Existence of Positive Solutions for Coupled Fractional Q-difference Problem with Coupled Integral Boundary Conditions*

This paper investigates a coupled fractional q-difference problem with coupled integral boundary conditions. First, we give the Green’s function for the problem and discuss some properties of the Green’s function. By using Fixed point theorem in Banach space and Leray-Schauder alternative, we conclude some existence results of positive solutions for the coupled system when the problem meets certain conditions. At last, examples are presented to illustrate our main results.