A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
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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.
Accepted for publication in the Journal of Mathematical Analysis and Applications
Accepted for publication in the Journal of Mathematical Analysis and Applications