Fractional Calculus of Variations in Terms of a Generalized Fractional   Integral with Applications to Physics
  We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to Physics discussed. 
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres
math.OC