Solvability for a Discrete Fractional Three-Point Boundary Value Problem at Resonance

Abstract

This paper is concerned with the existence of solutions to a discrete three-point boundary value problem at resonance involving the Riemann-Liouville fractional difference of order $\alpha \in (\mathrm{0,1}]$. Under certain suitable nonlinear growth conditions imposed on the nonlinear term, the existence result is established by using the coincidence degree continuation theorem. Additionally, a representative example is presented to illustrate the effectiveness of the main result.