Numerical solution for fractional-order differential systems with time domain and frequency domain methods

For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency domain method are compared, and the limitations of frequency domain method are discussed.