Investigation of a Lyapunov delta-type inequality with respect to a discrete fractional Green’s function

This article considers a Lyapunov delta-type inequality with Green's functions including fractional falling functions. We define a fractional difference problem of Riemann-Liouville type with a fractional boundary condition and, using the Green's function, obtain the ordering property in a discrete domain. Moreover, we apply the properties of this function to find the existence of a delta Lyapunov inequality.