Analysis of Memreactance with Fractional Kinetics

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.

Analytical model of inverse memelement with fractional order kinetic

“…19,20 By applying the fractional calculus concept, the modeling and analysis attempts of memelement with fractional order kinetic have been proposed in many previous works. [21][22][23][24] Since a novel circuit element with memory, namely, the inverse memristor, has been recently proposed [25][26][27] and often cited [28][29][30][31] where its behavior can be found/emulated in practice, [32][33][34][35] similarly to the memristor, it is worthy to introduce the fractional order kinetic to this new element and performing the modeling/analysis. By this motivation, the analytical model of inverse memelement which is a super set of inverse memristor, with fractional order kinetic, has been derived in this work.…”

“…Since the inverse memelement may employs fractional order input-output relationship similarly to the memelement, [41][42][43][44][45] the extension of the proposed model to such inverse memelement with fractional order input-output relationship or the fractional inverse memelement in short has been performed similarly to our previous work on the memreactance with fractional order kinetic. 24 The fractional inverse memristor has been analyzed. The equivalent circuit models of fractional inverse memelement have also been presented where those of the fractional inverse meminductor and memcapacitor are more complicated than those of the fractional inverse memresistor.…”

“…The applications of fractional calculus concept and fractional derivatives can be found in many research areas, for example, biomedical engineering, 10,11 control system, 12–14 electrical/electronic engineering, 15–18 and plasma physics 19,20 . By applying the fractional calculus concept, the modeling and analysis attempts of memelement with fractional order kinetic have been proposed in many previous works 21–24 …”

“…Since the inverse memelement may employs fractional order input–output relationship similarly to the memelement, 41–45 the extension of the proposed model to such inverse memelement with fractional order input–output relationship or the fractional inverse memelement in short has been performed similarly to our previous work on the memreactance with fractional order kinetic 24 . The fractional inverse memristor has been analyzed.…”

A novel generalized fractional‐order memristor model with fully explicit memory description

“…The detailed dynamical analysis and analysis of the Lissajous patterns have also been presented. Moreover, an application to the fractional-order memristor-based circuit and the extension to the fractional-order meminductor and fractional-order memcapacitor, 46,47 which are commonly referred to as the fractional-order memreactance, have also been presented. In summary, this is the first time that a nonsingular kernel fractional derivative has been applied to the fractional-order memristor modeling, and the resulting model with a fully explicit memory description has been proposed.…”