1 citations · 1 across the 3 of their papers we have counts for
5 papers
Non shifted calculus of variations on time scales with Nabla-differentiable Sigma
Loïc Bourdin
In calculus of variations on general time scales, an integral Euler-Lagrange equation is usually derived in order to characterize the critical points of non shifted Lagrangian func…
Existence of a weak solution for fractional Euler-Lagrange equations
Loïc Bourdin
In this paper, we state with a variational method a general theorem providing the existence of a weak solution for fractional Euler-Lagrange equations of the type: $$ \dfrac{\p…
Helmholtz's inverse problem of the discrete calculus of variations
Loïc Bourdin, Jacky Cresson
We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian f…
A continuous/discrete fractional Noether's theorem
Loïc Bourdin, Jacky Cresson, Isabelle Greff
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 cons…
Variational integrator for fractional Euler-Lagrange equations
Loïc Bourdin, Jacky Cresson, Isabelle Greff +1
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 all…