A formulation of Noether's theorem for fractional problems of the calculus of variations - Frederico, Gastão S.F.; Torres, Delfim F.M. (Journal of mathematical analysis and applications, 2007)
Fractional (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.