Analysis of electrical circuits including fractional order elements

Abstract

This paper deals with the analysis of electrical circuits with classical one-port elements including two novel defined one-port fractional order elements: fractional-order resistive-capacitive RC-α and fractional-order inductive RL-α element. The definitions and analytical relations between current, voltage and power of introduced fractional elements are provided. An example of fractional element realization via ladder electrical circuit composed of classical resistors, capacitors and/or inductors is presented. Several examples are analyzed to illustrate the behavior of electrical circuit with fractional order elements for different values of fractional order α including differentiator/integrator circuits as well as complex circuits without accumulated energy.