分数阶Birkhoff系统基于Caputo导数的Noether对称性与守恒量  

NOETHER SYMMETRY AND CONSERVED QUANTITY FOR FRACTIONAL BIRKHOFFIAN SYSTEMS IN TERMS OF CAPUTO DERIVATIVES

作　　者：周燕[1,2] 张毅[3] 

机构地区：[1]苏州科技学院数理学院,苏州215009 [2]苏州市工业园区娄葑学校,苏州215021 [3]苏州科技学院土木工程学院,苏州215011

出　　处：《动力学与控制学报》2015年第6期410-417,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10972151;11272227);江苏省普通高校研究生科研创新计划资助项目(CXZZ11_0949)~~

摘　　要：在Caputo分数阶导数下研究分数阶Birkhoff系统的Noether对称性与守恒量.首先,定义Caputo分数阶导数下的分数阶Pfaff作用量,建立分数阶Birkhoff方程及其相应的横截性条件;其次,基于Pfaff作用量在无限小变换下的不变性,分别在时间不变和时间变化的无限小变换下,给出了不变性条件.基于Frederico和Torres的分数阶守恒量概念,建立了分数阶Birkhoff系统的Noether定理,揭示了分数阶Noether对称性与分数阶守恒量之间的内在联系.This paper studies the Noether symmetry and corresponding conserved quantity for fractional Birkhoffian systems in terms of Caputo fractional derivatives. Firstly, the fractional Pfaff action is defined within Caputo fractional derivatives. The fractional Birkhoff＇ s equations and corresponding transversality conditions are also established. Secondly, based on the invariance of the Pfaff action under the infinitesimal transformations, the conditions of invariance are given under a special one-parameter group of infinitesimal transformations without transforming the time as well as a general one-parameter group with transforming the time, respectively. Finally, according to the notion of fractional conserved quantity presented by Frederico and Torres, the Noether theorem for the fractional Birkhoffian systems is constructed, which states the relationship between a fractional Noether symmetry and a fractional conserved quantity.

关 键 词：分数阶Birkhoff系统 分数阶Noether对称性 分数阶守恒量 分数阶Pfaff作用量 CAPUTO分数阶导数 

分 类 号：O316[理学—一般力学与力学基础]