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

The study of ψ−hyperholomorphic functions defined on domains in R4 with values in H, namely null-solutions of the ψ−Fueter operator, is a topic which captured great interest in quaternionic analysis. 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. To the best of our knowledge this work is the first investigation of results in quaternionic analysis in the setting of the (q,q′)−calculus theory.