Continuous-time fractional linear systems: Transient responses

This chapter presents an introduction to fractional continuous-time linear systems, based on suitable fractional derivatives. The usual tools, impulse response, transfer function, and frequency responses are defined, and the manner of their computation is given, considering both commensurate and noncommensurate cases. Properties of the systems, like causality, periodicity, and stability are also studied. The formulation in the commensurate case is done in a full agreement with classic results that are recovered when the derivative order becomes equal to 1. Multiple-input, multiple-output systems are also studied from the state-space point of view.