A quaternionic perturbed fractional $ψ-$Fueter operator calculus

Abstract

Quaternionic analysis offers a function theory focused on the concept of ψ−hyperholomorphic functions defined as null solutions of the ψ−Fueter operator, where ψ is an arbitrary orthogonal base (called structural set) of H 4 .The main goal of the present paper is to extend the results given in [12], where a fractional ψ−hyperholomorphic function theory was developed. We introduce a quaternionic perturbed fractional ψ−Fueter operator calculus, where Stokes and Borel-Pompeiu formulas in this perturbed fractional ψ−Fueter setting are presented.