Cauchy-Kovalevskaya extension theorem in fractional Clifford analysis (Q2350886)

The author gives the fractional Cauchy-Kovalevskaya extension (FCKFCK-extension) theorem for fractional monogenic functions defined on \(d\)-dimensional Euclidean space. Using this extension principle, fractional Fueter polynomials, forming a basis of fractional homogeneous polynomials, are introduced. The connection between the FCKFCK-extension of functions of a particular form and the classical Gegenbauer polynomials is studied. Finally, two examples of FCKFCK-extension are presented.