This paper investigates the dynamical characteristics for meminductor and memcapacitor via fractal–fractional-order domain of Caputo–Fabrizio. A chaos circuit is modeled for the highly nonlinear and non-fractional governing differential equations of meminductor and meminductor for knowing the hyperchaos, abrupt chaos and coexisting attractors. The time-scale transformation on dynamical equations is invoked within non-classical approach through newly presented fractal–fractional differential operator of Caputo–Fabrizio. The nonlinear fractionalized governing differential equations of meminductor and meminductor have been simulated by means of Adams–Bashforth–Moulton method. In order to disclose the functionalities of capacitive and inductive elements so-called meminductor and memcapacitor, we specified the fractal–fractional differential operator of Caputo–Fabrizio in three categories as (i) variation in both fractional and fractal parameters, (ii) variation in fractional parameter keeping fractal parameters equal to one, and (iii) variation in fractal parameter keeping fractional parameters equal to one. At the end, our numerically simulated results elaborate that chaotic behavior and unpinched hysteresis loops obtained via fractal–fractional approach are more efficient than ordinary approach.

本文通过Caputo–Fabrizio的分形-分数阶域研究了磁导体和电容器的动力学特性。建模了一个混沌电路，用于对电感器和电感器的高度非线性和非分数阶控制微分方程进行建模，以了解超混沌，突然的混沌和共存吸引子。通过新提出的Caputo–Fabrizio分形-分数微分算子，在非经典方法中调用了动力学方程的时标转换。利用Adams–Bashforth–Moulton方法模拟了磁化系数和磁化系数的非线性分数阶控制微分方程。为了揭示电容性和电感性元件的功能，即所谓的电感器和薄膜电容器，我们将Caputo–Fabrizio的分形-分形微分算子指定为三类：（i）分形和分形参数的变化，（ii）分形参数的变化，使分形参数等于1，以及（iii）分形参数的变化分数参数等于1。最后，我们的数值模拟结果详细说明了通过分形–分形方法获得的混沌行为和无捏滞后回线比普通方法更有效。