Fractional Euler-Lagrange differential equations via Caputo derivatives
  We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives. 
Ricardo Almeida, Agnieszka B. Malinowska, Delfim F. M. Torres
math.OC math.CA