Cauchy Problem for a Fractional Parabolic Equation with the Advection (Journal of Partial Differential Equations, 2018)
In this paper, we give an explicit formula of the solution to Cauchy problemof a fractional parabolic equation with the advection, and then prove the solvability ofCauchy problem and further Schauder-type regularity of the solution under appropriateconditions on the initial value and the right-hand side term.
Keywords: Fractional parabolic equation; Cauchy problem; existence; regularity