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A Fractional Borel–Pompeiu-Type Formula For Holomorphic Functions Of Two Complex Variables

Author

Listed:
  • JOSÉ OSCAR GONZà 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)

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.

Suggested Citation

  • Jos㉠Oscar Gonzã Lez-Cervantes & Juan Bory-Reyes, 2022. "A Fractional Borel–Pompeiu-Type Formula For Holomorphic Functions Of Two Complex Variables," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-13, June.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x2250092x
    DOI: 10.1142/S0218348X2250092X
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