In this paper, we consider an integro-implicit- \(q\) -difference equation with \(q\) -integral conditions in the fractional settings. This boundary value \(q\) -problem covers the Langevin \(q\) -difference and Pantograph \(q\) -difference equations in the general form and also, it is formulated by using the \(q\) -Caputo derivatives and \(q\) -Riemann-Liouville integrals. We first discuss on the existence and uniqueness of \(q\) -solutions with the Banach contraction principle and Krasnoselskii’s fixed point theorem. Moreover, the Ulam-Hyers stability analysis is conducted, and then, we prove the generalized Ulam-Hyers stability. To validate the results, we provide a numerical example.
