Green's function for a discrete fractional boundary value problem

. In this article, we deduce the expression and the main properties of the Green’s func- tion related to a general nabla fractional difference equation with constant coef fi cients coupled to Dirichlet conditions. In particular, we prove that such function has constant sign on their set of de fi nition, and also satis fi es some additional properties that are fundamental to de fi ne a suitable Banach space, where to ensure the existence and uniqueness of solutions of nonlinear problems.