Noether Symmetry and Conserved Quantity for a Fractional#br#
Actionlike Variational Problem in Phase Space

ZHANG Yi

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Noether Symmetry and Conserved Quantity for a Fractional#br# Actionlike Variational Problem in Phase Space

更新时间：2023-12-11

- Noether Symmetry and Conserved Quantity for a Fractional#br# Actionlike Variational Problem in Phase Space
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 52, Issue 4, Pages: 45-50(2013)
- 作者机构：
  
  苏州科技学院土木工程学院,江苏,苏州,215009
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2013，
  
  Published Online：25 July 2013，
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ZHANG Yi. Noether Symmetry and Conserved Quantity for a Fractional#br# Actionlike Variational Problem in Phase Space. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 52(4):45-50(2013)
DOI：

ZHANG Yi. Noether Symmetry and Conserved Quantity for a Fractional#br# Actionlike Variational Problem in Phase Space. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 52(4):45-50(2013) DOI：

摘要

基于El-Nabulsi提出的分数阶动力学建模方法，即类分数阶变分方法，研究相空间中类分数阶变分问题与Noether对称性和守恒量。建立了相空间中类分数阶变分问题，得到了类分数阶Hamilton正则方程；基于类分数阶Hamilton作用量在无限小群变换下的不变性，提出了相空间中类分数阶Noether（准）对称变换的定义和判据；给出了类分数阶Hamilton系统的Noether定理，建立了类分数阶Noether对称性与守恒量之间的内在关系，并举例说明结果的应用。

Abstract

The Noether symmetry and the conserved quantity for a fractional actionlike variational problem in phase space are studied based on the method of fractional dynamics modeling presented by El-Nabulsi

namely fractional actionlike variational approach. First

the fractional actionlike variational problem in phase space is established

and the fractional actionlike Hamilton canonical equations are obtained. Secondly

the definitions and criteria of the fractional actionlike Noether (quasi)symmetrical transformations are presented in terms of the invariance of the fractional actionlike integral of Hamilton under the infinitesimal transformation of group. Finally

the Noether theorems for the fractional actionlike Hamiltonian system are given

the relationship between the Noether symmetry and the conserved quantity of the system is established.An example is given to illustrate the application of the results.

关键词

类分数阶变分方法Noether定理相空间类分数阶对称变换守恒量

Keywords

fractional action-like variational approachNoether theoremphase spacefractional action-like symmetrical transformationconserved quantity

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Related Institution

．苏州科技学院数理学院

 2．苏州科技学院土木工程学院

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

广东省建筑科学研究院

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