Abstract
In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value conditions containing Riemann-Liouville fractional quantum integrals in four points. In this direction, we derive some criteria and conditions of the existence and uniqueness of solutions to a given Caputo fractional q-difference boundary value problem. Some pure techniques based on condensing operators and Sadovskii's measure and the eigenvalue of an operator are employed to prove the main results. Also, the Ulam-Hyers stability and generalized Ulam-Hyers stability are investigated. We examine our results by providing two illustrative examples.