Computational Methods, Existence and Uniqueness for Solving 2-D Fractional Nonlinear Fredholm Integro-Differential Equation

In this paper, we have investigated the two-dimensional fractional nonlinear Fredholm integro-differential equation (TDFNFI-DE). These equations are used in many fields, including particle dynamics in physics, biology, and control theory. We have developed an effective combined approach in our work that uses Homotopy analysis (HAM) and the Adomian decomposition method (ADM) to solve fractional integro-differential equations in two dimensions. Numerical experiment results show the effectiveness of our recently created technique. We prove the existence and uniqueness of the exact solution. To illustrate the numerical effectiveness of the suggested approach, we provide a number of numerical examples. The suggested approach is accurate and applicable to various nonlinear issues in science, according to theoretical and numerical results.