically, highlight the efficiency, systematic nature, and simplicity of the Homotopy perturbation transformation method (HPTM) in solving partial differential equations with fractional derivatives. Several attractive and insightful results have been obtained for the 2D fractional Bratu-type model.