| Summary: | Due to the great application potential of fractional <i>q</i>-difference system in physics, mechanics and aerodynamics, it is very necessary to study fractional <i>q</i>-difference system. The main purpose of this paper is to investigate the solvability of nonlinear fractional <i>q</i>-integro-difference system with the nonlocal boundary conditions involving diverse fractional <i>q</i>-derivatives and Riemann-Stieltjes <i>q</i>-integrals. We acquire the existence results of solutions for the systems by applying Schauder fixed point theorem, Krasnoselskii’s fixed point theorem, Schaefer’s fixed point theorem and nonlinear alternative for single-valued maps, and a uniqueness result is obtained through the Banach contraction mapping principle. Finally, we give some examples to illustrate the main results.
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