Li, Xitao; Xu, Meng; Zhou, Shulin Cauchy problem for a fractional parabolic equation with the advection. (English) Zbl 1424.35352 J. Partial Differ. Equations 31, No. 3, 252-273 (2018). Summary: In this paper, we give an explicit formula of the solution to Cauchy problem of a fractional parabolic equation with the advection, and then prove the solvability of Cauchy problem and further Schauder-type regularity of the solution under appropriate conditions on the initial value and the right-hand side term. MSC: 35R11 Fractional partial differential equations 35K15 Initial value problems for second-order parabolic equations 35C15 Integral representations of solutions to PDEs Keywords:fractional parabolic equation; Cauchy problem; existence; regularity PDFBibTeX XMLCite \textit{X. Li} et al., J. Partial Differ. Equations 31, No. 3, 252--273 (2018; Zbl 1424.35352) Full Text: DOI