Behavior characteristics of a cap-resistor, memcapacitor, and a memristor from the response obtained of RC and RL electrical circuits described by fractional differential equations

Authors: JOSE FRANCISCO GOMEZ AGUILAR

Abstract: This paper provides an analysis of RC and RL electrical circuits described by a fractional difierential equation of Caputo type. The order considered is ${0 \textless \gamma }\le ${ 1}. The Laplace transform of the fractional derivative is used. To keep the dimensionality of the physical quantities, R, C, L, and an auxiliary parameter $\sigma $ are introduced, characterizing the existence of fractional components in the system. The relationship between $\gamma$ and $\sigma $ is reported. The response obtained from the fractional RC and RL circuits exhibits the characteristic behaviors of a cap-resistor, memcapacitor, and memristor, as well as charge-voltage for memcapacitive systems and current-voltage for memristive systems. The relationship between Ohm's law and Faraday's laws for the charge stored in a capacitor and induction is reported. Illustrative examples are presented.

Keywords: Fractional calculus, Mittag-Leffler functions, electrical circuits, fractional differential equation, cap-resistor, memcapacitor, memristor

Full Text: PDF