@article{Bouzeffour2025, 
author = {Fethi Bouzeffour},
title = {Spectral analysis and integral representations of the tempered fractional Riesz derivative},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20571-20585},
keywords = {tempered fractional derivative, Fourier transform},
url = {https://www.sciopen.com/article/10.3934/math.2025918},
doi = {10.3934/math.2025918},
abstract = {In this work, we develop the harmonic analysis associated with the second-order differential operator              L        γ    =  −            d      2              d              x        2              −  2  γ        d          d      x        −      γ    2  . Fractional powers of              L        γ   are defined via spectral representation, and a singular integral representation is provided. Furthermore, we establish the equivalence between the fractional powers of              L        γ   and a tempered Riesz derivative.}
}