Abstract
This article is based upon work from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology). Research described in this paper was financed by the Ministry of Education, Youth and Sports under grant LTC18022 of Inter-Cost program.
Highlights
The term fractance or fractional-order capacitor (FOC), for an electrical element having properties between those of the resistance and capacitance, was suggested in 1983 by Alain Le Mehaute and Gilles Crepy for denoting electrical elements with non-integer order impedance [1]
The recent decades were marked by the development of fractional-order elements (FOEs) and different models of fractal electrodes describing the processes in electrochemical cells
The literature survey made in this study help us to trace the chronological evolution of the concepts and approximations
Summary
The term fractance or fractional-order capacitor (FOC), for an electrical element having properties between those of the resistance and capacitance, was suggested in 1983 by Alain Le Mehaute and Gilles Crepy for denoting electrical elements with non-integer order impedance [1]. Their impedance is described as Z(s) = K sα, where ω is the angular frequency with s = jω and the phase is given in radians (φ = απ/2) or in degrees (φ = 90α◦). The impedance of Type IV FOEs, i.e. FOCs in quadrant IV, corresponds to an order –1 < α < 0 and a pseudocapacitance Cα = 1/K, whereas FOIs in quadrant I (Type I) have an order of 0 < α < 1 and a pseudoinductance of Lα = K Their units are expressed as farad·sec−α−1 (F·s−α−1) and henry·secα−1 (H·sα−1), respectively. Higher order FOCs and FOIs with the described impedances have frequency responses in quadrants II and III (Type II and III), respectively Their characteristics such as the order (α), pseudocapacitance (Cα), pseudoinductance (Lα), constant phase zone (CPZ), Axis
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