Cauchy-Kovalevskaya extension theorem in fractional Clifford analysis

Abstract

In this paper, we establish the fractional Cauchy-Kovalevskaya extension (FCK-extension) theorem for fractional monogenic functions defined on 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 FCK-extension of functions of the form x^\alpha P_l and the classical Gegenbauer polynomials. Finally we present two examples of FCK-extension.