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本文引用格式:张宏彬.基于广义分数阶算子Birkhoff系统Noether定理[J].动力学与控制学报,2019,17(5):458~462;   Zhang Hongbin.Noether′s theorem of Birkhoffian systems with generalized fractional operators[J].Journal of Dynamics and Control,2019,17(5):458-462.
基于广义分数阶算子Birkhoff系统Noether定理    点此下载全文
张宏彬
巢湖学院 电子工程学院, 合肥 238000
基金项目:国家自然基金资助项目(10872037,11472063)
DOI:10.6052/1672-6553-2019-064
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.
关键词:分数阶Birkhoff系统,广义分数阶算子,Noether定理,对称性
Noether′s theorem of Birkhoffian systems with generalized fractional operators    Download Fulltext
Zhang Hongbin
Fund Project:
Abstract:
      A Noether type symmetry theorem for fractional Birkhoffian systems was proposed. Two new transformation 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.
Keywords:fractional Birkhoffian systems,generalized fractional operators,Noether′s theorem,symmetries
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