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

This paper is a continuation of our work [J. O. González Cervantes and J. Bory Reyes, A quaternionic fractional Borel–Pompeiu type formula, Fractal30(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. [ABSTRACT FROM AUTHOR]