Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference

Abstract

We consider a discrete fractional nonlinear boundary value problem in which nonlinear term $f$ is involved with the fractional order difference. And we transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.