[hal-00914059] Fractional Fokker-Planck equation

This paper deals with the long time behavior of solutions to a fractional Fokker-Planck equation of the form $\partialt f = If + \textdivxf$ where the operator $I$ stands for a fractional Laplacian We prove an exponential in time convergence towards equilibrium in new spaces Indeed such a result was already obtained in a $L^2$ space with a weight prescribed by the equilibrium in \citeGI We improve this result obtaining the convergence in a $L^1$ space with a polynomial weight To do that we take advantage of the recent paper \citeGMM in which an abstract theory of enlargement of the functional space of the semigroup decay is developed



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