Noether's theorems of a fractional Birkhoffian system within Riemann-Liouville derivatives

被引:11
作者
Yan, Zhou [1 ]
Yi, Zhang [2 ]
机构
[1] Suzhou Univ Sci & Technol, Coll Math & Phys, Suzhou 215009, Peoples R China
[2] Suzhou Univ Sci & Technol, Coll Civil Engn, Suzhou 215011, Peoples R China
基金
中国国家自然科学基金;
关键词
fractional Birkhoffian system; Noether's theorem; fractional conserved quantity; Riemann-Liouville fractional derivative; EULER-LAGRANGE EQUATIONS; FORMULATION; MECHANICS; TERMS;
D O I
10.1088/1674-1056/23/12/124502
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The Noether symmetry and the conserved quantity of a fractional Birkhoffian system are studied within the Riemann-Liouville fractional derivatives. Firstly, the fractional Birkhoff's equations and the corresponding transversality conditions are given. Secondly, from special to general forms, Noether's theorems of a standard Birkhoffian system are given, which provide an approach and theoretical basis for the further research on the Noether symmetry of the fractional Birkhoffian system. Thirdly, the invariances of the fractional Pfaffian action under a special one-parameter group of infinitesimal transformations without transforming the time and a general one-parameter group of infinitesimal transformations with transforming the time are studied, respectively, and the corresponding Noether's theorems are established. Finally, an example is given to illustrate the application of the results.
引用
收藏
页数:8
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