|Table of Contents|

Noether quasi-symmetry theorems for fractional Hamilton system in terms of Caputo derivatives(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2018年03期
Page:
374-
Research Field:
Publishing date:

Info

Title:
Noether quasi-symmetry theorems for fractional Hamilton system in terms of Caputo derivatives
Author(s):
Liu Yandong1Zhang Yi2
1.School of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China; 2.School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China
Keywords:
Caputo derivatives fractional Hamilton system Noether quasi-symmetry non-conservative dynamical systems fractional conserved quantities
PACS:
O316
DOI:
10.14177/j.cnki.32-1397n.2018.42.03.018
Abstract:
The fractional conserved quantities and the Noether quasi-symmetry for a fractional Hamilton system in terms of Caputo derivatives are proposed and studied to explore the internal relation between symmetry and conserved quantities for non-conservative dynamical systems under fractional models. The definition and the criterion of Noether quasi-symmetry for the fractional Hamilton system in terms of Caputo derivatives are established. The Noether quasi-symmetry theorem is deduced by using the time-reparameterization method based on the concept of Frederico-Torres fractional conserved quantity. A fractional Hamilton system is taken as an example,and the quasi-symmetries of the system and corresponding fractional conserved quantities are given. The methods and results of this study are universal and can be extended to non-holonomic non-conservative dynamic systems,etc.

References:

[1] Podlubny I. Fractional differential equations[M]. San Diego,USA:Academic Press,1999. [2]孙文,孙洪广,李西成. 力学与工程问题的分数阶导数建模[M]. 北京:科学出版社,2010. [3]Riewe F. Nonconservative Lagrangian and Hamiltonian mechanics[J]. Physical Review E,1996,53(2):1890-1899. [4]Riewe F. Mechanics with fractional derivatives[J]. Physical Review E,1997,55(3):3581-3592. [5]Agrawal O P. Formulation of Euler-Lagrange equations for fractional variational problems[J]. Journal of Mathematical Analysis and Applications,2002,272(1):368-379 [6]AtanackoviAc’ T M,Konjik S,PilipoviAc’ S. Variational problems with fractional derivatives:Euler-Lagrange equations[J]. Journal of Physics A:Mathematical and Theoretical,2008,41(9):095201. [7]Baleanu D,Trujillo J I. A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives[J]. Communications in Nonlinear Science and Numerical Simulation,2010,15(5):1111-1115. [8]Frederico G S F,Torres D F M. A formulation of Noether’s theorem for fractional problems of the calculus of variations[J]. Journal of Mathematical Analysis and Applications,2007,334(2):834-846. [9]Frederico G S F,Torres D F M. Fractional optimal control in the sense of Caputo and the fractional Noether’s theorem[J]. International Mathematical Forum,2008,3(10):479-493. [10]Zhou Sha,Fu Hao,Fu Jingli. Symmetry theories of Hamiltonian systems with fractional derivatives[J]. Science China(Physics,Mechanics & Astronomy),2011,54(10):1847-1853. [11]Zhou Yan,Zhang Yi. Noether’s theorems of a fractional Birkhoffian system within Riemann-Liouville deriva-tives[J]. Chinese Physics B,2014,23(12):124502. [12]Zhang Yi,Zhai Xianghua. Noether symmetries and conserved quantities for fractional Birkhoffian systems[J]. Nonlinear Dynamics,2015,81(1-2):469-480. [13]Zhai Xianghua,Zhang Yi. Noether symmetries and conserved quantities for fractional Birkhoffian systems with time delay[J]. Communications in Nonlinear Science and Numerical Simulation,2016,36:81-97. [14]张毅,周燕. 基于Riesz导数的分数阶Birkhoff系统的Noether对称性与守恒量[J]. 北京大学学报(自然科学版),2016,52(4):658-668. Zhang Yi,Zhou Yan. Noether symmetry and conserved quantity for fractional Birkhoffian systems in terms of Riesz derivatives[J]. Acta Scientiarum Naturalium Universitatis Pekinensis,2016,52(4):658-668. [15]张毅,丁金凤. 基于El-Nabulsi分数阶模型的广义Birkhoff系统Noether对称性研究[J]. 南京理工大学学报,2014,38(3):409-413. Zhang Yi,Ding Jinfeng. Noether symmetries of generalized Birkhoff systems based on El-Nabulsi fractional model[J]. Journal of Nanjing University of Science and Technology,2014,38(3):409-413. [16]张毅. Caputo导数下分数阶Birkhoff系统的准对称性与分数阶Noether定理[J]. 力学学报,2017,49(3):693-702. Zhang Yi. Quasi-symmetry and Noether’s theorem for fractional Birkhoffian systems in terms of Caputo derivatives[J]. Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):693-702. [17]Malinowska A B,Torres D F M. Introduction to the fractional calculus of variations[M]. London,UK:Imperial College Press,2012.

Memo

Memo:
-
Last Update: 2018-06-30