Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (a, (beta))

We derive Euler-Lagrange-type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann -Liouville derivatives of order (a, (beta)), a>0, (beta)>0, recently introduced by Cresson. Some interesting consequences are obtained and discussed.