分数阶Lagrange系统的共形不变性与守恒量

Conformal invariance and conserved quantity of a fractional Lagrange system

研究Riemann-Liouville导数下分数阶Lagrange系统的共形不变性与守恒量.首先,建立分数阶d′Alembert-Lagrange原理和分数阶Lagrange方程,给出分数阶Lagrange系统的共形不变性的定义及其确定方程;其次,通过研究分数阶Lagrange系统共形不变性和Lie对称性之间的关系,导出共形因子的表达式;最后,给出相应于分数阶Lagrange系统的共形不变性的Noether型分数阶守恒量.文末,给出算例以说明结果的应用.

The conformal invariance and conserved quantity for afractional Lagrange system in terms of Riemann-Liouville derivatives have been studied. Firstly, the fractional d′Alembert-Lagrange principle and the fractional Lagrange equations have been established, and the definition and corresponding determining equation of conformal invariance for the fractional Lagrange system have been given. Secondly, by studying the relationship between the conformal invariance and the Lie symmetry of the fractional Lagrange system, the conformal factor had derived. Finally, the fractional conserved quantity of Noether type corresponding to the conformal invariance of the fractional Lagrange system has been given. At the end of the paper, an example has been given to illustrate the application.