Abstract
In this present manuscript, by applying fractional quantum calculus, we study a nonlinear fractional pantograph q-difference equation with nonlocal boundary conditions. We prove the existence and uniqueness results by using the well-known fixed-point theorems of Schaefer and Banach. We also discuss the Ulam-Hyers stability of the mentioned pantograph q-difference problem. Lastly, the paper includes pertinent examples to support our theoretical analysis and justify the validity of the results.