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. © 2013 Versita Warsaw and Springer-Verlag Wien.