Analysis of<i>q</i>‐fractional implicit boundary value problems having Stieltjes integral conditions

Abstract

In this article, we make analysis of the implicit q ‐fractional differential equations involving integral boundary conditions associated with Stieltjes integral and its corresponding coupled system. We are using some sufficient conditions to achieve the existence and uniqueness results for the given problems by applying the Banach contraction principle, Schaefer's fixed point theorem, and Leray–Schauder result of cone type. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability using the classical technique of functional analysis. At the end, the results are verified with the help of examples.