Analysis of Some Semi-analytical Methods for the Solutions of a Class of Time Fractional Partial Integro-differential Equations

The goal of this article is to apply the meshfree techniques for solving the time-dependent partial integro-differential equations of fractional order. The homotopy analysis technique, the differential transform method, and the modified Laplace decomposition method are the three distinct approaches that have been successfully implemented. It is demonstrated that these strategies are quite effective and quickly approach the true solution. The convergence analysis of the proposed methods is discussed in detail. Additionally, certain graphs are drawn, and tabular data is collected, both of which demonstrate the correctness of the suggested methods.