Noether quasi-symmetry and conserved quantity for fractional Lagrange system in terms of Caputo derivatives

LIU Yandong; ZHANG Yi

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Noether quasi-symmetry and conserved quantity for fractional Lagrange system in terms of Caputo derivatives

更新时间：2023-12-11

- Noether quasi-symmetry and conserved quantity for fractional Lagrange system in terms of Caputo derivatives
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 57, Issue 3, Pages: 149-154(2018)
- 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：2018，
  
  Published Online：25 May 2018，
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LIU Yandong, ZHANG Yi. Noether quasi-symmetry and conserved quantity for fractional Lagrange system in terms of Caputo derivatives. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(3):149-154(2018)
DOI：

LIU Yandong, ZHANG Yi. Noether quasi-symmetry and conserved quantity for fractional Lagrange system in terms of Caputo derivatives. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(3):149-154(2018) DOI：

摘要

利用时间重新参数化方法，研究分数阶Lagrange系统的Noether准对称性与守恒量。首先，导出Caputo导数下的分数阶Lagrange方程。其次，给出分数阶Lagrange系统的分数阶守恒量的定义，在时间不变的特殊无限小变换群下给出分数阶Lagrange系统的Noether准对称性的定义和判据，并建立Noether准对称性定理。然后，利用时间重新参数化方法，给出在时间变化的一般无限小变换群下分数阶Lagrange系统的Noether准对称性的定义和判据，建立Noether准对称性定理。最后，举例说明结果的应用。

Abstract

The Noether quasi-symmetry and the conserved quantity for a fractional Lagrange system are studied by using the time-reparameterization method. Firstly

the fractional Lagrange equations in terms of Caputo derivatives are derived; Secondly

the definition of fractional conserved quantity for the fractional Lagrange system is given

and based on the special infinitesimal transformations of group without transforming time

the definition and the criterion of the Noether quasisymmetry for the fractional Lagrange system are given

and Noether's quasi-symmetry theorem is established; Finally

the definition and the criterion of Noether quasi-symmetry for the fractional Lagrange system under the general infinitesimal transformations of group with transforming time are given

Noether's quasi-symmetry theorem is derived by using the time-reparameterization method. An example is given to illustrate the application of the results.

关键词

时间重新参数化Caputo导数Lagrange系统Noether准对称性守恒量

Keywords

time-reparameterizationCaputo derivativeLagrange systemNoether quasi-symmetryconserved quantity

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Related Author

ZHU Jianqing

HE Shengxin

ZHANG Yi

ZHU Jianqing

HE Shengxin

ZHANG Yi

LONG Zixuan

Related Institution

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

 2．苏州科技学院土木工程学院

 苏州科技学院数理学院

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

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

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