Caputo fractional $q$-difference equations in Banach spaces

Abstract

This paper aims to explore the existence results of a certain type of Caputo fractional qq-difference equations in Banach spaces. To achieve this goal, we employ a fixed point theorem that relies on the concept of measure of noncompactness and the convex-power condensing operator. We give an illustrative example in the last section.

Keywords

• Fractional $q$-difference equation
• measure of noncompactness
• solution
• fixed point