Fracmemristor: Fractional-Order Memristor

This paper mainly discusses an interesting conceptual framework: the fractional-order memristor (fracmemristor). It is a challenging theoretical problem to determine what the fracmemristor interpolating characteristics between the memristor and the capacitor or inductor are, and where the positions of the fracmemristor in the Chua's axiomatic element system are. Motivated by this need, in this paper, we introduce an interesting conceptual framework of the fracmemristor, which joins the concepts underlying the fractional-order circuit element and the memristor. We use a state-of-the-art mathematical method, fractional calculus, to analyze the proposed conceptual framework. The term fracmemristor is a portmanteau of the fractional-order memristor. The term fracmemristance refers to the fractional-order impedance of a fracmemristor. First, the relationship between the fracmemristance and the fractance is discussed. Second, the fracmemristances of the purely ideal 1/2-order capacitive fracmemristor and inductive fracmemristor are studied, respectively. The third step is the proposal for the fracmemristances of the purely ideal arbitrary-order capacitive fracmemristor and inductive fracmemristor, respectively. Finally, the fracmemristor is achieved by numerical implementation, and its non-volatility property of memory and nonlinear predictive ability is analyzed in detail experimentally. The predictable characteristics of the fracmemristor are a major advantage when comparing with the classical first-order memristor.