Interpretation on nonlocal neutral functional differential equations with delay

Abstract

This work deals with the existence and continuous dependence of an integral solution for neutral integro-differential equations with a nonlocal condition. This result is established by using an integrated resolvent operator under conditions of Lipschitz continuity and uniqueness via the Banach fixed point technique. We also study the existence of a strict solution on reflexive and general Banach spaces. In the last section, an example is provided related to this theory.

Keywords

• integro-differential equations
• integrated resolvent operator
• lipschitz condition
• strict solution
• fixed point theorem