  In this paper, we investigate difference-differential operators of parabolic
and hyperbolic types. Namely, we consider non-homogenous heat and wave
equations for Rubin's difference operator. Well-posedness results are obtained
in appropriate Sobolev type spaces. In particular, we prove that the heat and
wave equations generated by Rubin's difference operator have unique solutions.
We even show that these solutions can be represented by explicit formulas
