A continuous/discrete fractional Noether’s theorem

Loïc Bourdin (1) , Jacky Cresson (2, 1) , Isabelle Greff (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides

We prove a fractional Noether's theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula which can be algorithmically implemented. In the discrete case, the conservation law is moreover computable in a finite number of steps.

Mots clés: Noether's theorem; Lagrangian systems; symmetries; fractional calculus

Domaines: Optimisation et contrôle [math.OC]; Systèmes dynamiques [math.DS]

Loïc Bourdin, Jacky Cresson, Isabelle Greff. A continuous/discrete fractional Noether’s theorem. Communications in Nonlinear Science and Numerical Simulation, 2013, 18 (4), pp.878-887. ⟨10.1016/j.cnsns.2012.09.003⟩. ⟨hal-00866949⟩