Fractional Order Derivatives in Systems Theory

The aim of this paper is to communicate to a broader audience in systems theory the relevance of dynamical phenomena that are described by fractional order derivatives. It is organized with four principal objectives in mind. First, it attempts to introduce the reader to the rich mathematical theory behind the definition of the term "fractional order derivative." Following this, it highlights the diversity of real-life problems in engineering, economics and the life sciences to which researchers have successfully applied models containing fractional order derivatives. Then, as an essential step for the consideration of such models in systems theory, it summarizes the state of research in the representation and analysis of dynamical systems with fractional order derivatives (also referred to as fractional systems). The paper concludes with some comments aimed at the development of a more general theory of fractional systems.