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.
Highlights
The notion of fractional differential equations (FDEs) has been a field of intense research for the last few decades
7 Conclusion In this article, we conducted our research on some mixed integral dynamic systems with impulsive effects on times scales in the fractional settings
We established our results by using the Leray–Schauder and Banach fixed point theorems in this regard
Summary
The notion of fractional differential equations (FDEs) has been a field of intense research for the last few decades. Impulsive differential equations are best tools to model a physical situation that contains abrupt changes at certain instants. These equations describe medicine, biotechnology process, population dynamics, biological systems, chemical energy, mathematical economy, pharmacokinetics, etc. There are a few articles that examined the existence, controllability, and Ulam type stability regarding a mixed structure of the impulsive fractional dynamical system on time scales. Inspired by the research conducted in [56], we study the following mixed integral fractional dynamic systems on the time scale T:.
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