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Advancing Fractional Riesz Derivatives through Dunkl Operators

Author

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  • Fethi Bouzeffour

    (Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

The aim of this work is to introduce a novel concept, Riesz–Dunkl fractional derivatives, within the context of Dunkl-type operators. A particularly noteworthy revelation is that when a specific parameter κ equals zero, the Riesz–Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

Suggested Citation

  • Fethi Bouzeffour, 2023. "Advancing Fractional Riesz Derivatives through Dunkl Operators," Mathematics, MDPI, vol. 11(19), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4073-:d:1247561
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