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

Jos㉠Oscar Gonzã Lez-Cervantes () and Juan Bory-Reyes
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Jos㉠Oscar Gonzã Lez-Cervantes: Departamento de Matemáticas, ESFM-Instituto Politécnico Nacional, 07338 Ciudad México, México
Juan Bory-Reyes: ��SEPI, ESIME-Zacatenco-Instituto Politécnico Nacional, 07338 Ciudad México, México

FRACTALS (fractals), 2022, vol. 30, issue 04, 1-13

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.

Keywords: Quaternionic Analysis; Fractional Derivatives; Borel–Pompeiu Formula; Holomorphic Functions of Several Complex Variables (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X2250092X

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