Advances in Difference Equations
Volume 2011 (2011), Article ID 934094, 12 pages
Research Article

Time-Delay and Fractional Derivatives

Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal

Received 7 January 2011; Accepted 4 February 2011

Academic Editor: J. J. Trujillo

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.


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.