Existence results for nonlocal boundary value problems of nonlinear fractional q-difference equations

Abstract

In this paper, we study a nonlinear fractional q -difference equation with nonlocal boundary conditions. The existence of solutions for the problem is shown by applying some well-known tools of fixed-point theory such as Banach’s contraction principle, Krasnoselskii’s fixed-point theorem, and the Leray-Schauder nonlinear alternative. Some illustrating examples are also discussed. MSC: 34A08, 39A05, 39A12, 39A13.