Abstract
In this work, the analysis of the memreactance, i.e., meminductor and memcapacitor, with fractional-order kinetics has been proposed. The meminductances, memcapacitances, and related parameters due to both DC and periodic input waveforms have been derived. The behavioral analysis has been thoroughly performed with the aid of numerical simulation. The effects of fractional-order kinetics have been explored where both linear and nonlinear dopant drift scenarios have been considered. Moreover, the emulation of memreactance with fractional-order kinetics by using the memristor and the effect of the fractional-order kinetics on the memreactance-based circuits have also been mentioned along with the extension of our results to the fractional-order memreactance.
Highlights
Apart from the basic circuit elements, the circuit elements with memory, i.e., memristor, meminductor, and memcapacitor, have been found by Leon Chua and his colleagues [1, 2]. e kinetics of the memristor has been further generalized in the fractional-order domain as proposed in previous works [3,4,5,6,7] by using the concept of fractional calculus
We analyze the memreactance with fractional-order kinetic transport in this work by means of fractional calculus
Novel fractional-order kinetics involved analytical expressions of memreactance in general; meminductances, memcapacitances, and related parameters due to both DC and periodic input waveforms including those with the nonlinear dopant drift which are rather complicated have been derived
Summary
Apart from the basic circuit elements, the circuit elements with memory, i.e., memristor, meminductor, and memcapacitor, have been found by Leon Chua and his colleagues [1, 2]. e kinetics of the memristor has been further generalized in the fractional-order domain as proposed in previous works [3,4,5,6,7] by using the concept of fractional calculus. E kinetics of the memristor has been further generalized in the fractional-order domain as proposed in previous works [3,4,5,6,7] by using the concept of fractional calculus By such a concept, the fractional derivative which is capable of including the effect of the past state, i.e., memory effect, of any system of the interested unlike the conventional derivative, has been used in the mathematical analysis. Motivated by the generalization of memristor kinetics, we generalize the kinetics of the meminductor and memcapacitor which are commonly referred to as memreactance [33,34,35] and have been adopted in many applications, e.g., electronic oscillator [36] and synaptic circuit [37, 38], in the fractional-order domain by applying the fractional calculus concept to the state equation of the memreactance and perform the modelling of such memreactance.
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