Analytical model of inverse memelement with fractional order kinetic

Abstract

In this work, the analytical model of inverse memelement with fractional order kinetic has been proposed. The classical yet noncontroversial Caputo fractional derivative has been adopted for modeling such fractional order kinetic due to its simplicity yet accuracy. Based on the proposed model, the analysis of fractional order kinetic inverse memristor has been thoroughly performed where both nonperiodic and periodic excitations have been considered. Analytical formulations of the related parameters, for example, the rate of changes of inverse memristance, area of inverse memristance loop, and area of pinched hysteresis loop, and so on, have been performed. The extension of the proposed model to the fractional inverse memelement has been performed where the fractional inverse memristor has been analyzed. We have found that the inverse memristor still behaves in an opposite manner to the memristor even with the fractional order kinetic. All obtained results have been found to be intuitively applicable to any inverse memelement. The equivalent circuit models of both fractional inverse memristor and fractional inverse memelement have also been presented. This work provides a comprehensive understanding on both inverse memelement with fractional order kinetic and fractional inverse memelement. The realization of the emulator of such inverse memelement with fractional order kinetic and the fractional inverse memelement emulator has been found to be interesting opened research questions.

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

“…The resulting model gives a fully explicit memory description beside being highly generic, well applied to the practical fractional‐order memristive circuit and extendable to the fractional‐order memreactance. Motivated our previous work, 60 which is based on the singular kernel fractional derivative and the achievement of fully explicit memory description, which is important to any circuit device with memory, by the usage of a nonsingular kernel operator, our tentative further study is to revisit such previous fractional‐order inverse memelement modeling attempt yet by employing a nonsingular kernel fractional derivative.…”

Generic analytical models of memelement and inverse memelement with time-dependent memory effects

“…For simplicity, we allow b = 0 for fixing ( x p ( α ( t )), y p ( α ( t ))) at (0, 0) and directly perform the integrations with respect to x ( t ) unlike those previous independent memory effect assumed works, e.g. Banchuin (2020) and Banchuin (2022), which the integrations have been performed with respect to t . Therefore, after some mathematical manipulation, we have: i.e.…”

“…For better modelling the memory effect, the fractional calculus-based analytical models of various memelement and inverse memelement have been proposed yet by assuming that such memory effect is time independent (Fouda and Radwan, 2015; Si et al , 2017; Banchuin, 2018; Banchuin, 2020; Khalil, 2020; Banchuin, 2022). However, it has been found that the memory effect of electrical circuit components including the memelement is in fact time dependent (Sheng et al , 2011; Sierociuk et al , 2012; Zhang et al , 2016, 2020; Atan, 2020; Li et al , 2021).…”

A unified modeling approach for characterization of fractional‐order memory elements

“…Both definitions are equivalent if . Obviously, models such as the “inverse memristors” in Banchuin 10 and Fouda et al 11 and some of the models in Maundy et al 12 do not fit into the classification, even though their hysteresis loops are pinched and frequency dependent. Thus, having a pinched frequency‐dependent hysteresis loop is not enough criteria to classify as a memristor: Frequency‐dependent pinched hysteresis are also observed in models of nonlinear capacitors and nonlinear inductors.…”