An efficient approach for solving a class of fractional anomalous diffusion equation with convergence

This article presents a study on Fractional Anomalous Diffusion (FAD) and proposes a novel numerical algorithm for solving Caputo's type fractional sub-diffusion equations to convert the fractional model into a set of nonlinear algebraic equations. These equations are efficiently solved using the Levenberg-Marquardt algorithm. The study provides the error analysis to validate the proposed method. The effectiveness and accuracy of the method are demonstrated through several test problems, and its performance and reliability are compared with other existing methods in the literature. The results indicate that the proposed method is a reliable and efficient technique for solving fractional sub-diffusion equations, with better accuracy and computational efficiency than other existing methods. The study's findings could provide a valuable tool for solving FAD in various applications, including physics, chemistry, biology, and engineering.