Fractional-Order Memristor response to periodic current functions

The Memristor is a new passive element representing relationship between electric charge q and flux ϕ. The concept of memristors in the generalized fractional order domain has gained much relevance due to their unique behavior which cannot be obtained in conventional elements. The generalized state equations of the memristor is discussed in the fractional-order sense and the effects of the added fractional-order parameter on the memristor characteristics and output behavior are studied. Numerical analyses of the model are presented for case 0<α<1 with sinusoidal, symmetric sawtooth and square-wave excitation currents. The instantaneous power and area under the v-i curves at values of fractional order is observed and it is found that the shape and the area enclosed by the hysteresis loop depend on the fractional-order and excitation frequency; the area is less dependent on frequency for the square wave current excitation.