The Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential ‎Equations

Subject Areas : International Journal of Industrial Mathematics

A. Alvandi ¹ , M. Paripour ²

1 - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
2 - Department of Computer Engineering and Information Technology, Hamedan University of Technology, Hamedan, Iran.

Received: 2016-03-28 Accepted : 2017-10-21 Published : 2018-11-01

Keywords: Reproducing kernel, Fractional differential equation, Kennel, Taylor series,

Abstract :

‎This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo \cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert space. This method cannot be used directly to solve these equations, so an equivalent transformation is made by using Taylor series. Some numerical examples are studied to demonstrate the accuracy of the given ‎method.‎