An ordering on Green's function and a Lyapunov-type inequality for a family of nabla fractional boundary value problems

Abstract

In this article, we consider a family of two-point Riemann–Liouville type nabla fractional boundary value problems involving a fractional difference boundary condition. We construct the corresponding Green’s function and deduce its ordering property. Then, we obtain a Lyapunov-type inequality using the properties of the Green’s function, and illustrate a few of its applications. Mathematics subject classification (2010): 34A08, 39A10, 39A12, 34B15.