Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift.

We study the fractional Fokker-Planck-Kolmogorov equation with the fractional index α ∈ [ 1 , 2) and use a vector-valued Calderón-Zygmund theorem to obtain the existence and uniqueness of L p ([ 0 , T ] ; C b α + β (R d)) ∩ W 1 , p ([ 0 , T ] ; C b β (R d)) solution under the assumptions that the drift coefficient and nonhomogeneous term are in L p ([ 0 , T ] ; C b β (R d)) with p ∈ [ α / (α - 1) , + ∞ ] and β ∈ (0 , 1) . As applications, we prove the unique strong solvability as well as Davie's type uniqueness of time inhomogeneous stochastic differential equation with the drift in L p ([ 0 , T ] ; C b β (R d ; R d)) and driven by the α -stable process for β > 1 - α / 2 and p > 2 α / (α + 2 β - 2) . [ABSTRACT FROM AUTHOR]