相空间中类分数阶变分问题的Noether对称性与守恒量

Noether Symmetry and Conserved Quantity for a Fractional Action-like Variational Problem in Phase Space

基于El-Nabulsi提出的分数阶动力学建模方法,即类分数阶变分方法,研究相空间中类分数阶变分问题与Noether对称性和守恒量。建立了相空间中类分数阶变分问题,得到了类分数阶Hamilton正则方程;基于类分数阶Hamilton作用量在无限小群变换下的不变性,提出了相空间中类分数阶Noether(准)对称变换的定义和判据;给出了类分数阶Hamilton系统的Noether定理,建立了类分数阶Noether对称性与守恒量之间的内在关系,并举例说明结果的应用。

The Noether symmetry and the conserved quantity for a fractional action-like variational prob- lem in phase space are studied based on the method of fractional dynamics modeling presented by E1- Nabulsi, namely fractional action-like variational approach. First, the fractional action-like variational problem in phase space is established, and the fractional action-like Hamilton canonical equations are ob- tained. Secondly, the definitions and criteria of the fractional action-like Noether （quasi-） symmetrical transformations are presented in terms of the invariance of the fractional action-like integral of Hamilton under the infinitesimal transformation of group. Finally, the Noether theorems for the fractional action- like Hamiltonian system are given, the relationship between the Noether symmetry and the conserved quantity of the system is established. An example is given to illustrate the application of the results.