Dissipative and generative fractional electric elements in modeling $${\varvec{RC}}$$ and $${\varvec{RL}}$$ circuits

Two types of constitutive equations consisting of instantaneous and power type hereditary contributions are proposed in order to model generalized capacitor (inductor). The first one, that expresses charge (magnetic flux) in terms of voltage (current) memory, proved to describe a dissipative electric element, while the second one, that expresses voltage (current) in terms of charge (magnetic flux) memory, proved to describe a generative electric element. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits’ frequency characteristics including their asymptotic behavior.