On qualitative analysis of boundary value problem of variable order fractional delay differential equations

Abstract

Variable order differential equations are the natural extension of the said area. In many situations, such problems have the ability to describe real-world problems more concisely. Therefore, keeping this validity in mind, we have considered a class of boundary value problems (BVPs) under the variable order differentiation. For the suggested problems, we have developed the existence and uniqueness (EU) by using some fixed point results due to Banach and Schauder. Sufficient adequate results have been established for the required need. Some stability results have also been elaborated based on the concepts of Ulam, Hyers, and Rassias. Proper examples have also been provided with detailed analysis to verify our results.