A notion of fractional slice monogenic functions with respect to a pair of real valued functions

TL;DR

This paper develops a theory of fractional slice monogenic functions valued in Clifford algebras, based on null-solutions of a fractional Cauchy-Riemann operator in the Riemann-Liouville and Caputo sense, extending classical function theories.

Contribution

It introduces a novel framework for fractional slice monogenic functions defined via a fractional Cauchy-Riemann operator with respect to real-valued functions.

Findings

Established basic elements and results of the fractional slice monogenic functions theory.

Defined the fractional Cauchy-Riemann operator in the Riemann-Liouville and Caputo sense.

Extended classical monogenic function theory to a fractional setting.

Abstract

This work presents the basic elements and results of a Clifford algebra valued fractional slice monogenic functions theory defined from the null-solutions of a suitably fractional Cauchy-Riemann operator in the Riemann-Liouville and Caputo sense with respect to a pair of real valued functions on certain domains of Euclidean spaces.