2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132205Fractional (or non-integer) differentiation is an important concept both from theoretical and applicational points of view. The study of problems of the calculus of variations with fractional derivatives is a rather recent subject, the main result being the fractional necessary optimality condition of Euler-Lagrange obtained in 2002. Here we use the notion of Euler-Lagrange fractional extremal to prove a Noether-type theorem. For that we propose a generalization of the classical concept of conservation law, introducing an appropriate fractional operator.Accepted for publication in the Journal of Mathematical Analysis and ApplicationsOptimization and ControlMathematical Physics49K05; 26A33text