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

doi:10.1088/1674-1056/23/12/124502

中国物理B ›› 2014, Vol. 23 ›› Issue (12): 124502-124502.doi: 10.1088/1674-1056/23/12/124502

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

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

周燕^a, 张毅^b

a College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
b College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

收稿日期:2014-05-13 修回日期:2014-06-03 出版日期:2014-12-15 发布日期:2014-12-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10972151 and 11272227) and the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province, China (Grant No. CXZZ11₀949).

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

Zhou Yan (周燕)^a, Zhang Yi (张毅)^b

a College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
b College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Received:2014-05-13 Revised:2014-06-03 Online:2014-12-15 Published:2014-12-15
Contact: Zhang Yi E-mail:weidiezh@gmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10972151 and 11272227) and the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province, China (Grant No. CXZZ11₀949).

摘要/Abstract

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 Birhoffian 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.

关键词: fractional Birkhoffian system, Noether', s theorem, fractional conserved quantity, Riemann–, Liouville fractional derivative

Abstract:

Key words: fractional Birkhoffian system, Noether', s theorem, fractional conserved quantity, Riemann–, Liouville fractional derivative

中图分类号: (Perturbation and fractional calculus methods)

45.10.Hj

45.20.Jj (Lagrangian and Hamiltonian mechanics) 11.30.Na (Nonlinear and dynamical symmetries (spectrum-generating symmetries)) 02.30.Xx (Calculus of variations)

周燕, 张毅. Noether's theorems of a fractional Birkhoffian system within Riemann–Liouville derivatives[J]. 中国物理B, 2014, 23(12): 124502-124502.

Zhou Yan (周燕), Zhang Yi (张毅). Noether's theorems of a fractional Birkhoffian system within Riemann–Liouville derivatives[J]. Chin. Phys. B, 2014, 23(12): 124502-124502.

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

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

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