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中文摘要：
20世纪90年代以来,分数阶微积分理论与方法已被广泛地应用到自然科学和社会科学的各个领域,动力学与控制是其中的一个重要应用领域.为了进一步研究分数阶力学系统,本文基于Riemann-Liouville分数阶导数,讨论了分数阶Birkhoff系统Noether对称性的摄动与绝热不变量问题.首先,给出分数阶Birkhoff系统的运动微分方程及精确不变量;其次,给出绝热不变量的定义,并研究分数阶Birkhoff系统的绝热不变量;文末举例说明结果的应用.
英文摘要：
Since the 1990s, the theory and method of fractional calculus have been widely applied to various fields of natural science and social science, of which dynamics and control is an important application field. In order to further study the fractional dynamical systems, the perturbation to Noether symmetry and adiabatic invariants for fractional Birkhoffian systems are investigated in this paper based on the Riemann-Liouville fractional derivatives. Firstly, differential equations of motion and exact invariants for fractional Birkhoffian systems are presented. Secondly, the definition of adiabatic invariant is given, and adiabatic invariants for fractional Birkhoffian systems are investigated. And finally, an example is given to demonstrate the application of the results.
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