Simulation method of fractional systems based on the discrete-time approximation of the Caputo fractional derivatives

This paper proposes a new method for the simulation of the fractional systems. It deals with the approximation methods of the fractional derivative. It compare the approximation based on Grünwald with Caputo approximation. The efficiency of each approximation methods in terms of execution time and quadratic error is evaluated for different differential orders and stepsize. The best approximation method is used to develop an original simulation method to demonstrate its effectiveness.