Calculating area of fractional‐order memristor pinched hysteresis loop

Abstract

A fractional-order current-controlled memristor pinched hysteresis looparea is calculated in this study. The area is divided into two parts:one equals to the half of instantaneous power and the other is the partmemory of the memristor. Moreover, two parts of the area are affectednot only by the cosine components, but also by the sine components. Thevoltage of the fractional-order current-controlled memristor is nolonger an odd function with respect to time and the coefficient ofcos(omega t) in its Fourier series is zero. In a closed loop, theaverage power and the memory rely only on sine harmonics of the voltage.Meanwhile, the power and the memory are related to the order of thefractional-order derivative.