On the Ulam’s Types Stability Results of Non–Linear Volterra Fredholm Integro–Delay Dynamic System on Time Scale

Abstract

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