Two System Modeling Methods Using Fractional Calculus

An introduction of the definitions of Riemann-Liouville and Caputo fractional calculus is given as well as some of their properties. The general form of fractional linear time-invariant (LTI) equations is proposed, and it is pointed out that they are the generalizations of integer LTI equations. The transfer function and the state-space representation are given for fractional LTI systems, and a comparison is made with integer LTI systems, and their differences and similarities are also pointed out. Two solving methods are deduced using Laplace transform: the direct solving method and the state-space method. Finally an example is given to show the effectiveness of the two methods aforementioned.