Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Time-Delay and Fractional Derivatives | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 934094 12 pages doi 2011 934094 Research Article Time-Delay and Fractional Derivatives J. A. Tenreiro Machado Department of Electrical Engineering Institute of Engineering of Porto Rua Dr. Antonio Bernardino de Almeida 431 4200-072 Porto Portugal Correspondence should be addressed to J. A. Tenreiro Machado jtm@ 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. 1. Introduction Fractional calculus FC deals with the generalization of integrals and derivatives to a noninteger order 1-7 . In the last decades the application of FC verified a large development in the areas of physics and engineering and considerable research about a multitude of applications emerged such as viscoelasticity signal processing diffusion modeling and control 8-17 . The area of dynamical systems and control has received a considerable attention and recently several papers addressing evolutionary concepts and fractional algorithms can be mentioned 18 19 . Nevertheless the algorithms involved in the calculation of fractional derivatives require the adoption of numerical approximations 2026 and new research directions are clearly needed. .
