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Advances in Mechanical Engineering Volume 11 ,Issue 7 ,2019-07-01
The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators
Research Article
Muhammad Altaf Khan 1
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DOI:10.1177/1687814019866540
Received 2019-3-17, accepted for publication 2019-7-9, Published 2019-7-9
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摘要

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter α . We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

关键词

numerical simulation;Atangana–Baleanu derivative;Caputo–Fabrizio derivative;New chaotic system

授权许可

© The Author(s) 2019
This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).

通讯作者

Muhammad Altaf Khan.Muhammad Altaf Khan, Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan. .Email:altafdir@gmail.com

推荐引用方式

Muhammad Altaf Khan. The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators. Advances in Mechanical Engineering ,Vol.11, Issue 7(2019)

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