This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stability and Hyers-Ulam-Rassias stability results. There are some primary lemmas, inequalities and relevant assumptions that helps in our stability results.

Keywords: Hyers-Ulam stability, Time scale, Impulses, Delay dynamic system, Gr"{o}nwall's inequality, Abstract Gr"{o}nwall lemma, Banach fixed point theorem.

Full-Text [PDF 330 kb]