<p>This work investigates a boundary value problem for a fractional-loaded hyperbolic equation with one spatial variable that generalizes the classical equation of string vibrations. The equation contains the fractional derivative of Riemann-Liouville, and the load is carried out at a time-dependent point. The purpose of the study is to construct an explicit solution to the problem. To find a solution, the initial problem is reduced to a Volterra-type integral equation. A representation of the solution is obtained in the form of the sum of two integrals corresponding to different areas of variable definition. It is shown that there is a unique solution to the problem. The conditions for the functions included in the equation are given for which a solution exists. The results obtained can be used in modeling processes described by hyperbolic equations with fractional derivatives.</p>