Fractional Noether's Theorem with Classical and Riemann-Liouville   Derivatives
  We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed classical/fractional Euler-Lagrange extremals. Both Lagrangian and Hamiltonian versions of the Noether theorem are obtained. Finally, we extend our Noether's theorem to more general problems of optimal control with classical and Riemann-Liouville derivatives. 
Gastao S. F. Frederico, Delfim F. M. Torres
math.OC