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Analysis of fractional electrical circuit with sinusoidal input signal using Caputo and conformable derivative definitions

Piotrowska Ewa

Poznan University of Technology Academic Journals. Electrical Engineering

2019

No. 97

155--167

This paper presents 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 definition and the conformable fractional derivative definition are given the solutions in the case of: 1) control in the form of sine function at zero initial states 2) control in the form of cosine function at zero initial states 3) control in the form of the sine function with phase shift at zero initial states. The solutions are shown for capacitor voltages for fractional derivative orders of 0.7; 0.8; 1.0. The results were compared using graphs.

Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo

Piotrowska E.

Archives of Electrical Engineering

2018

Vol. 67, nr 3

629–-639

The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.

Analysis of fractional electrical circuit with rectangular input signal using Caputo and conformable derivative definitions

Piotrowska E.

Archives of Electrical Engineering

2018

Vol. 67, nr 4

789--802

An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations. The paper used the definition of the integral derivative Caputo and CDF conformable fractional definition. An electrical circuit solution using Caputo and CDF definitions for rectangular with zero initial conditions was developed. The results obtained using the Caputo and CDF definitions were compared. The solutions are shown for capacitor voltages, for fractional derivative orders of 0.6, 0.8, 1. The results were compared using graphs.