A Numerical Solution and Comparative Study of the Symmetric Rossler Attractor with the Generalized Caputo Fractional Derivative via Two Different Methods

Mohamed Elbadri, Mohamed A. Abdoon, Mohammed Berir and Dalal Khalid Almutairi ()
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Mohamed Elbadri: Department of Mathematics, Faculty of Sciences and Arts, Jouf University, Tubarjal 74713, Saudi Arabia
Mohamed A. Abdoon: Department of Basic Sciences (Mathematics), Deanship of Preparatory Year, Shaqra University, Riyadh 15342, Saudi Arabia
Mohammed Berir: Department of Mathematics, Faculty of Science, Bakht Al-Ruda University, Duwaym 999129, Sudan
Dalal Khalid Almutairi: Department of Mathematics, College of Education (Majmaah), Majmaah University, Al-Majmaah 11952, Saudi Arabia

Mathematics, 2023, vol. 11, issue 13, 1-11

Abstract: 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.

Keywords: numerical solution; the Apc-ABM method; ? -Laplace DM; generalized Caputo fractional derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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