Machado, J. A. Tenreiro2015-11-252015-11-252013http://hdl.handle.net/10400.22/7003This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.engFractional calculusFractional operatorsControl systemsModeling and controlHeat diffusion systemsElectromagnetismFractional electrical impedancesEvolutionary algorithmsRoboticsNonlinear system controlbook part10.1007/978-1-4614-7828-7_20