On the Ulam Type Stabilities of a General Iterative Integro-Differential Equation Including a Variable Delay

Abstract

This work is interested in the existence and uniqueness of solutions, the Hyers-Ulam stability (HUS) and the Hyers-Ulam-Rassias stability (HURS) of a new and general iterative integro-delay differential equation (IIDDE) of first order including a variable delay. We prove the results regarding the HUS and the HURS of the considered problem on a bounded interval, half infinite intervals and an infinite interval using the Banach fixed point theorem (BFPT). The outcomes of this research work are new and they allow new enhancements to the existence theory, the HUS and HURS of the nonlinear IIDDEs of first order including a variable delay.