Higher-order nonlocal multipoint q-integral boundary value problems for fractional q-difference equations with dual hybrid terms

Abstract

In this article, we introduce and study a new class of higher-order fractional q-difference equations involving Riemann-Liouville q-derivatives with dual hybrid terms, supplemented with nonlocal multipoint q-integral boundary conditions. The existence of a unique solution to the given problem is shown by applying Banach’s fixed point theorem. We also present existing criteria for solutions to the problem at hand with the aid of Krasnoselskii’s fixed point theorem and Leray-Schauder’s nonlinear alternative. Illustrative examples are given to demonstrate the application of the obtained results.

Keywords

• q-difference equation
• riemann-liouville q-derivative
• q-integral
• nonlocal boundary conditions
• existence
• fixed point
• 34a08
• 39a13
• 34b10
• 34b15