Non-Trivial Solutions of Non-Autonomous Nabla Fractional Difference Boundary Value Problems

Abstract

In this article, we present a two-point boundary value problem with separated boundary conditions for a finite nabla fractional difference equation. First, we construct an associated Green’s function as a series of functions with the help of spectral theory, and obtain some of its properties. Under suitable conditions on the nonlinear part of the nabla fractional difference equation, we deduce two existence results of the considered nonlinear problem by means of two Leray–Schauder fixed point theorems. We provide a couple of examples to illustrate the applicability of the established results.

Keywords

• nabla fractional difference
• boundary value problem
• separated boundary conditions
• Green’s function
• existence of solutions