Fractional-order Memristor Response Under DC and Periodic Signals

Recently, there is an essential demand to extend the fundamentals of the conventional circuit theory to include the new generalized elements, fractional-order elements, and mem-elements due to their unique properties. This paper presents the relationships between seven different elements based on the four physical quantities and the fractional-order derivatives. One of them is the Fractional-order memristor, where the memristor dynamic is expressed by fractional-order derivative. This element merge the memristive and fractional-order concepts together where the conventional modeling becomes a special case. Moreover, the mathematical modeling of the fractional-order memristor is introduced. In addition, the response of applying DC, sinusoidal, and nonsinusoidal periodic signals is discussed. Finally, different numerical simulations are presented.