Analysis of Fractional Electrical Circuit Using Caputo and Conformable Derivative Definitions

Abstract

The paper presents an analysis of the fractional electrical circuit in the transient state described by the fractional-order state-space equations. General solutions to the fractional state-space equations containing two types of definitions of fractional derivative: Caputo fractional order derivative and the Conformable Fractional Derivative (CFD) definitions. The solutions are given in three cases: (1) nonzero initial conditions and zero input signal, (2) the input signal in the form of a step function and zero initial conditions; (3) the general case where the input and initial conditions are nonzero. The results for voltages across the capacitors for derivatives of fractional orders equal \(\alpha =0.7; 0.8; 0.9\) are shown. The comparison of those two definitions is presented and discussed.