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

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.

Accepted for publication in the Journal of Mathematical Analysis and Applications

References in corpus (1)

• Quasi-Invariant Optimal Control Problems

Cited by in corpus (5)

• Fractional conservation laws in optimal control theory
• Fractional Action-Like Variational Problems
• Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
• Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order $(\alpha ,\beta )$
• Noether's Theorem on Time Scales