Caputo导数下分数阶Lagrange系统的Noether准对称性与守恒量

Noether quasi-symmetry and conserved quantity for fractional Lagrange system in terms of Caputo derivatives

利用时间重新参数化方法,研究分数阶Lagrange系统的Noether准对称性与守恒量。首先,导出Caputo导数下的分数阶Lagrange方程。其次,给出分数阶Lagrange系统的分数阶守恒量的定义,在时间不变的特殊无限小变换群下给出分数阶Lagrange系统的Noether准对称性的定义和判据,并建立Noether准对称性定理。然后,利用时间重新参数化方法,给出在时间变化的一般无限小变换群下分数阶Lagrange系统的Noether准对称性的定义和判据,建立Noether准对称性定理。最后,举例说明结果的应用。

The Noether quasi-symmetry and the conserved quantity for a fractional Lagrange studied by using the time-reparameterization method. Firstly, the fractional Lagrange equations in terms of Caputo derivatives are derived; Secondly, the definition of fractional conserved quantity for the fractional Lagrange system is given, and based on the special infinitesimal transformations of group without transforming time, the definition and the criterion of the Noether quasi-symmetry for the fractional Lagrange system are given, and Noether＇s quasi-symmetry theorem is established; Finally, the definition and the criterion of Noether quasi-symmetry for the fractional Lagrange system under the general infinitesimal transformations of group with transforming time are given , Noethds quasi-symmetry theorem is derived by using the time-reparameterization method. An example is given to illustrate the application of the results.