A Hybrid Approach for Solving Fractional Caputo Partial Differential Equations with Convergence Analysis

In this research, fractional Caputo partial differential equations are addressed using the q-Homotopy analysis method merged with the Sawi transform method through the construction of a novel algorithm. This approach combines the Sawi transform with the q-Homotopy analysis method to demonstrate how complex fractional differential equations can be solved analytically in a straightforward manner. The proposed algorithm illustrates the effectiveness of applying the Sawi transform in conjunction with the q-Homotopy method to overcome the challenges associated with handling nonlinear terms numerically. Several examples are provided to verify the accuracy and efficiency of the proposed approach. The results indicate that the method converges to the exact solutions when suitable parameters are chosen. Therefore, the proposed method proves to be a robust and flexible algorithm for solving nonlinear fractional partial differential equations.