The article considers a boundary value problem for a fractional-loaded heat equation in the first quadrant. The loaded term has the form of a fractional derivative in the sense of Riemann-Liouville in a spatial variable, and the order of the derivative in the loaded term is less than the order of the differential part. The study is based on the reduction of the boundary value problem to the Volterra integral equation of the second kind. The kernel of the resulting integral equation contains a special function — a Wright type function. In the article, the conditions for the solvability of the integral equation are obtained and it is shown that the existence and uniqueness of solutions to the integral equation depends both on the order of the fractional derivative in the loaded term of the initial-boundary value problem and on the law of motion of the load.