On Applications of Fractional Derivatives in Circuit Theory

J. Gulgowski (Univ. Gdansk, Poland), T. Stefanski (Gdansk Univ. of Techn., Poland), D. Trofimowicz (SpaceForest Ltd., Poland)

In this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited applicability in the circuit theory. That is, the Riemann-Liouville and Caputo derivatives with finite base point have a limited applicability whereas the Gruenwald-Letnikov and Marchaud derivatives lead to reasonable results of the circuit-level modelling.