Cauchy Problem for a Loaded Fractional Diffusion Equation

We consider the Cauchy problem for a loaded fractional diffusion equation. The loaded term is specified as a composition of the fractional derivative (or integral) of the desired function with respect to the time variable and the substitution operator, and has a power coefficient. The problem is reduced to an integral equation, in terms of which the solution of the problem is constructed. We find sufficient conditions on the parameters of the problem that ensure the existence and uniqueness of the solution. It is shown that violation of some of the specified conditions leads to non-uniqueness of the solution of the problem under consideration.