A new approximate method to the time fractional damped Burger equation-Reference-Cited by-同舟云学术

A new approximate method to the time fractional damped Burger equation

Published:2023 Issue:6 Volume:8 Page:13317-13324
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Liu Jian-Gen¹,Zhang Jian²

Affiliation:

1. School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, Jiangsu, China

2. School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

Abstract

<abstract><p>In this article, we study a Caputo fractional model, namely, the time fractional damped Burger equation. As the main mathematical tool of this article, we apply a new approximate method which is called the approximate-analytical method (AAM) to deal with the time fractional damped Burger equation. Then, a new approximate solution of this considered equation was obtained. It may be used to characterize nonlinear phenomena of the shallow water wave phenomena. Thereby, it provides a new window for us to find the time fractional damped Burger equation new evolutionary mechanism.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference23 articles.

1. D. J. Kaup, C. N. Alan, An exact solution for a derivative nonlinear Schrödinger equation, J. Math. Phys., 19 (1978), 798–801. https://doi.org/10.1063/1.523737

2. K. R. Rajagopal, A. S. Gupta, An exact solution for the flow of a non-Newtonian fluid past an infinite porous plate, Meccanica, 19 (1984), 158–160. https://doi.org/10.1007/BF01560464

3. X. Li, L. Wang, Z. Zhou, Y. Chen, Z. Yan, Stable dynamics and excitations of single-and double-hump solitons in the Kerr nonlinear media with $PT$-symmetric HHG potentials, Nonl. Dyn., 108 (2022), 4045–4056. https://doi.org/10.1007/s11071-022-07362-1

4. J. G. Liu, X. J. Yang, Y. Y. Feng, P. Cui, Nonlinear dynamic behaviors of the generalized (3+1)-dimensional KP equation, Z. Angew. Math. Mech., 102 (2022), e202000168. https://doi.org/10.1002/zamm.202000168

5. J. G. Liu, X. J. Yang, J. J. Wang, A new perspective to discuss Korteweg-de Vries-like equation, Phys. Lett. A, 451 (2022), 128429. https://doi.org/10.1016/j.physleta.2022.128429

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