Cauchy–Kovalevskaya Extension Theorem in Fractional Clifford Analysis

Abstract

In this paper, we establish the fractional Cauchy–Kovalevskaya extension (\(\textit{FCK}\)-extension) theorem for fractional monogenic functions defined on \(\mathbb {R}^d\). Based on this extension principle, fractional Fueter polynomials, forming a basis of the space of fractional spherical monogenics, i.e. fractional homogeneous polynomials, are introduced. We studied the connection between the \(\textit{FCK}\)-extension of functions of the form \(x^\alpha P_l\) and the classical Gegenbauer polynomials. Finally we present two examples of \(\textit{FCK}\)-extension.