Numerical Solution Of Fractional Differential Equations Using Iterative Reproducing Kernel Method

Abstract

In this work, an accurate numerical approximation algorithm based on the reproducing kernel Hilbert space (RKHS) approach has been proposed to solve a class of fractional differential equations within the framework of the Caputo sense. The analytical solution is presented as a convergent series with accurately computable structures in the reproducing kernel space. The n-term approximation has been obtained and proven to converge uniformly to the analytical solution. The main advantage of the RKHS approach is its direct application without requiring linearization or perturbation, thereby avoiding errors associated with discretization. Several numerical examples are provided to demonstrate the accuracy of the computations and the effectiveness of the proposed approach. The numerical results indicate that the RKHS method is a powerful tool for finding effective approximated solutions to such systems arising in applied mathematics, physics, and engineering.