Copyright © 2011 J. A. Tenreiro Machado. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper proposes the calculation of fractional algorithms based on time-delay systems. The study starts by analyzing the memory properties of fractional operators and their relation with time delay. Based on the Fourier analysis an approximation of fractional derivatives through time-delayed samples is developed. Furthermore, the parameters of the proposed approximation are estimated by means of genetic algorithms. The results demonstrate the feasibility of the new perspective.