2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144945We derive Euler-Lagrange type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann-Liouville derivatives of order $(α,β)$, $α> 0$, $β> 0$, recently introduced by J. Cresson and S. Darses. Some interesting consequences are obtained and discussed.This is a preprint of an article accepted for publication (28-02-2007) in Math. Methods Appl. SciMathematical PhysicsOptimization and Control49K05; 49S05; 70H33; 26A33text