An Analytical-Numerical Method for the Solution of Nonlinear Fractional Fredholm Integro-Differential Equations With Logarithmic Weakly Singular Kernel

In this work, we investigate a numerical method for solving nonlinear fractional Fredholm integro-differential equations with logarithmic weakly singular kernels. Since the direct solution of these equations using classical methods results in low accuracy and high computational cost due to the singular behavior of the exact solution at both endpoints of the interval, we consider two approaches for the numerical solution. The first is the use of an analytical-iterative method to transform the nonlinear equation into a sequence of linear equations, which avoids the occurrence of nonlinear systems. The second is the use of a regularization technique, which regularizes the exact solution of the equation, making it possible to achieve high accuracy using common numerical methods. To test the accuracy and performance of the proposed method and to compare theoretical and numerical results, several test problems are solved using the presented method, and the results obtained from them are analyzed.