Electronic�realization�of�the�fractional-Order�system

Mathematical Problems in Engineering

2020

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.

Section: Introductionmentioning

confidence: 99%

Analysis of Memreactance with Fractional Kinetics

Mathematical Problems in Engineering

2020

“…Since the order of the parasitic fractional element can be fractional, the fractional differential equation (FDE), which its order can be fractional, must be used for modeling the memristor and the memristor-based circuits under the effects of such parasitic fractional element instead of the ordinary differential equation (ODE) which its order is strictly integer. e FDE is the extension of the ODE in the domain of fractional calculus which plays a fundamental role in various engineering fields, e.g., bioengineering, control theory, electronics, robotics, and signal processing [14][15][16][17][18]. e analytical solutions of the formulated FDEs, which are nonlinear, have been determined by using the Adomian decomposition method [19].…”

Section: Introductionmentioning

confidence: 99%

Effects of Parasitic Fractional Elements to the Dynamics of Memristor

Journal of Electrical and Computer Engineering

2019

In this research, we study the effects of the parasitic fractional elements to the dynamic of the memristor where both flux- and charge-controlled memristors have been considered. For doing so, the fractional differential equation-based approach has been used for modeling the memristor and the memristor-based circuits under the effects of the parasitic fractional elements where the resulting equations have been solved both analytically and numerically. From the obtained solutions and simulations, the effects of the parasitic fractional elements to the dynamic of the memristor have been studied. We have found that the parasitic fractional elements cause the charge and flux decay of the memristor similarly to the conventional parasitic elements. Moreover, the impasse points of the phase portraits between flux and charge of the memristor-based circuits can also be broken by the parasitic fractional elements. The effects of the order and the nonlinearity of the parasitic fractional elements have also been studied.

“…Recently, a state-of-the-art electrical circuit element, namely, fractional order memristor, is often cited. This circuit element can be obtained from the generalization of the 4th electrical circuit element, namely, memristor, that has been theoretically found by Leon Chua since 1971 [1], by using the concept of fractional calculus which have been adopted in various disciplines, e.g., biomedical engineering [2,3], control system [4][5][6], and electronic engineering [7][8][9]. For decades after Chua proposed his original work, the memristor has been practically realized by a research group in Hewlett Packard (HP) labs [10] in 2008.…”

Section: Introductionmentioning

confidence: 99%

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

Active and Passive Electronic Components

2018

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.