On the singularities of fractional differential systems, using a mathematical limiting process based on physical grounds
Résumé
Fractional systems are associated to irrational transfer functions for which non unique 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.