In recent decades, time scales theory has been an active area of research as a generalization of continuous and discrete analysis. The introduction of time scales makes it possible to model systems where time is represented discretely, continuously, or a combination of them, which is relevant for the analysis of hybrid discrete-continuous dynamic models of processes in physics, economics, biology, medicine, and computer science.

We study a boundary-value problem for a system of dynamic equations on a fixed time scale. By using a generalization of the Dzhumabaev parameterization method, we derive solvability conditions and present an algorithm for the numerical solution of the problem.