Abstract
We introduce a fractional version of the d-bar derivative operator acting on quaternionic functions. Some natural properties of this new operator are shown, including composition properties and its action on certain functions such as Fueter polynomials, which help to demonstrate its suitability compared with other attempts to define fractional quaternionic and Clifford derivatives.
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Acknowledgements
This research is financially supported by Eastern Mediterranean University via a BAP-C grant with project number BAPC-04-22-03. The first two authors are also grateful to the Ghent Analysis & PDE group for hosting them during the period this research began.
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Fernandez, A., Güder, C., Yasin, W. (2024). On Fractional Quaternionic d-Bar Derivatives. In: Ruzhansky, M., Torebek, B. (eds) Extended Abstracts MWCAPDE 2023. MWCAPDE 2023. Trends in Mathematics(), vol 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-41665-1_3
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DOI: https://doi.org/10.1007/978-3-031-41665-1_3
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