OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

On the singularities of fractional differential systems, using a mathematical limiting process based on physical grounds

Mignot, Rémi and Hélie, Thomas and Matignon, Denis On the singularities of fractional differential systems, using a mathematical limiting process based on physical grounds. (2009) Physica Scripta, vol. T136 (n° 014023). ISSN 0031-8949

[img] (Document in English)

PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
290kB

Official URL: http://dx.doi.org/10.1088/0031-8949/2009/T136/014023

Abstract

Fractional systems are associated with irrational transfer functions for which nonunique analytic continuations are available (from some right-half Laplace plane to a maximal domain). They involve continuous sets of singularities, namely cuts, which link fixed branching points with an arbitrary path. In this paper, an academic example of the 1D heat equation and a realistic model of an acoustic pipe on bounded domains are considered. Both involve a transfer function with a unique analytic continuation and singularities of pole type. The set of singularities degenerates into uniquely defined cuts when the length of the physical domain becomes infinite. From a mathematical point of view, both the convergence in Hardy spaces of some right-half complex plane and the pointwise convergence are studied and proved.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE
Other partners > Institut de Recherche et Coordination Acoustique/Musique - IRCAM (FRANCE)
Laboratory name:
Statistics:download
Deposited By: Denis Matignon

Repository Staff Only: item control page