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In this paper, we look at the two-point boundary value problem for a finite nabla fractional difference equation with dual non-local boundary conditions. First, we derive the associated Green’s function and some of its properties. Using the Guo–Krasnoselkii fixed point theorem on a suitable cone and under appropriate conditions on the non-linear part of the difference equation, we establish sufficient requirements for at least one and at least two positive solutions of the boundary value problem. Next, we discuss the existence and uniqueness of solutions to the considered problem. For this purpose, we use Brouwer and Banach fixed point theorem, respectively. Finally, we provide a few examples to illustrate the applicability of established results.

Existence and Uniqueness of Solutions to a Nabla Fractional Difference Equation with Dual Nonlocal Boundary Conditions