A fractional Borel-Pompeiu type formula and a related fractional $\psi-$Fueter operator with respect to a vector-valued function

TL;DR

This paper develops a fractional calculus framework combining $ extit{ extbf{ extpsi}}$-hyperholomorphic functions with fractional derivatives, establishing a new Borel-Pompeiu formula for a fractional $ extit{ extpsi}$-Fueter operator involving vector-valued functions.

Contribution

It introduces a novel fractional Borel-Pompeiu formula linked to a fractional $ extit{ extpsi}$-Fueter operator, integrating fractional calculus with hyperholomorphic function theory.

Findings

Established a fractional Borel-Pompeiu type formula.

Connected fractional calculus with $ extit{ extpsi}$-hyperholomorphic functions.

Extended the theory to vector-valued functions.

Abstract

In this paper we combine the fractional $\psi-$hyperholomorphic function theory with the fractional calculus with respect to another function. As a main result, a fractional Borel-Pompeiu type formula related to a fractional $\psi-$Fueter operator with respect to a vector-valued function, is proved.