Remark on the analyticity of the fractional Fokker-Planck equation

Abstract

In this note, we study the Cauchy problem of the fractional Fokker-Planck equation. We prove that the solution to the Cauchy problem enjoys the analytic smoothing effect with an L2{L}^{2} initial datum for positive time, and the evolution of the analytic radius is similar to the heat equation.

Keywords

• fractional fokker-planck equation
• analytic smoothing effect
• commutator estimations
• 35b65
• 76p05
• 82c40