On fraction order modeling and control of dynamical systems

This paper demonstrates the feasibility of modeling any dynamical system using a set of fractional order di®erential equations, including distributed and lumped systems. Fractional order differentiators and integrators are the basic elements of these equations representing the real model of the dynamical system, which in turn implies the necessity of using fractional order controllers instead of controllers with integer order. This paper proves that fractional order differential equations can be used to model any dynamical system whether it is continuous or lumped.