Through this article, a numerical scheme based upon the modified fractional Euler method (MFEM) is introduced to find the numerical
solutions of linear and nonlinear systems of fractional differential equations (SFDEs) as well as nonlinear multi-order fractional
differential equations (MOFDEs). The fractional derivatives are defined by Caputo. The proposed algorithm is very simple and provides
the solutions directly without linearization, perturbations or any other assumptions. Illustrating examples with numerical comparisons
between the proposed algorithm and the exact and/or fourth order Runge Kutta method (RK4) are given to reveal the efficiency and the
accuracy of our algorithm.