A FRACTIONAL BOREL-POMPEIU-TYPE FORMULA FOR HOLOMORPHIC FUNCTIONS OF TWO COMPLEX VARIABLES

José Oscar González-Cervantes, Juan Bory-Reyes

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Abstract

This paper is a continuation of our work [J. O. González Cervantes and J. Bory Reyes, A quaternionic fractional Borel-Pompeiu type formula, Fractal 30(1) (2022) 2250013], where we introduced a fractional operator calculus related to a fractional ψ-Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the quaternionic structure, that depends on an additional vector of complex parameters with fractional real parts. This allowed us also to study a pair of lower order fractional operators and prove the associated analogues of both Stokes and Borel-Pompieu formulas for holomorphic functions in two complex variables.

Original languageEnglish
Article number2250092
JournalFractals
Volume30
Issue number4
DOIs
StatePublished - 1 Jun 2022

Keywords

  • Borel-Pompeiu Formula
  • Fractional Derivatives
  • Holomorphic Functions of Several Complex Variables
  • Quaternionic Analysis

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