Diffusive representation of Riemann-Liouville fractional integrals and derivatives

This paper presents a novel equivalent description of fractional-order integrals and derivatives via an auxiliary integral function of two variables. Employing the concept of Laguerre integration, a novel approximate scheme for the resulting infinite dimensional state space model is derived. A simple example with numerical simulations is provided to show the superiority and effectiveness of the proposed method in comparison with some related works from the previous results.