Fractional Calculus of Variations for Double Integrals
  We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. 
Tatiana Odzijewicz, Delfim F. M. Torres
math.OC