Narrow Results

In this paper, we introduce and investigate a new class of coupled fractional $q$-integro-difference equations involving Riemann–Liouville fractional $q$-derivatives and $q$-integrals of different orders, equipped with $q$-integral-coupled boundary conditions. The given problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed-points coincide with solutions of the problem at hand. The existence and uniqueness results for the given problem are, respectively, derived by applying Leray–Schauder nonlinear alternative and Banach contraction mapping principle. Illustrative examples for the obtained results are constructed. This paper concludes with some interesting observations and special cases dealing with uncoupled boundary conditions, and non-integral and integral types nonlinearities.