Hyers-Ulam Stability of Non-Linear Volterra Integro-Delay Dynamic System with Fractional Integrable Impulses on Time Scales

Abstract

. 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 so-lutions. By means of abstract Gr¨onwall lemma, Gr¨onwall’s inequality on time scales, we establish Hyers–Ulam stability and Hyers–Ulam–Rassias stability results. There are some primary lemmas, inequalities and rele-vant assumptions that helps in our stability results.