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arXiv · 2111.04156

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

The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$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.

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José Oscar González-Cervantes, Juan Bory-Reyes. 2021-11-07. A fractional Borel-Pompeiu type formula for holomorphic functions of two complex variables. https://doi.org/10.1142/s0218348x2250092x

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