Abstract
This work introduces fractional d-bar derivatives in the setting of quaternionic analysis, by giving meaning to fractional powers of the quaternionic d-bar derivative. The definition is motivated by starting from nth-order d-bar derivatives for \(n\in {\mathbb {N}}\), and further justified by various natural properties such as composition laws and its action on special functions such as Fueter polynomials.
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Acknowledgements
The first two authors would like to thank Eastern Mediterranean University for financial support via a BAP-C grant with project number BAPC-04-22-03, and they are also grateful to the Ghent Analysis and PDE group for hosting them during the period this research began.
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This paper is part of the Topical Collection on the International Conference on Mathematical Methods in Physics (ICMMP23) edited by P. Cerejeiras, H. Hedenmalm, Z. Mouayn, and S. Najoua Lagmiri.
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Fernandez, A., Güder, C. & Yasin, W. Fractional Powers of the Quaternionic d-Bar Derivative. Adv. Appl. Clifford Algebras 34, 2 (2024). https://doi.org/10.1007/s00006-023-01306-7
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DOI: https://doi.org/10.1007/s00006-023-01306-7