On the solvability of the first boundary value problem for the loaded equation of heat conduction

Abstract

In this paper we consider the first boundary value problem for the loaded equation of heat conduction in a
quarter plane. The loaded term is the trace of the fractional derivative of order ν, 0 ≤ ν ≤ 1 with respect
to the time variable on the line x = t. It is shown that when 0 ≤ ν ≤ 1 and ∀λ ∈C, then the load is a weak
perturbation, that is, the studied problem has a unique solution in the class of bounded functions.