Variational integrator for fractional Euler–Lagrange equations

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

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

We extend the notion of variational integrator for classical Euler-Lagrange equations to the fractional ones. As in the classical case, we prove that the variational integrator allows to preserve Noether-type results at the discrete level.

Mots clés: fractional calculus; Euler-Lagrange equations; variational integrator; Noether's theorem

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

Loïc Bourdin, Jacky Cresson, Isabelle Greff, Pierre Inizan. Variational integrator for fractional Euler–Lagrange equations. Applied Numerical Analysis and Computational Mathematics, 2013, 71, pp.14-23. ⟨10.1016/j.apnum.2013.03.003⟩. ⟨hal-00866948⟩