Hyers-Ulam-Rassias stability of the first order nonhomogeneous linear dynamic equation and volterra integro-dynamic equation on time scale

In this thesis, firstly, the Hyers-Ulam-Rassias stability of the first-order non-homogeneous linear dynamic equation on the time scale was demonstrated using the Jung (2006a) method. Next, the Hyers-Ulam-Rassias stability of the Volterra integro-dynamic equation is shown on the time scale using the weighted space method. The weighted space method applies the Banach Fixed Point Theorem on the metric space provided by the metric created by multiplying a weight function by the standard metric. The weighted space method was first used by Gavruta and Gavruta (2010) to show the Hyers-Ulam-Rassias stability. The Hyers-Ulam-Rassias stability of these two equations considered in this study is examined for a closed and bounded interval 〖[a,b]〗_T of the set of real numbers,a and b real numbers and a