  Fractional kinetic theory plays a vital role in describing anomalous
diffusion in terms of complex dynamics generating semi-Markovian processes.
Recently, the variational principle and associated Levy Ansatz have been
proposed in order to obtain an analytic solution of the fractional
Fokker-Planck equation. Here, based on the action integral introduced in the
variational principle, the Hamiltonian formulation is developed for the
fractional Fokker-Planck equation. It is shown by the use of Dirac's
generalized canonical formalism how the equation can be recast in the
Liouville-like form. A specific problem arising from temporal nonlocality of
fractional kinetics is nonuniqueness of the Hamiltonian: it has two different
forms. The non-equal-time Dirac-bracket relations are set up , and then it is
proven that both of the Hamiltonians generate the identical time evolution.
