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

Abstract

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.