Abstract

We study the existence, uniqueness and stability solutions of new Volterra integrodifferential equations of the first order by using Picard approximation method, Banach fixed point theorem. Theorems on the existence, uniqueness and stability solutions are established under some necessary and sufficient conditions on closed and bounded domains. Furthermore the study of such nonlinear of Volterra integro-differential equations leads us to improve and extend the above methods and thus the non-linear Volterra integrodifferential equations that we have introduced in this study become more general and detailed than those introduced some results by Butris and Rafeq (2011).

Keywords: Existence, uniqueness and stability solution, Integro-differential equation, Picard approximation method, Banach fixed point theorem