On a control problem for the subdiffusion equation with a fractional derivative in the sense of caputo

In the rectangle for a differential equation of fractional order in the sense of Caputo, we study the control problem with the help of a source function. In other words, the task is to find the source function f(x;y) in such a way that, as a result, at the time t = Θ the temperature of the object under study should be distributed as a given function Ψ(x;y). Sufficient conditions are found for the function Ψ(x;y), which ensure both the existence and uniqueness of the solution to the control problem.