The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1813–1826 | Cite as

Fractional calculus of variations of several independent variables

  • T. OdzijewiczEmail author
  • A. B. Malinowska
  • D. F. M. Torres
Regular Article


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.


European Physical Journal Special Topic Fractional Derivative Fractional Calculus Fractional Integral Part Formula 
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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • T. Odzijewicz
    • 1
    Email author
  • A. B. Malinowska
    • 2
  • D. F. M. Torres
    • 1
  1. 1.CIDMA – Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Faculty of Computer ScienceBialystok University of TechnologyBiałystokPoland

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