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

Document Type : Research Paper


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.


‎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.‎