Generalized modeling of the fractional-order memcapacitor and its character analysis

Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α=1,β=0 and to the conventional memristor as α=0,β=1. Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v−q and v−i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v−q and v−i curves of the other fractional-order models are transition curves between the four basic patterns.