Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives

doi:10.1088/1674-1056/25/1/014501

中国物理B ›› 2016, Vol. 25 ›› Issue (1): 14501-014501.doi: 10.1088/1674-1056/25/1/014501

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

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

收稿日期:2015-06-26 修回日期:2015-08-28 出版日期:2016-01-05 发布日期:2016-01-05
通讯作者: Jing-Li Fu E-mail:sqfujingli@163.com
基金资助:
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).

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

Received:2015-06-26 Revised:2015-08-28 Online:2016-01-05 Published:2016-01-05
Contact: Jing-Li Fu E-mail:sqfujingli@163.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: conformable fractional derivative, Hamilton', s canonical equation, non-Noether conserved quantity

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.

Key words: conformable fractional derivative, Hamilton's canonical equation, non-Noether conserved quantity

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

45.10.Hj

02.30.Xx (Calculus of variations) 11.10.Ef (Lagrangian and Hamiltonian approach)

王琳莉, 傅景礼. Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives[J]. 中国物理B, 2016, 25(1): 14501-014501.

Lin-Li Wang (王琳莉) and Jing-Li Fu(傅景礼). Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives[J]. Chin. Phys. B, 2016, 25(1): 14501-014501.

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Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives

Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives

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