Multiple Positive Solutions of Discrete Fractional Boundary Value Problems

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