Existence of Extremal Solutions for a Nonlinear Fractional <Emphasis Type="Italic">q</Emphasis>-Difference System

In this paper, we study the boundary value problem of a fractional q-difference system with nonlocal integral boundary conditions involving the fractional q-derivatives of the Riemann–Liouville type. Using the properties of the Green function, and monotone iterative method, the extremal solutions were obtained. Finally, an example is presented to illustrate our main results.