  In this work, we investigate a variational formulation for a time-fractional
Fokker-Planck equation which arises in the study of complex physical systems
involving anomalously slow diffusion. The model involves a fractional-order
Caputo derivative in time, and thus inherently nonlocal. The study follows the
Wasserstein gradient flow approach pioneered by [26]. We propose a JKO type
scheme for discretizing the model, using the L1 scheme for the Caputo
fractional derivative in time, and establish the convergence of the scheme as
the time step size tends to zero. Illustrative numerical results in one- and
two-dimensional problems are also presented to show the approach.
