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. 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.