Variable Order Fractional Variational Calculus for Double Integrals
  We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain a fractional Euler-Lagrange necessary optimality condition for variable order two-dimensional fractional variational problems. 
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres
math.OC