Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/26180
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 |
URI: | http://hdl.handle.net/10773/26180 |
DOI: | 10.1002/mma.5602 |
ISSN: | 0170-4214 |
Publisher Version: | https://onlinelibrary.wiley.com/doi/10.1002/mma.5602 |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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artigo35.pdf | 479.38 kB | Adobe PDF | View/Open |
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