Mathematical modelling of fractional order circuit elements and bioimpedance applications

Abstract In this work a classical derivation of fractional order circuits models is presented. Generalised constitutive equations in terms of fractional Riemann–Liouville derivatives are introduced in the Maxwell’s equations for each circuit element. Next the Kirchhoff voltage law is applied in a RCL circuit configuration. It is shown that from basic properties of Fractional Calculus, a fractional differential equation model with Caputo derivatives is obtained. Thus standard initial conditions apply. Finally, models for bioimpedance are revisited.