Existence Results for Nonlinear Fractional $q$-Difference Equations with Nonlocal Riemann--Liouville $q$-Integral Boundary Conditions

Wengui Yang

This paper deals with the existence and uniqueness of solutions for a class of nonlinear fractional $q$-difference equations boundary value problems involving four-point nonlocal Riemann--Liouville $q$-integral boundary conditions of different order. Our results are based on some well-known tools of fixed point theory such as Banach contraction principle, Krasnoselskii fixed point theorem, and the Leray--Schauder nonlinear alternative. As applications, some interesting examples are presented to illustrate the main results.