分数阶Birkhoff系统的积分因子与守恒量  

Integrating factors and conserved quantities for fractional Birkhoffian system

作　　者：杨丽霞 张毅[2] YANG Lixia;ZHANG Yi(College of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou,Jiangsu 215009,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou,Jiangsu 215011,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009 [2]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《华中师范大学学报（自然科学版）》2020年第1期30-35,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11572212,11272227)

摘　　要：基于Riemann-Liouville导数的分数阶Birkhoff系统,提出了用积分因子理论寻找分数阶Birkhoff系统的守恒量的一种新思路.先由分数阶Birkhoff系统方程,给出了其积分因子的定义;其次,建立了由该系统积分因子理论得到的该系统守恒定理.为了进一步得到该系统的守恒量,给出了分数阶Birkhoff系统的广义Killing方程.分数阶Hamilton系统的守恒定理为本文特例.最后,举例说明结果的应用.In terms of Riemann-Liouville derivatives, a new method of finding the conserved quantities of fractional Birkhoff system by using the integral factor theory was proposed. Firstly, based on the fractional Birkhoffian equations, the definition of integrating factors was given. Secondly, the relation between the integrating factors and the conserved quantities was studied. The conservation theorem for the fractional Birkhoffian system was established. The results contain the conservation theorem for the fractional Hamiltonian system as special. At the end of the paper, an example was given to illustrate the application of the results.

关 键 词：分数阶Birkhoff系统 积分因子 守恒量 

分 类 号：O316[理学—一般力学与力学基础]