In this paper, we study the fractional Fokker-Planck equation and obtain the existence and uniqueness of weak L p -solutions (1 p ∞) under the assumptions that the coefficients are only in Sobolev spaces. Moreover, to L ∞ -solutions, we gain the well-posedness for BV coefficients. Besides, the non-negative weak L p -solutions and renormalized solutions are derived. After then, we achieve the stability for stationary solutions. C 2015 AIP Publishing LLC. [http://dx.

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We consider nonlocal PDEs driven by additive white noises on R d . For L q integrable coefficients, we derive the existence and uniqueness, as well as Hölder continuity, of mild solutions. Precisely speaking, the unique mild solution is almost surely Hölder continuous with Hölder index 0 < θ < (1/2 -d/(qα))(1 ∧ α). Moreover, we show that any order γ (< q) moment of Hölder normal for u on every bounded domain of R + × R d is finite. MSC: 60H15; 35R60

This paper considers the existence and uniqueness of stochastic entropy solution for a nonlinear transport equation with a stochastic perturbation. The uniqueness is based on the doubling variable method. For the existence, we develop a new scheme of parabolic approximation motivated by the method of vanishing viscosity given by Feng and Nualart (J. Funct. Anal. 2008, 255, 313-373). Furthermore, we prove the continuous dependence of stochastic strong entropy solutions on the coefficient b and the nonlinear function f .

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