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.
Tokmagambetov et al. (Sat,) studied this question.