On \(q^2\) -Analogue of the One-Dimensional Non-Homogeneous Heat Equation

In this paper, we discuss the \(q^2\) -analogue of non-homogeneous heat equation in one dimension. Namely, we consider non-homogeneous heat equation for Rubin’s difference operator. Well-posedness results are presented in appropriate Sobolev-type spaces. In particular, we show that the heat equation generated by Rubin’s difference operator have unique solutions. We even show that these solutions can be represented by explicit formulas. The presentation is based on the joint work with M. Ruzhansky and S. Shaimardan.