  The study of $\psi-$hyperholomorphic functions defined on domains in $\mathbb
R^4$ with values in $\mathbb H$, namely null-solutions of the $\psi-$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 $\psi-$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.
