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Chin. Phys. B, 2016, Vol. 25(1): 014501    DOI: 10.1088/1674-1056/25/1/014501
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives

Lin-Li Wang (王琳莉) and Jing-Li Fu(傅景礼)
Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract  In this paper, we present the fractional Hamilton's canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton's canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results.
Keywords:  conformable fractional derivative      Hamilton's canonical equation      non-Noether conserved quantity     
Received:  26 June 2015      Published:  05 January 2016
PACS:  45.10.Hj (Perturbation and fractional calculus methods)  
  02.30.Xx (Calculus of variations)  
  11.10.Ef (Lagrangian and Hamiltonian approach)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272287 and 11472247), the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT13097), and the Key Science and Technology Innovation Team Project of Zhejiang Province, China (Grant No. 2013TD18).
Corresponding Authors:  Jing-Li Fu     E-mail:  sqfujingli@163.com

Cite this article: 

Lin-Li Wang (王琳莉) and Jing-Li Fu(傅景礼) Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives 2016 Chin. Phys. B 25 014501

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