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

Gastao S. F. Frederico·Delfim F. M. Torres
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Abstract

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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Gastao S. F. Frederico, Delfim F. M. Torres. 2007-01-06. A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations. https://doi.org/10.1016/j.jmaa.2007.01.013

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