Mathematics, Vol. 11, Pages 2997: A Numerical Solution and Comparative Study of the Symmetric Rossler Attractor with the Generalized Caputo Fractional Derivative via Two Different Methods

Mathematics, Vol. 11, Pages 2997: A Numerical Solution and Comparative Study of the Symmetric Rossler Attractor with the Generalized Caputo Fractional Derivative via Two Different Methods

Mathematics doi: 10.3390/math11132997

Authors: Mohamed Elbadri Mohamed A. Abdoon Mohammed Berir Dalal Khalid Almutairi

This study focuses on the solution of the rotationally symmetric Rossler attractor by using the adaptive predictor–corrector algorithm (Apc-ABM-method) and the fractional Laplace decomposition method (ρ-Laplace DM). Furthermore, a comparison between the proposed methods and Runge–Kutta Fourth Order (RK4) is made. It is discovered that the proposed methods are effective and yield solutions that are identical to the approximate solutions produced by the other methods. Therefore, we can generalize the approach to other systems and obtain more accurate results. In addition to this, it has been shown to be useful for correctly discovering examples via the demonstration of attractor chaos. In the future, the two methods can be used to find the numerical solution to a variety of models that can be used in science and engineering applications.