On the Bielecki–Hyers–Ulam Stability of Non–linear Impulsive Fractional Hammerstein and Mixed Integro–dynamic Systems on Time Scales

Abstract

This article is about the examination of existence as well as uniqueness of solutions, Bielecki–Hyers–Ulam stability and Bielecki–Hyers–Ulam–Rassias stability of non–linear impulsive fractional Hammerstein integro–delay dynamic system and non–linear impulsive fractional mixed integro–dynamic system, in the context of time scales domain. The Banach contraction principle and Picard operator are the main tools that are applied to verify the existence along with uniqueness of solutions for both models. Also, Bielecki–Ulam’s type stability is obtained by utilizing Grönwall’s inequality on time scale. To overcome the hurdles in achieving desired outcomes, some assumptions are provided. At the end, the results are demonstrated with the help of examples.