A polynomial fractional-order charge-controlled memristor model

Abstract

In this paper, the fractional calculus is introduced into charge-controlled memristor to establish a fractional-order charge-controlled memristor model. The fractional derivative is a generalization of integer derivatives. Memristor represents the missing relation between the charge and flux among the conventional elements. A unified cubic model is proposed which is more general and comprehensive, and the model is analyzed when the fractional-order a change in the range of 0 to 1.0. Some integer-order memristor model simulation are given to have a better understanding for the fractional-order model. Some interesting phenomena are found when researching the fractional-order model that the V-I characteristic is not the conventional double-loop V-I curves, but an curve can be called triple-loop V-I curves. The area inside the hysteresis loops decreases by the increasing of input frequency and the decreasing of the fractional-order α.