On the Fractional-order Memristor Model

Fractional order calculus is the general expansion of linear integerorder calculus and is considered as one of the novel topics for modelling dynamical systems in different applications. In this paper, the generalized state equation of the nonlinear two-terminal element which is called memristor is discussed in the fractional-order sense. The effect of the added fractional-order parameter on the memristor characteristics and output behaviour are introduced. The fractional order resistance of the memristor in general for any applied voltage is derived. The generalized formulas and numerical analysis of the step response of the memristor including the instantaneous resistance, startup time and saturation time are studied which will be reduced to the conventional memristor response as α = 1.