Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 375858, 19 pages
doi:10.1155/2010/375858
Review Article

Fractional Order Calculus: Basic Concepts and Engineering Applications

Ricardo Enrique Gutiérrez,1 João Maurício Rosário,1 and José Tenreiro Machado2

1Department of Mechanical Engineering, UNICAMP, 13083-970 Campinas, Brazil
2Department of Electrical Engineering, ISEP, 4200-072 Oporto, Portugal

Received 7 October 2009; Revised 19 February 2010; Accepted 2 March 2010

Academic Editor: Katica R. (Stevanovic) Hedrih

Copyright © 2010 Ricardo Enrique Gutiérrez et al. 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

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.