Volterra integral equations of the first kind arise naturally in the description of problems in electrical engineering, the modeling of dynamic impulse systems, nonlinear dynamic systems identification, and of many phenomena in the applied sciences. In particular, Volterra integral equations of the first kind, in which both limits of integration are functions of time, play an important role in the modeling of developing dynamical systems.

The authors are concerned with the existence of solutions and their asymptotic behavior. A constructive approach is developed in order to obtain continuous solutions. Examples are provided to illustrate the theoretical results. The paper is interesting and well written. However, the smoothness assumptions on the functions involved might be quite restrictive in many real-world applications. Finally, the authors should have mentioned the paper by N. A. Sidorov et al. [1] in the bibliography.