This article establishes a comparison principle for the nabla fractional difference operator ∇ρ(a)ν, 1<ν<2. For this purpose, we consider two-point boundary value problem with separated conditions and derive corresponding Green’s function. I prove that function satisfies positivity property. Then, deduce relatively general result considered problem.

In this study, we investigate the norm of difference operator on some sequence spaces such as Hilbert and Cesaro matrix domains. Therefore present study is a complement for those results obtained in [1].