Abstract
Chua’s circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua’s circuit is obtained by transforming the classical model of Chua’s circuit into novel forms of various fractional derivatives. The new obtained system is then named fractional Chua’s circuit model. The modified system is then analyzed by the optimal perturbation iteration method. Illustrations are given to show the applicability of the algorithms, and effective graphics are sketched for comparison purposes of the newly introduced fractional operators.
Highlights
Over the last two decades, the interest in fractional derivatives and their implementations has been intensified
In order to overcome these problems, Baleanu and Atangana came up with new fractional operators, namely Atangana–Baleanu (AB) derivative operators, with fractional order based upon the recognized Mittag-Leffler function [1]
Modeling and analysis of the fractional HBV model with the Atangana–Baleanu derivative have been studied in [3]. These operators have been applied to nanofluids to enhance the performance of solar collectors, and the same researchers have compared Atangana–Baleanu and Caputo–Fabrizio fractional models [4]
Summary
Over the last two decades, the interest in fractional derivatives and their implementations has been intensified. Most of the dynamical systems have long-range temporal memory Modeling of these systems with fractional-order derivatives has more advantages than classical models such as in [36,37,38]. The jerk model has been investigated using the concept of fractional derivative, and a chaotic attractor has been obtained with the system order as low as 2.1 [40]. In this paper we try to solve the above system by using the optimal perturbation iteration algorithms (OPIAs) and different fractional operators This technique has been applied to many types of ODEs and PDEs such as Bratu-type [43], Riccati differential equation [44], heat transfer equations [45], nonlinear systems [46], Lane–Emden types [47], generalized regularized long wave equations [48].
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