Laguerre Polynomial Approximation of Fractional Order Linear Systems

This paper presents a finite dimensional approximation of fractional order linear systems and its connection with transport equation. The main results show, that the linear fractional order system can be approximated by a finite number of linear differential equations. Appropriate error estimate in C-0 norm is presented. Next, the solution of fractional order linear system is presented as a linear functional of the solution of transport equation. This result establishes a connection between the semi groups theory and fractional system theory. Considerations are illustrated with simple example of fractional oscillator.