Numerical Study and Chaotic Analysis of Meminductor and Memcapacitor Through Fractal–Fractional Differential Operator

Abstract

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.