Fractional variational calculus for nondifferentiable functions
  We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free boundary conditions is considered, as well as problems with isoperimetric and holonomic constraints. 
Ricardo Almeida, Delfim F. M. Torres
math.OC