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Noether’s Symmetries and Its Inverse for Fractional Logarithmic Lagrangian Systems

  • Jun Jiang , Yuqiang Feng EMAIL logo and Shuli Xu
Published/Copyright: March 18, 2019
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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.


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)


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Received: 2017-12-24
Accepted: 2018-02-07
Published Online: 2019-03-18

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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