基于广义分数阶算子Birkhoff系统Noether定理  

NOETHER’S THEOREM OF BIRKHOFFIAN SYSTEMS WITH GENERALIZED FRACTIONAL OPERATORS

作　　者：张宏彬 Zhang Hongbin(College of Electronic Engineering,Chaohu University,Hefei 238000,China)

机构地区：[1]巢湖学院电子工程学院

出　　处：《动力学与控制学报》2019年第5期458-462,共5页Journal of Dynamics and Control

基　　金：国家自然基金资助项目(10872037,11472063)~~

摘　　要：本文就广义分数阶导数算子,提出两个新的“变换公式”,将其应用于分数阶Birkhoff系统,并导出分数阶Birkhoff系统的Noether定理.这个定理提供了一个计算分数阶Birkhoff系统运动常数的方法,克服了先前文献研究分数阶动力学系统守恒量的一些缺陷,并在文末给出两个推论.A Noether type symmetry theorem for fractional Birkhoffian systems was proposed.Two new transfor mation formulas for generalized fractional derivative operators were derived,and thus,the constants of motion that are valid along Birkhoffian equations extremals were obtained.This theorem provides an explicit algorithmic way to compute a constant for any Birkhoffian systems.It overcomes some defects of existing methods for studying the conserved quantities of fractional order dynamical systems.Finally,two corollaries were given.

关 键 词：分数阶Birkhoff系统 广义分数阶算子 NOETHER定理 对称性 

分 类 号：O31[理学—一般力学与力学基础]