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Fractal Fract
Volume 8
Issue 7
10.3390/fractalfract8070383
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain

by
Wei Zhang
1,
Haijing Wang
2,
Haolu Zhang
3,4,
Zhiyuan Li
5,* and
Xiaoyu Li
5,*
1
Institute of Economics and Management, Jining Normal University, Ulanqab 012000, China
2
Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China
3
CCCC Comprehensive Planning and Design Institute Co., Ltd., Beijing 100024, China
4
School of Civil Engineering, Inner Mongolia University of Technology, Hohhot 010051, China
5
College of Date Science and Application, Inner Mongolia University of Technology, Hohhot 010080, China
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2024, 8(7), 383; https://doi.org/10.3390/fractalfract8070383
Submission received: 8 May 2024 / Revised: 15 June 2024 / Accepted: 26 June 2024 / Published: 28 June 2024
(This article belongs to the Special Issue Numerical Solutions of Caputo-Type Fractional Differential Equations and Derivatives)
Versions Notes

Abstract

The fractional-order Benjamin-Bona-Mahony-Burgers (BBMB) equation is a generalization of the classical BBMB equation. It’s dynamic behaviors is much more complex than that of the corresponding integer-order BBMB equation. The main purpose of this paper is to explore the dynamic behaviors of the fractional-order BBMB equations by using the Fourier spectral method. Firstly, the numerical solution is compared with the exact solution. It is proved that the proposed method is effective and high precision for solving the spatial fractional order BBMB equation. Then, some dynamical behaviors of fractional order BBMB equations are obtained by using the present method, and some novel fractal waves of the the fractional-order BBMB equation on unbounded domain are shown.
Keywords: dynamical behavior; Fractional Benjamin-Bona-Mahony-Burgers equation; fourier spectral method; numerical solution dynamical behavior; Fractional Benjamin-Bona-Mahony-Burgers equation; fourier spectral method; numerical solution

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MDPI and ACS Style

Zhang, W.; Wang, H.; Zhang, H.; Li, Z.; Li, X. Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain. Fractal Fract. 2024, 8, 383. https://doi.org/10.3390/fractalfract8070383

AMA Style

Zhang W, Wang H, Zhang H, Li Z, Li X. Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain. Fractal and Fractional. 2024; 8(7):383. https://doi.org/10.3390/fractalfract8070383

Chicago/Turabian Style

Zhang, Wei, Haijing Wang, Haolu Zhang, Zhiyuan Li, and Xiaoyu Li. 2024. "Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain" Fractal and Fractional 8, no. 7: 383. https://doi.org/10.3390/fractalfract8070383

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