A new approximate method to the time fractional damped Burger equation

Jian-Gen Liu; Jian Zhang; Jian-Gen Liu; Jian Zhang

doi:10.3934/math.2023674

AIMS Mathematics

2023, Volume 8, Issue 6: 13317-13324. doi: 10.3934/math.2023674

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A new approximate method to the time fractional damped Burger equation

Jian-Gen Liu ^{1
,
,},
Jian Zhang ²

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

Received: 08 February 2023 Revised: 18 March 2023 Accepted: 20 March 2023 Published: 04 April 2023
MSC : 35L05, 35Qxx

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.
- time fractional damped Burger equation,
- approximate-analytical method,
- approximate solution,
- Caputo fractional derivative,
- nonlinear phenomena
Citation: Jian-Gen Liu, Jian Zhang. A new approximate method to the time fractional damped Burger equation[J]. AIMS Mathematics, 2023, 8(6): 13317-13324. doi: 10.3934/math.2023674

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Abstract

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.

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