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Diffusive representations for fractional Laplacian: systems theory framework and numerical issues

Matignon, Denis Diffusive representations for fractional Laplacian: systems theory framework and numerical issues. (2009) Physica Scripta, vol. T136 (n° 014009). pp. 1-6. ISSN 0031-8949

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Official URL: http://dx.doi.org/10.1088/0031-8949/2009/T136/014009

Abstract

Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not an easy task either. Thus, the framework of diffusive representations, as already developed for causal fractional integrals and derivatives, is being applied to fractional Laplacian: it can be seen as an extension of the Wiener-­Hopf factorization and splitting techniques to irrational transfer functions.

Item Type:Article
Audience (journal):International peer-reviewed journal
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Institution: Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE
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Deposited By: Denis Matignon
Deposited On:03 May 2010 10:07

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