arXiv subjects
Publications and source records attributed to Alaa E. Hamza.
In this article, we investigate the method of upper and lower solutions for Volterra integral equation of the first kind on arbitrary time scale $\mathbb{T}$. We establish some existence results in a certain sector. Moreover, monotone iterative technique is used to obtain maximal and minimal solutions of the considered equation.
In this paper, we study Hyers-Ulam stability for integral equation of Volterra type in time scale setting. Moreover we study the stability of the considered equation in Hyers-Ulam-Rassias sense. Our technique depends on successive approximation method, and we use time scale variant of induction principle to show that equation (1.1) is stable on unbounded domains in Hyers-Ulam-Rassias sense.
In this paper we study well posedness of a certain nonlinear Volterra-Fredholm dynamic integral and integro-dynamic equations on unbounded interval from arbitrary time scale. We derive the time scale analogue of certain integral inequalities of Pachpatte type and using them with Banach's fixed-point theorem to establish the results.