Numerical Simulation for a Class of Fractional Differential Equations Using Reproducing Kernel Hillbert Space Method

Abstract

In this work, we introduce an efficient numerical scheme, the reproducing kernel Hilbert space method, for providing numerical approximate solutions of a certain class of fractional differential equations in Caputo-Fabrizio sense within favorable aspects of the reproducing kernel Hilbert space. The algorithm methodology is based on generating an orthonormal basis from the reproducing kernel property to formulate the solution in the form of uniformly convergent series, in accordance with the constrain conditions in the space W_2^m [a,b]. Additionally, we present numerical experiments to test our hypothesis and confirm the design procedure of the proposed algorithm. Our results demonstrate that the the reproducing kernel Hilbert space method is a significant development tool for handling issues arising in computer science, physics, and engineering fields.