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

Wasserstein Gradient Flow Formulation of the Time-Fractional Fokker-Planck Equation