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