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

TL;DR

This paper extends quaternionic analysis by developing a perturbed fractional $$ueter operator calculus, including integral formulas, to advance the theory of $$hyperholomorphic functions.

Contribution

It introduces a novel perturbed fractional $$ueter operator calculus in quaternionic analysis, expanding the framework of $$hyperholomorphic functions with new integral formulas.

Findings

Derived Stokes and Borel-Pompeiu formulas in the perturbed fractional setting

Extended the fractional $$ueter function theory

Provided new tools for quaternionic analysis

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.