Abstract: Fractional Calculus (FC) started in 1695 when L'Hopital wrote a letter to Leibniz asking for the meaning of Dny for n = 1/2. Starting with the ideas of Leibniz many important mathematicians developed the theoretical concepts. During the thirties A. Gemant and O. Heaviside applied FC in the areas of mechanical and electrical engineering, respectively. Nevertheless, these important contributions were somehow forgotten and only during the eighties FC emerged associated with phenomena such as fractal and chaos and, consequently, in the modeling of dynamical systems. This lecture introduces the FC fundamental mathematical concepts, and reviews the main approaches for implementing fractional operators. Based on the FC concepts, are presented several applications in the areas of modeling and control, namely fractional PID, electromagnetism, fractional electrical impedances, evolutionary algorithms, nonlinear system control, and finance.

Brief Biography of the Speaker:
J. A. Tenreiro Machado was born at 1957, graduated with ‘Licenciatura’ (1980), PhD (1989) and ‘Habilitation’ (1995) degrees in Electrical and Computer Engineering at the University of Porto.
During 1980-1998 worked as Professor at the Department of Electrical and Computer Engineering of the University of Porto. Since 1998 is Coordinator Professor at the Institute of Engineering of the Polytechnic Institute of Porto, Department of Electrical Engineering.
The main research interests are: Nonlinear Dynamics, Modeling, Fractional Calculus, Evolutionary Computing, Control, and Robotics.