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Title: A higher dimensional fractional Borel‐Pompeiu formula and a related hypercomplex fractional operator calculus
Author: Ferreira, Milton
Kraußhar, R. Sören
Rodrigues, M. Manuela
Vieira, Nelson
Keywords: Fractional Clifford analysis
Fractional derivatives
Stokes's formula
Borel-Pompeiu formula
Hodge-type decomposition
Cauchy-Green formula
Issue Date: 2019
Publisher: Wiley
Abstract: In this paper we develop a fractional integro-differential operator calculus for Clifford-algebra valued functions. To do that we introduce fractional analogues of the Teodorescu and Cauchy-Bitsadze operators and we investigate some of their mapping properties. As a main result we prove a fractional Borel-Pompeiu formula based on a fractional Stokes formula. This tool in hand allows us to present a Hodge-type decomposition for the fractional Dirac operator. Our results exhibit an amazing duality relation between left and right operators and between Caputo and Riemann-Liouville fractional derivatives. We round off this paper by presenting a direct application to the resolution of boundary value problems related to Laplace operators of fractional order.
Peer review: yes
DOI: 10.1002/mma.5602
ISSN: 0170-4214
Publisher Version:
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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