Novel Existence and Uniquenss results for Seqential Fractional Neutral Functional Differential Equations

Abstract

This work was devoted to the study of the existence and uniqueness of solutions for two classes of sequential fractional neutral functional differential equations. The first category is the Caputo-Hadamard type, while the second is the ψ-Caputo operator type. The method used to study this type of equation depends on converting the equation to an integral equation before using the appropriate fixed point theory. Banach's fixed point theorem, a nonlinear alternative of the Leray-Schauder type, and Krasnoselski's fixed point theorem are used to obtain the desired results. Finally, examples illustrating the main results are presented.