The unique solution for a fractional q-difference equation with three-point boundary conditions

The aim of this paper is to investigate the existence and uniqueness of solutions for nonlinear fractional q-difference equations with three-point boundary conditions. Our approach relies on a new fixed point theorem of increasing ψ−(h,r)−concave operators defined on ordered sets. Further, we can construct a monotone explicit iterative scheme to approximate the unique solution. Finally, the main results are illustrated with the aid of two interesting examples.