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

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

Abstract

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.

Keywords: fractional Birkhoffian system Noether' s theorem fractional conserved quantity Riemann– Liouville fractional derivative

Received: 13 May 2014
Revised: 03 June 2014
Accepted manuscript online:

PACS:	45.10.Hj	(Perturbation and fractional calculus methods)
	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	11.30.Na	(Nonlinear and dynamical symmetries (spectrum-generating symmetries))
	02.30.Xx	(Calculus of variations)

Fund:

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).

Corresponding Authors: Zhang Yi
E-mail: weidiezh@gmail.com

Cite this article:

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


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

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