Fractional Calculus of Variations of Several Independent Variables

We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians depending on generalized partial integrals and derivatives. A generalized fractional Noether's theorem, a formulation of Dirichlet's principle and an uniqueness result are given.