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Fractional Calculus of Variations of Several Independent Variables (1308.4585v1)
Published 21 Aug 2013 in math-ph, math.MP, and math.OC
Abstract: 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.