The Cauchy problem for the heat equation with a fractional load

In this paper, we study the solvability of a direct problem for a multidimensional fractionally loaded heat equation in Holder spaces. In the problem under consideration, the loaded term is represented in the form of a fractional Riemann-Liouville integral operator with respect to the time variable. This study aims to prove unique solvability and construct a representation of the solution to the problem by the method of the integral equation.

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