M. A. Biot, Theory of Propagation of Elastic Waves in a Fluid???Saturated Porous Solid. I. Low???Frequency Range, The Journal of the Acoustical Society of America, vol.28, issue.2, pp.28-30, 1956.
DOI : 10.1121/1.1908239

URL : https://hal.archives-ouvertes.fr/hal-01368668

M. A. Biot, Theory of Propagation of Elastic Waves in a Fluid???Saturated Porous Solid. II. Higher Frequency Range, The Journal of the Acoustical Society of America, vol.28, issue.2, pp.28-30, 1956.
DOI : 10.1121/1.1908241

URL : https://hal.archives-ouvertes.fr/hal-01368668

J. M. Carcione, Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media, 2007.

J. M. Carcione, C. Morency, and J. E. Santos, Computational poroelasticity -A review, Geophysics, pp.75-80, 2010.

G. Chiavassa, B. Lombard, and J. Piraux, Numerical modeling of 1- D transient poroelastic waves in the low-frequency range, J. Comput. Appl. Math, pp.234-240, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00193103

G. Chiavassa and B. Lombard, Time domain numerical modeling of wave propagation in 2D heterogeneous porous media, Journal of Computational Physics, vol.230, issue.13, pp.230-243, 2011.
DOI : 10.1016/j.jcp.2011.03.030

URL : https://hal.archives-ouvertes.fr/hal-00547008

G. Chiavassa and B. Lombard, Abstract, Communications in Computational Physics, vol.7, issue.04, 2012.
DOI : 10.1016/j.crme.2003.11.004

W. Desch and R. Miller, Exponential stabilization of volterra integral equations with singular kernels, Journal of Integral Equations and Applications, vol.1, issue.3, pp.1-3, 1988.
DOI : 10.1216/JIE-1988-1-3-397

F. Dubois, A. Galucio, and N. Point, IntroductionàIntroductionà la dérivation fractionnaire : théorie et applications, 2010.

H. Emmerich and M. Korn, Incorporation of attenuation into timedomain computations of seismic wave fields, Geophysics, pp.52-61, 1987.

A. Ezziani, Modélisation mathématique et numérique de la propagation d'ondes dans les milieux viscoélastiques et poroélastiques, 2005.

Z. E. Fellah, J. Y. Chapelon, S. Berger, W. Lauriks, and C. Depollier, Ultrasonic wave propagation in human cancellous bone: application of Biot theory, J. Acoust. Soc. Am, pp.116-117, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00105792

G. Gautier, J. P. Groby, O. Dazel, L. Kelders, L. De-ryck et al., Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material, The Journal of the Acoustical Society of America, vol.130, issue.3, pp.130-1390, 2011.
DOI : 10.1121/1.3605530

URL : https://hal.archives-ouvertes.fr/hal-01323683

J. P. Groby and C. Tsogka, A TIME DOMAIN METHOD FOR MODELING VISCOACOUSTIC WAVE PROPAGATION, Journal of Computational Acoustics, vol.14, issue.02, pp.14-16, 2006.
DOI : 10.1142/S0218396X06003001

URL : https://hal.archives-ouvertes.fr/hal-00088882

H. Haddar, J. R. Li, and D. Matignon, Efficient solution of a wave equation with fractional-order dissipative terms, Journal of Computational and Applied Mathematics, vol.234, issue.6, pp.234-240, 2010.
DOI : 10.1016/j.cam.2009.08.051

URL : https://hal.archives-ouvertes.fr/hal-00743823

D. Heleschewitz, Analyse et simulation de systeme différentiels fractionnaires et pseudo-différentiels linéaires sous représentation diffusive, 2000.

D. L. Johnson, J. Koplik, and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, Journal of Fluid Mechanics, vol.24, issue.-1, pp.379-402, 1987.
DOI : 10.1121/1.388036

D. Lafarge, P. Lemarinier, and J. F. Allard, Dynamic compressibility of air in porous structures at audible frequencies, The Journal of the Acoustical Society of America, vol.102, issue.4, pp.102-106, 1997.
DOI : 10.1121/1.419690

G. Lefeuve-mesgouez, A. Mesgouez, G. Chiavassa, and B. Lombard, Semi-analytical and numerical methods for computing transient waves in 2D acoustic/poroelastic stratified media, Wave Motion, vol.49, issue.7, pp.49-667, 2012.
DOI : 10.1016/j.wavemoti.2012.04.006

URL : https://hal.archives-ouvertes.fr/hal-00667795

R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, 2002.
DOI : 10.1017/CBO9780511791253

B. Lombard and J. Piraux, Numerical treatment of two-dimensional interfaces for acoustic and elastic waves, Journal of Computational Physics, vol.195, issue.1, pp.195-196, 2004.
DOI : 10.1016/j.jcp.2003.09.024

URL : https://hal.archives-ouvertes.fr/hal-00004813

B. Lombard and J. Piraux, Numerical modeling of transient twodimensional viscoelastic waves, J. Comput. Phys, pp.230-245, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00545843

J. F. Lu and A. Hanyga, Wave field simulation for heterogeneous porous media with singular memory drag force, Journal of Computational Physics, vol.208, issue.2, pp.208-210, 2005.
DOI : 10.1016/j.jcp.2005.03.008

C. Lubich, Discretized Fractional Calculus, SIAM Journal on Mathematical Analysis, vol.17, issue.3, pp.704-719, 1986.
DOI : 10.1137/0517050

Y. J. Masson and S. R. Pride, Finite-difference modeling of Biot's poroelastic equations across all frequencies, Geophysics, pp.75-77, 2010.

C. B. Moler and C. F. Van-loan, Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later, SIAM Review, vol.45, issue.1, pp.45-48, 2003.
DOI : 10.1137/S00361445024180

T. M. Müller and P. N. Sahay, Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media, The Journal of the Acoustical Society of America, vol.129, issue.5, pp.129-134, 2011.
DOI : 10.1121/1.3560918

T. M. Müller and P. N. Sahay, Stochastic theory of dynamic permeability in poroelastic media, Physical Review E, vol.84, issue.2, p.26329, 2011.
DOI : 10.1103/PhysRevE.84.026329

T. J. Plona, Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies, Applied Physics Letters, vol.36, issue.4, pp.36-40, 1980.
DOI : 10.1063/1.91445

T. Schwartzkopff, M. Dumbser, and C. Munz, Fast high order ADER schemes for linear hyperbolic equations, Journal of Computational Physics, vol.197, issue.2, pp.197-199, 2004.
DOI : 10.1016/j.jcp.2003.12.007

N. Sebaa, Z. E. Fellah, M. Fellah, E. Ogam, A. Wirgin et al., Ultrasonic characterization of human cancellous bone using the Biot theory: Inverse problem, The Journal of the Acoustical Society of America, vol.120, issue.4, pp.120-124, 2006.
DOI : 10.1121/1.2335420

URL : https://hal.archives-ouvertes.fr/hal-00134021

O. J. Staffans, Well-posedness and stabilizability of a viscoelastic equation in energy space, Transactions of the American Mathematical Society, vol.345, issue.2, pp.345-347, 1994.
DOI : 10.1090/S0002-9947-1994-1264153-X

F. Torres, P. Vaudon, and B. Jecko, Application of fractional derivatives to the FDTD modeling of pulse propagation in a Cole-Cole dispersive medium, Microwave Opt, Technol. Lett, pp.13-18, 1996.