Some Qualitative Analyses of Neutral Functional Differential Equations with and without Delay

Abstract

In this memory, we first transform our main problems into an equivalent fractional integral equation. After that, based on some fixed point theorems namely, Banach’s fixed point theorem and Krasnoselskii’s fixed point theorem and by applying Schauder’s fixed point theorem in generalized Banach spaces, and Perov’s fixed point theorem combined with the Bielecki norm, the existence and uniqueness of solutions to the proposed problems are discussed theoretically. Furthermore, examples are presented to illustrate our theoretical findings.