A Borel-Pompeiu formula in a (q,q')-model of quaternionic analysis

The study of ψ-hyperholomorphic functions defined on domains in ℝ^4 with values in ℍ, namely null-solutions of the ψ-Fueter operator, is a topic which captured great interest in quaternionic analysis. This class of functions is more general than that of Fueter regular functions. In the setting of (q,q')-calculus, also known as post quantum calculus, we introduce a deformation of the ψ-Fueter operator written in terms of suitable difference operators, which reduces to a deformed q calculus when q'=1. We also prove the Stokes and Borel-Pompeiu formulas in this context. This work is the first investigation of results in quaternionic analysis in the setting of the (q,q')-calculus theory.