Modeling and character analyzing of current-controlled memristors with fractional kinetic transport

Memristors have come into limelight again after it was realized by HP researchers. This paper proposes a memristor model which can be called fractional-order current-controlled memristor, and it is more general and comprehensive. We introduce the fractional integral/differential to the current-controlled memristor model and model memristor with fractional kinetic of charge transport. An interesting phenomena found out is that the I-V characteristic is a triple-loop curve (0 < α < 1) and not the conventional double-loop I-V curve (α=1). Memristance (RM) is analyzed versus the fractional order α and time(t), and it reach saturation faster when 0 < α < 1. The saturation (Rmin → Rmax) time is given and analyzed versus different orders α and frequencies ω, which increase with α increasing and ω decreasing. More importantly, the memristors can't reach the Rmax  in some cases. Energy loss of the model is analyzed, and the I-P curves isn't origin-symmetric when 0 < α < 1 which is very different with curves when α=1.