A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations

Details A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations

2007-01-06

arxiv.org/abs/math/0701187v1

J. Math. Anal. Appl. 334 (2007) 834--846, doi:10.1016/j.jmaa.2007.01.013

Mathematics

Optimization and Control

Accepted for publication in the Journal of Mathematical Analysis and Applications

Scientific paper

10.1016/j.jmaa.2007.01.013

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.

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