文摘
Fractional calculus generalizes integer-order derivatives and integrals. Memristor represents the missing relation between the charge and flux among the conventional elements. This paper introduces the fractional calculus into charge-controlled memristor to establish a unified cubic fractional-order charge-controlled memristor model, which is more general and comprehensive, and the model is analyzed when the fractional-order \(\alpha \) change in the range of 0–1. Some interesting phenomena are found that the I–V characteristic is not the conventional double-loop I–V curves, but which can be called triple-loop I–V curves. The area inside the hysteresis loops decreases not only by the fractional-order \(\alpha \) decreasing, but also by the input frequency \(\omega \) increasing.