Multiple positive solutions of Nabla fractional boundary value problems

Abstract

In this work, we deal with the following two-point Dirichlet boundary value problem for a finite nabla fractional difference equation: First, we establish an associated Green’s function, and obtaino some of its properties. Under suitable conditions on the non-linear part of the difference equation, we deduce some results on at least one and at least three positive solutions of the considered problem. For this purpose, we use a few prominent conical shell fixed-point theorems.