Hyers-Ulam stability and existence of solutions for high-order fractional q-difference equations on infinite intervals

Recently, fractional q-difference equations on infinite intervals have attracted much attention due to their potential applications in many fields. In this paper, we investigate a class of nonlinear high-order fractional q-difference equations with integral boundary conditions on infinite intervals, where the nonlinearity contains Riemann-Liouville fractional q-derivatives of different orders of unknown function. By means of Schaefer fixed point theorem, Leray-Schauder nonlinear alternative and Banach contraction mapping principle, we acquire the existence and uniqueness results of solutions. Furthermore, we establish the Hyers-Ulam stability for the proposed problem. In the end, several concrete examples are utilized to demonstrate the validity of main results.