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].

A method, called “the discrete variational method”, has been recently presented by Furihata and Matsuo for designing finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations (PDEs). In this paper the method is enhanced so that the derived schemes be highly accurate in space by introducing higher order spatial difference ope...