On the Memristances, Parameters, and Analysis of the Fractional Order Memristor

In this work, the analytical expressions of memristances, related parameters, and time domain behavioral analysis of the fractional order memristor have been proposed. Both DC with arbitrary delay and many AC waveforms including arbitrary phase sinusoidal and cosinusoidal waveform along with arbitrary periodic waveform have been taken into account. Unlike the previous works, the formerly ignored dimensional consistency has been taken into account and the analytical modelling of the boundary effect has been performed. Moreover, both transient and asymptotic behaviors of the fractional order memristor excited by AC waveform have been distinguished and analyzed. The effect of phase of AC waveform has also been studied. The influence of the fractional order to the areas of voltage-current hysteresis loop and memristance-current lissajous curve has also been clearly discussed and the usage of fractional order memristor in the memristor based circuit has also been demonstrated.