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中文摘要：
提出并研究基于Caputo分数阶导数的含时滞的力学系统的Noether对称性与守恒量。建立了含时滞的非保守系统的分数阶运动微分方程;根据系统的含时滞的分数阶Hamilton作用量在无限小群变换下的泛函不变性,给出了含时滞的分数阶Noether对称变换,Noether准对称变换以及Noether广义准对称变换的定义判据;研究了含时滞的分数阶Noether对称性与守恒量之间的联系,并举例说明结果的应用。
英文摘要：
The Noether symmetries and the conserved quantities of a mechanical system with time delay based on Caputo fractional derivatives are proposed and studied. Firstly,the fractional Lagrange equations with time delay are established. Secondly,based upon the invariance of the fractional Hamilton action with time delay under the group of infinitesimal transformations,the fractional Noether symmetric transformations,the definitions and criteria of the Noether quasi-symmetric transformations and generalized Noether quasi-symmetric transformations with time delay are given. Finally,the relationship between the fractional symmetries and the fractional conserved quantities with time delay are studied. At the end,an example is given to illustrate the application of the results.
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