Analysis of a Capacitor Modelled with Conformable Fractional Derivative Under DC and Sinusoidal Signals

Abstract

Fractional order circuit elements are successfully used to model circuits and systems in the last few decades. There are different types of fractional derivatives. Recently, another one named “the conformable fractional derivative” (CFD) has been introduced and shown to give good results for modeling supercapacitors. It is imperative to know how circuit elements behave for different current and voltage waveforms in circuit theory so that they can be exploited at their full potential. A CFD capacitor is not a well-known element and its usage and circuit solutions are rarely addressed in literature. In this study, it is examined how a CFD capacitor would behave under DC and AC excitations when it is fed by not only a current source but also a voltage source.