  In this paper, we develop an operator splitting scheme for the fractional
kinetic Fokker-Planck equation (FKFPE). The scheme consists of two phases: a
fractional diffusion phase and a kinetic transport phase. The first phase is
solved exactly using the convolution operator while the second one is solved
approximately using a variational scheme that minimizes an energy functional
with respect to a certain Kantorovich optimal transport cost functional. We
prove the convergence of the scheme to a weak solution to FKFPE. As a
by-product of our analysis, we also establish a variational formulation for a
kinetic transport equation that is relevant in the second phase. Finally, we
discuss some extensions of our analysis to more complex systems.
