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

作     者：Jun JIANG Yuqiang FENG Shuli XU 

作者机构：School of ScienceWuhan University of Science and Technology Hubei Province Key Laboratory of Systems Science in Metallurgical ProcessWuhan University of Science and Technology 

出 版 物：《Journal of Systems Science and Information》 (系统科学与信息学报（英文）)

年 卷 期：2019年第10卷第1期

页      面：90-98页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 071101[理学-系统理论] 

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

主　　题：fractional derivatives nonstandard Lagrangians Hamilton’s principle Noether’s theorem Noether’s inverse theorem 

摘      要：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.