In this manuscript, we present the existence, uniqueness, -Ulam-Hyers stability, and -Ulam-Hyers-Rassias stability of semilinear nonautonomous impulsive dynamic systems on timescales, with the help of fixed point approach. We use Grönwall inequality on timescale, abstract Gröwall lemma, and Picard operator as basic tools to develop our main results. At the end, an example is given to demonstrate the validity of our main theoretical result. KEYWORDSBanach fixed point theorem, dynamic system, impulses, timescale, semilinear nonautonomous system, -Ulam-Hyers stability MSC CLASSIFICATION 34N05; 34G20; 35B35; 45J05 Math Meth Appl Sci. 2020;43:5097-5113. wileyonlinelibrary.com/journal/mma

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.

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