Advancing Fractional Riesz Derivatives through Dunkl Operators

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

Mathematics, 2023, vol. 11, issue 19, 1-10

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.

Keywords: Fractional Riesz derivative; Dunkl operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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