Solvability of the Cauchy problem for a fractionally loaded equation with variable coefficients

In this chapter, we study the well-posed problem for a heat equation with variable coefficients, including derivative and loaded terms in Holder spaces. In the problem under consideration, the loaded term is under the action of the fractional Riemann–Liouville integral operator. We will prove the unique solvability of the problem and construct a representation of the solution using the method of integral equations.