Fischer Decomposition in Generalized Fractional Ternary Clifford Analysis

Abstract

This paper describes the generalized fractional Clifford analysis in the ternary setting. We will give a complete algebraic and analytic description of the spaces of monogenic functions in this sense, their analogous Fischer decomposition, concluding with a description of the basis of the space of fractional homogeneous monogenic polynomials that arise in this case and an explicit algorithm for the construction of this basis.