Stability of a Volterra Integral Equation on Time Scales

TL;DR

This paper investigates the Hyers-Ulam stability of Volterra integral equations within the time scale calculus framework, extending stability analysis to unbounded domains and considering Hyers-Ulam-Rassias stability using an approximation method.

Contribution

It introduces a novel stability analysis of Volterra integral equations on time scales, employing a time scale induction principle and approximation techniques.

Findings

Established Hyers-Ulam stability on unbounded domains.

Extended stability concepts to Hyers-Ulam-Rassias sense.

Demonstrated the effectiveness of the successive approximation method.

Abstract

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.