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Advancing Fractional Riesz Derivatives through Dunkl Operator
Version 1
: Received: 4 September 2023 / Approved: 5 September 2023 / Online: 5 September 2023 (11:46:40 CEST)
A peer-reviewed article of this Preprint also exists.
Bouzeffour, F. Advancing Fractional Riesz Derivatives through Dunkl Operators. Mathematics 2023, 11, 4073. Bouzeffour, F. Advancing Fractional Riesz Derivatives through Dunkl Operators. Mathematics 2023, 11, 4073.
Abstract
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.
Keywords
fractional calculus; difference-differential operator; special function
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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