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Cauchy problem for a fractional parabolic equation with the advection. (English) Zbl 1424.35352

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
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