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[HAD 03] H ADDAR H, H LIE T, M ATIGNON D, A Webster-Lokshin model for waves with viscothermal losses and impedance boundary conditions: strong solutions , Mathematical and Numerical Aspects of Wave Propagation, p 66 71, Springer Verlag, 2003 [HAD 08a] H ADDAR H, L I J-R, M ATIGNON D, Ef cient solution of a wave equation with fractional order dissipative terms , J Comput & Appl Maths, 2008, forthcoming [HAD 08b] H ADDAR H, M ATIGNON D, Theoretical and numerical analysis of the Webster-Lokshin model, Report, Institut National de la Recherche en Informatique et Automatique (INRIA), 2008, Research Report no 6558 [HEL 00] H ELESCHEWITZ D, Analyse et simulation de syst mes diff rentiels fractionnaires et pseudo-diff rentiels lin aires sous repr sentation diffusive, PhD Thesis, ENST, December 2000 [H L 06a] H LIE T, M ATIGNON D, Diffusive reprentations for the analysis and simulation of ared acoustic pipes with visco-thermal losses , Math Models Meth Appl Sci, vol 16, p 503 536, January 2006 [H L 06b] H LIE T, M ATIGNON D, Representations with poles and cuts for the time-domain simulation of fractional systems and irrational transfer functions , Signal Processing, vol 86, p 2516 2528, July 2006 [KOE 84] KOELLER RC, Applications of fractional calculus to the theory of viscoelasticity , J Appl Mech, vol 51, p 299 307, 1984 [KOE 86] KOELLER RC, Polynomial operators, Stieljes convolution, and fractional calculus in hereditary mechanics , Acta Mech, vol 58, p 251 264, 1986 [KOL 69] K LBIG KS, Laplace transform, Lectures in the academic training programme, CERN, Geneva, Switzerland, 1968 1969 [LEM 90] L E M EHAUT A, Les g om tries fractales, Hermes, Paris, 1990 [LOK 78a] L OKSHIN AA, Wave equation with singular retarded time , Dokl Akad Nauk SSSR, vol 240, p 43 46, 1978 [LOK 78b] L OKSHIN AA, ROK VE, Fundamental solutions of the wave equation with retarded time , Dokl Akad Nauk SSSR, vol 239, p 1305 1308, 1978 [MAT 94] M ATIGNON D, Repr sentations en variables d tat de mod les de guides d ondes avec d rivation fractionnaire, PhD Thesis, University of Paris XI, November 1994 [MAT 95a] M ATIGNON D, D A NDR A -N OVEL B, D composition modale fractionnaire de l quation des ondes avec pertes viscothermiques , in Journ es d tudes : les syst mes d ordre non entier en automatique, Groupe de recherche Automatique du CNRS, April 1995 [MAT 95b] M ATIGNON D, D A NDR A -N OVEL B, Spectral and time-domain consequences of an integro-differential perturbation of the wave PDE , in Third International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena (Mandelieu, France), INRIA, SIAM, p 769-771, April 1995.

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[MAT 96a] M ATIGNON D, Fractional modal decomposition of a boundary-controlled-and-observed in nite-dimensional linear system , in Mathematical Theory of Networks and Systems (Saint-Louis, Missouri), MTNS, June 1996 [MAT 96b] M ATIGNON D, Stability results for fractional differential equations with applications to control processing , in Computational Engineering in Systems Applications (Lille, France), IMACS, IEEE-SMC, vol 2, p 963 968, July 1996 [MAT 96c] M ATIGNON D, D A NDR A -N OVEL B, Some results on controllability and observability of nite-dimensional fractional differential systems , in Computational Engineering in Systems Applications (Lille, France), IMACS, IEEE-SMC, vol 2, p 952 956, July 1996 [MAT 97] M ATIGNON D, D A NDR A -N OVEL B, Observer-based controllers for fractional differential systems , in Conference on Decision and Control (San Diego, California), IEEE-CSS, SIAM, p 4967 4972, December 1997 [MAT 98a] M ATIGNON D, Stability properties for generalized fractional differential systems , in ESAIM: Proceedings, vol 5, p 145 158, December 1998 (available at http://wwwedpsciencesorg/articlesproc/Vol5/) [MAT 98b] M ATIGNON D, AUDOUNET J, M ONTSENY G, Energy decay for wave equations with damping of fractional order , in Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena (Golden, Colorado), INRIA, SIAM, p 638 640, June 1998 [MAT 98c] M ATIGNON D, M ONTSENY G (Eds), Fractional differential systems: Models, methods, and applications, ESAIM, Proceedings 5, December 1998 (available at http://wwwedpsciencesorg/articlesproc/Vol5/) [MAT 05] M ATIGNON D, P RIEUR C, Asymptotic stability of linear conservative systems when coupled with diffusive systems , ESAIM Control Optim Calc Var, vol 11, p 487 507, July 2005 [MAT 06] M ATIGNON D, Asymptotic stability of the Webster-Lokshin model , Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, 11 p (CD-Rom), July 2006, (invited session) [MAT 08] M ATIGNON D, Z WART H, Standard diffusive systems as well-posed linear systems , 2008, submitted [MIL 93] M ILLER KS, ROSS B, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, 1993 [MIT 04] M ITTAG -L EFFLER G, Sur la repr sentation analytique d une branche uniforme d une fonction monog ne , Acta Math, vol 29, p 101 168, 1904 [MON 97] M ONTSENY G, AUDOUNET J, M ATIGNON D, Fractional integro-differential boundary control of the Euler-Bernoulli beam , in Conference on Decision and Control (San Diego, California), IEEE-CSS, SIAM, p 4973 4978, December 1997 [MON 98] M ONTSENY G, Diffusive representation of pseudo-differential time-operators , in ESAIM: Proceedings, vol 5, p 159 175, December 1998 (available at http://wwwedpsciencesorg/articlesproc/Vol5/).

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