Investigation of hybrid fractional q-integro-difference equations supplemented with nonlocal q-integral boundary conditions

Abstract

In this article, we introduce and study a new class of hybrid fractional qq-integro-difference equations involving Riemann-Liouville qq-derivatives, supplemented with nonlocal boundary conditions containing Riemann-Liouville qq-integrals of different orders. The existence of a unique solution to the given problem is shown by applying Banach’s fixed point theorem. We also present the existing criteria for solutions to the problem at hand by applying Krasnoselskii’s fixed point theorem and Leray-Schauder’s nonlinear alternative. Illustrative examples are given to demonstrate the application of the obtained results. Some new results follow as special cases of this work.

Keywords

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