In order to expand the theory of fractional q-difference equations, the existence of solutions to boundary value problems of a class of iterative functional higher-order fractional q-difference equations with integral boundary conditions on infinite intervals was studied. Firstly, the Green[DK]’s function of fractional difference equation boundary value problem was calculated and its properties were studied. Secondly, an appropriate Banach space and norm were introduced, and the integral operator was then constructed. Thirdly, the existence theorem of positive solution of the problem was obtained by using monotone iterative technique and upper and lower solution method. Finally, the effectiveness and practicability of the main results were verified by a concrete example. The results show that under certain growth conditions of the nonlinear term g, there exists at least one positive solution to the boundary value problem of iterative functional fractional quantum difference equations on infinite intervals. The research results enrich the solvability theory of fractional q-difference equations, reflect the influence of feedback iterative terms on the existence of solutions, and provide certain theoretical guidance for the application of iterative functional fractional q-difference equations in many fields such as control engineering, biomedicine, population theory, and social economy.