Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/39466
Title: On fractional semidiscrete Dirac operators of Lévy-Leblond type
Author: Faustino, Nelson
Keywords: Fractional semidiscrete Dirac operators
Riemann–Liouville fractional derivative
Fractional discrete Laplacian
Issue Date: Jul-2023
Publisher: Wiley
Abstract: In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L\'evy-Leblond type on the semidiscrete space-time lattice $h\mathbb{Z}^n\times[0,\infty)$ ($h>0$), resembling to fractional semidiscrete counterparts of the so-called parabolic Dirac operators. The methods adopted here are fairly operational, relying mostly on the algebraic manipulations involving Clifford algebras, discrete Fourier analysis techniques as well as standard properties of the analytic fractional semidiscrete semigroup $\left\{\exp(-te^{i\theta}(-\Delta_h)^{\alpha})\right\}_{t\geq 0}$, carrying the parameter constraints $0<\alpha\leq 1$ and $|\theta|\leq \frac{\alpha \pi}{2}$. The results obtained involve the study of Cauchy problems on $h\mathbb{Z}^n\times[0,\infty)$.
Peer review: yes
URI: http://hdl.handle.net/10773/39466
DOI: 10.1002/mana.202100234
ISSN: 0025-584X
Appears in Collections:CIDMA - Artigos
DMat - Artigos
CHAG - Artigos

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