Noether's theorem for fractional variational problems of variable order

Abstract

We prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether's theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo.

This is a preprint of a paper whose final and definite form will appear in Central European Journal of Physics. Paper submitted 30-Jan-2013; revised 12-March-2013; accepted for publication 15-March-2013

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Cited by in corpus (4)

• Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order
• Fractional Herglotz variational problems of variable order
• The Legendre Condition of the Fractional Calculus of Variations
• Conformal and Non-Minimal Couplings in Fractional Cosmology