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

Jiang Jun (), Feng Yuqiang () and Xu Shuli ()
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Jiang Jun: School of Science, Wuhan University of Science and Technology, Wuhan430065, China
Feng Yuqiang: School of Science, Wuhan University of Science and Technology, Wuhan430065, China
Xu Shuli: School of Science, Wuhan University of Science and Technology, Wuhan430065, China

Journal of Systems Science and Information, 2019, vol. 7, issue 1, 90-98

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.

Keywords: fractional derivatives; nonstandard Lagrangians; Hamilton’s principle; Noether’s theorem; Noether’s inverse theorem (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:7:y:2019:i:1:p:90-98:n:6

DOI: 10.21078/JSSI-2019-090-09

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