Noether's Symmetries and Its Inverse for Fractional Logarithmic Lagrangian Systems
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Journal of Systems Science and Information  2019, Vol. 7 Issue (1): 90-98    DOI: 10.21078/JSSI-2019-090-09
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Noether's Symmetries and Its Inverse for Fractional Logarithmic Lagrangian Systems
Jun JIANG1, Yuqiang FENG1, Shuli XU2
1. School of Science, Wuhan University of Science and Technology, Wuhan 430065, China;
2. School of Science, Wuhan University of Science and Technology, Wuhan 430065, China;Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, China
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Abstract 

In this paper, Noether's theorem and its inverse theorem are proved for the fractional variational problems based on logarithmic Lagrangian systems. The Hamilton principle of the systems is derived. And the definitions and the criterions of Noether's symmetry and Noether's quasi-symmetry of the systems based on logarithmic Lagrangians are given. The intrinsic relation between Noether's symmetry and the conserved quantity is established. At last an example is given to illustrate the application of the results.

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Jun JIANG
Yuqiang FENG
Shuli XU
Key wordsfractional derivatives   nonstandard Lagrangians   Hamilton's principle   Noether's theorem   Noether's inverse theorem     
Received: 2017-12-24;
Fund:

Supported by the National Natural Science Foundation of China (61473338) and Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Y201514)

Corresponding Authors: Yuqiang FENG   
 E-mail: yqfeng6@126.com
Cite this article:   
Jun JIANG,Yuqiang FENG,Shuli XU. Noether's Symmetries and Its Inverse for Fractional Logarithmic Lagrangian Systems[J]. Journal of Systems Science and Information, 2019, 7(1): 90-98.
URL:  
http://123.57.41.99/Jwk_si/EN/10.21078/JSSI-2019-090-09     or     http://123.57.41.99/Jwk_si/EN/Y2019/V7/I1/90
 
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