A quaternionic fractional Borel-Pompeiu type formula

Abstract

Quaternionic analysis relies heavily on results on functions defined on domains in ${\mathbb{R}}^4$ (or ${\mathbb{R}}^3$) with values in $\mathbb{H}$. This theory is centered around the concept of $\psi -$hyperholomorphic functions i.e., null-solutions of the $\psi -$Fueter operator related to a so-called structural set $\psi$ of ${\mathbb{H}}^4$. Fractional calculus, involving derivatives-integrals of arbitrary real or complex order, is the natural generalization of the classical calculus, which in the latter years became a well-suited tool by many researchers working in several branches of science and engineering. In theoretical setting, associated with a fractional $\psi -$Fueter operator that depends on an additional vector of complex parameters with fractional real parts, this paper establishes a fractional analogue of Borel-Pompeiu formula as a first step to develop a fractional $\psi -$hyperholomorphic function theory and the related operator calculus.

References in corpus (1)

• Biquaternionic Reformulation of a Fractional Monochromatic Maxwell System