Calculating area of fractional‐order memristor pinched hysteresis loop

Abstract

A fractional-order current-controlled memristor pinched hysteresis loop area 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 part memory of the memristor. Moreover, two parts of the area are affected not only by the cosine components, but also by the sine components. The voltage of the fractional-order current-controlled memristor is no longer an odd function with respect to time and the coefficient of cos(ωt) in its Fourier series is zero. In a closed loop, the average power and the memory rely only on sine harmonics of the voltage. Meanwhile, the power and the memory are related to the order of the fractional-order derivative.