Generalized modeling of the fractional-order memcapacitor and its character analysis

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.

Section: Extension To the Fractional Inverse Memelementmentioning

confidence: 99%

“…Therefore, we further extend 11 by using the concept of fractional calculus in order to obtain such relationship in the context of this research. Since the fractional derivative has been applied for extending the input–output relationship of the memelement to fractional order, 44,45 we employ the fractional integral for the inverse memelement; thus, we have

y_{F} ((), t) goodbreak= ((), \sum_{k = 0}^{K} {(\frac{{({\overset{true¯}{h}}_{k})}^{1 / k}}{Γ (1 - α)} \int_{0}^{t} {((), t goodbreak- τ)}^{- α} \frac{dx (τ)}{italicdτ} d τ])}^{k}) J_{t}^{β} ([], x ((), t))

where

J_{t}^{β} ([], \begin{array}{c}  \end{array})

and y F ( t ), respectively, denote the β th order fractional integral operator and response of the fractional memelement.…”

Section: Extension To the Fractional Inverse Memelementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical model of inverse memelement with fractional order kinetic

Banchuin

2022

“…Various memelements models in IO and FO have since captured the attention of researchers. 3,[9][10][11] They have also been used as nonlinear components in studies like neuromorphic and multi-level memory systems, 12,13 memristorbased Neural-Networks, 14 chaotic and oscillator circuits, [15][16][17][18] logic and combinatoral circuits, [19][20][21] and even as nonlinear loads in DC-DC converters in literature. 22,23 It is thus important to fully understand their underlying properties.…”

Section: Introductionmentioning

confidence: 99%

Conditions for realization of multiple pinch‐off points in generalized fractional‐order memory elements

et al. 2023

Self Cite

SummaryMemelements (memristor, meminductor, and memcapacitor) have gained wide interests due to their useful hysteresis and nonlinear properties. In this work, fractional‐order current‐controlled memelements are modeled using an ‐order polynomial. By decomposing the ‐order polynomial into some sets of current‐controlled functions, we were able to theoretically analyze and establish the general conditions necessary for all memelements' voltage‐current dynamics to create up to number of lobes and hence pinch‐off points in their hysteresis. The exact coordinate locations of the pinch‐off points on the ‐axis and ‐axis are calculated in all cases. The observations made in this work are novel and contributes to how all multiple‐lobed memory elements are analyzed. A general emulator circuit is then designed to verify the theoretical deductions, the emulator output agrees with the numerical results.

“…While previous works [16][17][18][19][20][21] have presented several analytical and practical studies on CPEs, only recently did Fouda et al 32 looked into the energy relations of CPEs (supercapacitors and fractional-order coils). Also, memelements in integer an fractional orders have been analyzed in notable works, 5,22,25,26,31,[33][34][35][36] and previous studies 23,24,[27][28][29][30]37 even focused on designing different forms of memelement emulator circuits. In this work, however, we generalize the relation of these ideal memelements and the CPEs using a single mathematical model with three different FO indexes, which enables more comparative studies.…”

Section: Introductionmentioning

confidence: 99%

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

Oresanya

et al. 2023

Self Cite

SummaryA generalized mathematical model for current‐controlled fractional‐order memory elements is introduced in this work. The model characterizes constant‐phase elements (CPEs) when its nonlinearity parameter is zero (); otherwise (), it characterizes three main types of fractional‐order memory elements (memristor, meminductor, and memcapacitor). Time‐domain analyses of the voltage and energy relations of the model are derived and verified via numerical and circuit simulations. Some new deductions on the effects of the respective fractional‐order values are recorded: Each fractional‐order element transposes into their corresponding resistive or memristive properties as their fractional‐order values are varied; the meminductor's voltage response have undesired initial trails due to the fractional differentiator; the hysteresis loop of the meminductor is only pinched when its fractional‐order values are unequal. A new CPE emulator circuit is designed, and a generalized memelement emulator is also designed and verified in PSpice circuit simulator: Circuit simulation results confirm the numerical analysis in all cases.