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

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