Fractional RLC circuit in transient and steady state regimes

Abstract

Assuming accumulated charge being dependent on capacitor voltage memory as well as by expressing magnetic flux in inductor in terms of current memory, generalized capacitor and inductor are constitutively modeled by the sum of terms containing instantaneous and power type hereditary contributions. Constitutive models are further used in analyzing transient and steady state responses of series RLC circuit subject to electromotive force. Depending on model parameters, the character of transfer function changes the behavior of fractional RLC circuit's impulse response in transient regime from aperiodic, over critically aperiodic, to damped oscillatory. Transition from transient to steady state regime is also analyzed, so as its predominant type depending on element's fractional order.