A quaternionic perturbed fractional $\psi -$Fueter operator calculus

Abstract

Quaternionic analysis offers a function theory focused on the concept of $\psi -$hyperholomorphic functions defined as null solutions of the $\psi -$Fueter operator, where $\psi$ is an arbitrary orthogonal base (called structural set) of ${\mathbb{H}}^4$. The main goal of the present paper is to extend the results given in \cite{BG2}, where a fractional $\psi -$hyperholomorphic function theory was developed. We introduce a quaternionic perturbed fractional $\psi -$Fueter operator calculus, where Stokes and Borel-Pompeiu formulas in this perturbed fractional $\psi -$Fueter setting are presented.

arXiv admin note: substantial text overlap with arXiv:2109.09604; text overlap with arXiv:2111.04156