Abstract
This paper aims to provide a numerical method for solving systems of fractional (Caputo sense) differential equations (FDEs). This method is based on the fractional finite difference method (FDM), where we implemented the Grunwald-Letnikov's approach. This method is computationally very efficient and gives very accurate solutions. In this study, the stability of the obtained numerical scheme is given. The numerical results show that the proposed approach is easy to be implemented and are accurate when applied to system of FDEs. The method introduces promising tool for solving many systems of FDEs. Two examples are given to demonstrate the applicability and the effectiveness of our method.