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On the Fractional Dunkl–Laplacian

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Abstract

In this paper, we introduce a novel approach to the fractional Dunkl–Laplacian within a framework derived from specific reflection symmetries in Euclidean spaces. Our primary contributions include pointwise formulas, Bochner subordination, and addressing an extension problem for the fractional Dunkl–Laplacian.

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Acknowledgements

The authors are immensely grateful to the Editor and the reviewers for their invaluable insights, exceptionally pertinent commentary, and astute remarks. The first-named author expresses appreciation for the support provided by Researchers Supporting Project Number (RSPD2023R974), King Saud University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of mathematics, College of Sciences, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

    Fethi Bouzeffour

  2. Department of Statistics & OR, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

    Wissem Jedidi

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  1. Fethi Bouzeffour
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  2. Wissem Jedidi
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All authors contributed equally to the writing of this paper.

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Correspondence to Fethi Bouzeffour.

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Bouzeffour, F., Jedidi, W. On the Fractional Dunkl–Laplacian. Fract Calc Appl Anal 27, 433–457 (2024). https://doi.org/10.1007/s13540-023-00225-5

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