Lie symmetry and conserved quantity of fractional Lagrange system based on El-Nabulsi models

ZHANG Xiaocai; ZHANG Yi

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Lie symmetry and conserved quantity of fractional Lagrange system based on El-Nabulsi models

更新时间：2023-12-11

- Lie symmetry and conserved quantity of fractional Lagrange system based on El-Nabulsi models
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 55, Issue 3, Pages: 97-101(2016)
- 作者机构：
  
  1. 苏州科技大学数理学院,江苏,苏州,215009
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2016，
  
  Published Online：25 May 2016，
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ZHANG Xiaocai, ZHANG Yi. Lie symmetry and conserved quantity of fractional Lagrange system based on El-Nabulsi models. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 55(3):97-101(2016)
DOI：

ZHANG Xiaocai, ZHANG Yi. Lie symmetry and conserved quantity of fractional Lagrange system based on El-Nabulsi models. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 55(3):97-101(2016) DOI：

摘要

研究基于El-Nabulsi模型的分数阶Lagrange系统的Lie对称性与守恒量。基于按Riemann-Liouville积分拓展的类分数阶变分问题导出El-Nabulsi模型的DAlembert-Lagrange原理，得到系统的运动微分方程；给出分数阶Lie对称性的定义和判据，建立了Lie对称性确定方程，并提出广义Hojman定理，给出广义Hojman守恒量存在的条件及其形式；最后，建立了广义Noether定理，给出分数阶Lie对称性导致Noether守恒量的条件及其形式，并给出两个算例以说明结果的应用。

Abstract

The Lie symmetry and the conserved quantity of fractional Lagrange system based on El-Nabulsi models are studied. Firstly

the D-Alembert-Lagrange principle of the El-Nabulsi models is deduced based on the fractional action-like variational problem which is expanded by the Riemann-Liouville integral

and the differential equations of motion of the system are obtained. Secondly

the definition and the criterion of the Lie symmetry are given

the determination equations of the Lie symmetry of the system are established

and the generalized Hojman theorem is put forward. At the same time

the existence condition and the form of the generalized Hojman conserved quantity are obtained. Then

the generalized Noether theorem is established

the existence condition and the form of the Noether conserved quantity led by the Lie symmetry are given. Finally

two examples are given to illustrate the application of the results.

关键词

分数阶Lagrange系统El-Nabulsi模型Lie对称性守恒量

Keywords

fractional Lagrange systemEl-Nabulsi modelLie symmetryconserved quantity

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Related Author

LIN Wei

ZHU Jianqing

ZHANG Yi

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DING Jinfeng

ZHANG Yi

JIN Shixin

Related Institution

College of Mathematics and Physics, Jiangsu University of Science and Technology

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou

College of Civil Engineering, Suzhou University of Science and Technology

College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China

College of Mathematics and Physics, Suzhou University of Science and Technology

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