中文摘要：

提出并研究了非保守力学系统的分数阶Noether对称性及其守恒量。基于非保守系统的Hamilton原理,导出了分数阶模型下非保守系统的运动微分方程;根据分数阶Hamilton作用量在时间,广义坐标和广义速度的无限小群变换下的不变性,给出了非保守力学系统的分数阶Noether准对称性的定义和判据,建立了分数阶Noether准对称性与守恒量之间的联系,得到了分数阶Noether守恒量;最后,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 Noether symmetries and conserved quantities for non-conservative systems are proposed and studied with fractional model. Based on the Hamilton principle for the non-conservative systems,the fractional differential equations of motion are derived. With using the invariance of the fractional Hamilton action under the infinitesimal transformations of group which depends on the time,the generalized coordinates and velocities,the definition and the criterion of the fractional Noether generalized quasi-symmetry for the non-conservative systems are given. The relation between the fractional Noether quasi-symmetry and the conserved quantity is established,and the fractional conserved quantities are obtained. The special cases,which the generalized nonpotential forces do 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.