南京航空航天大学学报（英文版）2022，Vol.39Issue(4)：499-506,8.
分数阶Birkhoff系统的广义正则变换
Generalized Canonical Transformations for Fractional Birkhoffian Systems
摘要
Abstract
This paper presents fractional generalized canonical transformations for fractional Birkhoffian systems within Caputo derivatives. Firstly,based on fractional Pfaff-Birkhoff principle within Caputo derivatives,fractional Birkhoff's equations are derived and the basic identity of constructing generalized canonical transformations is proposed. Secondly,according to the fact that the generating functions contain new and old variables,four kinds of generating functions of the fractional Birkhoffian system are proposed,and four basic forms of fractional generalized canonical transformations are deduced. Then,fractional canonical transformations for fractional Hamiltonian system are given. Some interesting examples are finally listed.关键词
分数阶Birkhoff系统/广义正则变换/分数阶Pfaff-Birkhoff原理/母函数Key words
fractional Birkhoffian system/generalized canonical transformation/fractional Pfaff-Birkhoff principle/generating function分类
数理科学引用本文复制引用
张毅..分数阶Birkhoff系统的广义正则变换[J].南京航空航天大学学报（英文版）,2022,39(4):499-506,8.基金项目
This work was supported by the Na-tional Natural Science Foundations of China(Nos.  （）
11972241,11572212,11272227)and the Natural Science Foundation of Jiangsu Province(No.BK20191454). （No.BK20191454）
