中文摘要：

提出并讨论了相空间中非保守力学系统的分数阶Noether对称性与守恒量。给出非保守Hamilton系统的分数阶Hamilton原理,建立了分数阶Hamilton正则方程;依据分数阶Hamilton作用量在无限小群变换下的不变性,得到了非保守相空间中分数阶Noether准对称变换的定义和判据,建立了非保守相空间中分数阶Noether准对称性与守恒量之间的联系,得到了相空间中分数阶守恒量;讨论了不存在非势广义力或规范函数等于零的特例,并举例说明结果的应用。

英文摘要：

The fractional Noether symmetries and fractional conserved quantities for a non-conservative system in phase space are proposed and discussed. Firstly,the fractional Hamilton canonical equations for the non-conservative system are established. Secondly,based upon the invariance of the fractional Hamilton action under the infinitesimal transformations of group,the definitions and criterion of fractional Noether quasi-symmetric transformations are obtained,then the relationship between a fractional Noether symmetry and a fractional conserved quantity of nonconservative system in phase space is established,and the fractional conserved quantity is obtained. Finally,the special cases,which the generalized nonpotential forces are not exit or the gauge function is equal to zero,are discussed. At the end,two examples are given to illustrate the application of the results.