Ulam Stabilities for Nonlinear Volterra Delay Integro-differential Equations

The present paper is devoted to the study of existence and uniqueness of a solution and Ulam type stabilities for Volterra delay integro-differential equations on a finite interval. Our analysis is based on the Pachpatte’s inequality and Picard operator theory. Examples are provided to illustrate the stability results obtained in the case of a finite interval. Also, we give an example to illustrate that the Volterra delay integro-differential equations are not Ulam-Hyers stable on the infinite interval.