Stability analysis of first‐order impulsive nonautonomous system on timescales

Abstract

In this manuscript, we present the existence, uniqueness, β‐Ulam‐Hyers stability, and β‐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.