Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain-Reference-Cited by-同舟云学术

Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain

Published:2024-06-28 Issue:7 Volume:8 Page:383
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Zhang Wei¹^ORCID,Wang Haijing²,Zhang Haolu³⁴^ORCID,Li Zhiyuan⁵^ORCID,Li Xiaoyu⁵^ORCID

Affiliation:

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

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.

Funder

Doctor innovation research fund project of Jining Normal University

Publisher

MDPI AG

Link

https://www.mdpi.com/2504-3110/8/7/383/pdf