Fractional calculus of variations of several independent variables
1 CIDMA – Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
2 Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok, Poland
Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
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.
© EDP Sciences, Springer-Verlag, 2013