Abstract:
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.