Fractional Hamiltonian analysis of higher order derivatives systems
  The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives. 
Dumitru Baleanu, Sami I. Muslih, Kenan Tas