Abstract
Due to the great application potential of fractional q-difference system in physics, mechanics and aerodynamics, it is very necessary to study fractional q-difference system. The main purpose of this paper is to investigate the solvability of nonlinear fractional q-integro-difference system with the nonlocal boundary conditions involving diverse fractional q-derivatives and Riemann-Stieltjes q-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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