Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator

Abstract

In this paper, a new class of a neutral functional delay differential equation involving the generalized $\psi$ -Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results.