An analysis on the controllability and stability to some fractional delay dynamical systems on time scales with impulsive effects

Abstract

Abstract In this article, we establish a new class of mixed integral fractional delay dynamic systems with impulsive effects on time scales. We investigate the qualitative properties of the considered systems. In fact, the article contains three segments, and the first segment is devoted to investigating the existence and uniqueness results. In the second segment, we study the stability analysis, while the third segment is devoted to investigating the controllability criterion. We use the Leray–Schauder and Banach fixed point theorems to prove our results. Moreover, the obtained results are examined with the help of an example.

Keywords

• Time scales
• Dynamic system
• Hyers–Ulam stability
• Controllability
• Impulsive effects