The Reproducing Kernel Hilbert Space method for solving a fractional order differential equations problem

Abstract

In this article, we present a new approach based on the analytical method known as the Reproducing Kernel Hilbert Space Method (RKHSM), which is used for approximating the solution of fractional order differential equations. The results obtained demonstrate that RKHSM exhibits rapid uniform convergence of the approximate solution, along with high precision and efficiency. In this method, the solution is expressed in series form. To illustrate the effectiveness of the method, we provide numerical results including the exact solution, the approximate solution, and the absolute error.