Daoud, Maha; Laamri, El Haj Fractional Laplacians : a short survey. (English) Zbl 1496.35001 Discrete Contin. Dyn. Syst., Ser. S 15, No. 1, 95-116 (2022). The authors give an overview of the different operators which extend the Laplacian one to the fractional derivatives context. They concentrate on their very definitions and basic properties, stressing on some differences among them and the classical Laplacian, also by making use of explicit examples. Alongside, Sobolev spaces of fractional order are presented. Reviewer: Nicola Abatangelo (Bologna) Cited in 10 Documents MSC: 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 26A33 Fractional derivatives and integrals 35R11 Fractional partial differential equations 58J35 Heat and other parabolic equation methods for PDEs on manifolds Keywords:fractional Laplacian; nonlocal operators; regional fractional Laplacian; spectral fractional Laplacian; fractional Poisson equations PDFBibTeX XMLCite \textit{M. Daoud} and \textit{E. H. Laamri}, Discrete Contin. Dyn. Syst., Ser. S 15, No. 1, 95--116 (2022; Zbl 1496.35001) Full Text: DOI References: [1] N. Abatangelo, Large solutions for fractional Laplacian Operators, Ph.D thesis, 2015. [2] N. Abatangelo and L. Dupaigne, Nonhomogeneous boundary conditions for the spectral fractional Laplacian, Ann. Inst. H. Poincaré Anal. 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