A quaternionic fractional BorelPompeiu 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., nullsolutions of the $\psi$Fueter operator related to a socalled structural set $\psi$ of $\mathbb H^4$. Fractional calculus, involving derivativesintegrals of arbitrary real or complex order, is the natural generalization of the classical calculus, which in the latter years became a wellsuited 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 BorelPompeiu formula as a first step to develop a fractional $\psi$hyperholomorphic function theory and the related operator calculus.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.09604
 Bibcode:
 2021arXiv210909604G
 Keywords:

 Mathematics  Complex Variables;
 30G30;
 30G35;
 32A36;
 35A08;
 35R11;
 45P05