The time scale calculus is a mathematical theory used to depict the engineering systems relating to the continuous and the discrete analysis. This mathematical field helps to confer more credibility and diversity for the prospective findings. In addition, it can be employed in various domains such as : economic modeling, mechanical systems, population’s modelization, dynamic programming, robotics and other scientific fields. Since its appearance, several mathematicians played an influential role in the development of this theory. The present research intends to extend and generalize some results for potential possible applications.