Advancing Fractional Riesz Derivatives through Dunkl Operator

Fethi Bouzeffour

doi:10.20944/preprints202309.0262.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 4 September 2023 / Approved: 5 September 2023 / Online: 5 September 2023 (11:46:40 CEST)

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ 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.

fractional calculus; difference-differential operator; special function

Computer Science and Mathematics, Mathematics

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Advancing Fractional Riesz Derivatives through Dunkl Operator

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