南京航空航天大学学报（英文版）2021，Vol.38Issue(1)：84-95,12.
基于准分数阶模型的分数阶Birkhoff动力学及其Lie对称性
Fractional Birkhoffian Dynamics Based on Quasi-fractional Dynamics Models and Its Lie Symmetry
摘要
Abstract
In order to investigate the dynamic behavior of non-conservative systems, the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied. The quasi-fractional dynamics model here refers to the variational problem based on the definition of Riemann-Liouville fractional integral(RLFI),the variational problem based on the definition of extended exponentially fractional integral(EEFI),and the variational problem based on the definition of fractional integral extended by periodic laws(FIEPL). First,the fractional Pfaff-Birkhoff principles based on quasi-fractional dynamics models are established,and the corresponding Birkhoff's equations and the determining equations of Lie symmetry are obtained. Second,for fractional Birkhoffian systems based on quasi-fractional models,the conditions and forms of conserved quantities are given,and Lie symmetry theorems are proved. The Pfaff-Birkhoff principles,Birkhoff's equations and Lie symmetry theorems of quasi-fractional Birkhoffian systems and classical Birkhoffian systems are special cases of this article. Finally,some examples are given.关键词
准分数阶动力学模型/Lie对称性/守恒量/分数阶Birkhoff系统/Riemann-Liouville导数Key words
quasi-fractional dynamics model/Lie symmetry/conserved quantity/fractional Birkhoffian system/Riemann-Liouville derivative分类
数理科学引用本文复制引用
贾云碟,张毅..基于准分数阶模型的分数阶Birkhoff动力学及其Lie对称性[J].南京航空航天大学学报（英文版）,2021,38(1):84-95,12.基金项目
This work was supported by the Na?tional Natural Science Foundation of China(Nos.11972241,11572212 and 11272227)and the Natural Sci?ence Foundation of Jiangsu Province(No.BK20191454). （Nos.11972241,11572212 and 11272227）
