Abstract
In this work, the existence of solutions for boundary value problems involving nonlinear fractional $$q$$ -difference equations is investigated. By applying methods from q-calculus and fractional differentiation theory, the original differential equation is reduced to an integral equation through the construction of a Green’s function. The existence of solutions is established using the Banach contraction principle, Krasnoselskii’s fixed point theorem, and the Leray–Schauder nonlinear alternative. Illustrative examples demonstrate the practical applicability of the obtained results.