On linear systems with a fractional derivation: Introductory theory and examples

Linear systems with a derivation of non-integer order are examined as a special case of systems described by Mikusiński operators. Controllability and observability are examined using the theory of modules, as well as regulation of finite-dimensional systems. A stability result is obtained based upon the asymptotic properties of generalized Mittag-Leffler exponents. A solution of the tracking problem for σ-controllable fractional delay systems is presented. The article includes examples of a finite-dimensional fractional system and a fractional delay system.