D. Clarke, M. Meerschaert, and S. Wheatcraft, Fractal travel time estimates for dispersive contaminants, Ground Water, vol.43, issue.3, pp.401-407, 2005.

S. Wheatcraft and S. Tyler, An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry, Water Resources Research, vol.24, issue.4, pp.566-578, 1988.

R. Metzler and J. Klafter, The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, Journal of Physics A: Mathematical and General, vol.37, issue.31, p.161, 2004.

J. Clark, M. Silman, R. Kern, E. Macklin, and J. Hillerislambers, Seed dispersal near and far: Patterns across temperate and tropical forests, Ecology, vol.80, issue.5, pp.1475-1494, 1999.

S. Fedotov and A. Iomin, Migration and proliferation dichotomy in tumor-cell invasion, Phys. Rev. Lett, vol.98, p.118101, 2007.

D. Benson, R. Schumer, M. Meerschaert, and S. Wheatcraft, Fractional dispersion, lévy motion, and the made tracer tests, Transport in Porous Media, vol.42, issue.1, pp.211-240, 2001.

Z. Deng, V. Singh, and L. Bengtsson, Numerical solution of fractional advection-dispersion equation, Journal of Hydraulic Engineering, vol.130, issue.5, pp.422-431, 2004.

D. Benson, S. Wheatcraft, and M. Meerschaert, The fractional-order governing equation of lévy motion, Water Resources Research, vol.36, issue.6, pp.1413-1423, 2000.

R. Schumer, D. Benson, M. Meerschaert, and S. Wheatcraft, Eulerian derivation of the fractional advection-dispersion equation, Journal of Contaminant Hydrology, vol.48, issue.1-2, pp.170-174, 2001.

J. Kelly, D. Bolster, M. Meerschaert, J. Drummond, and A. Packmann, Fracfit: A robust parameter estimation tool for fractional calculus models, Water Resources Research, vol.53, pp.2559-2567, 2017.

S. Samko and A. ,

O. Kilbas and . Marichev, Fractional integrals and derivatives: theory and applications, 1993.

Z. Yong, D. Benson, M. Meerschaert, and H. Scheffler, On using random walks to solve the space-fractional advection-dispersion equations, Journal of Statistical Physics, vol.123, issue.1, pp.89-110, 2006.

M. Meerschaert and A. Sikorskii, Stochastic models for fractional calculus, Studies in Mathematics, vol.43, 2012.

F. Delay, P. Ackerer, and C. Danquigny, Simulating solute transport in porous or fractured formations using random walk particle tracking, Vadose Zone Journal, vol.4, issue.2, pp.360-379, 2005.

I. Ginzburg, Equilibrium-type and link-type lattice boltzmann models for generic advection and anisotropic-dispersion equation, Advances in Water Resources, vol.28, pp.1171-1195, 2005.

A. Kyprianou, Introductory Lectures on Fluctuations of Lévy processes with Applications, 2006.

V. Guillon, M. Fleury, D. Bauer, and M. C. Neel, Superdispersion in homogeneous unsaturated porous media using nmr propagators, Phys. Rev. E, vol.87, p.43007, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01337653

M. Néel, D. Bauer, and M. Fleury, Model to interpret pulsed-field-gradient nmr data including memory and superdispersion effects, Phys. Rev. E, vol.89, p.62121, 2014.

A. Zoia, A. Rosso, and M. Kardar, Fractional laplacian in bounbded domains, Phys. Rev. E, vol.76, p.21116, 2007.

M. Néel, A. Abdennadher, and M. Joelson, Fractional fick's law: the direct way, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.29, p.8299, 2007.

B. Baeumer, M. Kovács, M. Meerschaert, and H. Sankanarayanan, Boundary conditions for fractional diffusion, Journal of Computational and Applied Mathematics, vol.336, pp.408-424, 2018.

R. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini, and P. Paradisi, Discrete random walk models for space-time fractional diffusion, Chemical Physics, vol.284, issue.1-2, pp.521-541, 2002.

M. Meerschaert, H. Scheffler, and C. Tadjeran, Finite difference methods for two-dimensional fractional dispersion equation, Journal of Computational Physics, vol.211, issue.1, pp.249-261, 2006.

G. Fix and J. Roop, Least squares finite-element solution of a fractional order two-point boundary value problem, Computers & Mathematics with Applications, vol.48, issue.7-8, pp.1017-1033, 2004.

B. Servan-camas and F. Tsai, Lattice boltzmann method with two relaxation times for advection-diffusion equation: third order analysis and stability analysis, Advances in Water Resources, vol.31, issue.8, pp.1113-1126, 2008.

H. Yoshida and M. Nagaoka, Multiple-relaxation-time lattice boltzmann model for the convection and anisotropic diffusion equation, Journal of Computational Physics, vol.229, pp.7774-7795, 2010.

J. J. Huang, C. Shu, and Y. T. Chew, Mobility-dependent bifurcations in capillarity-driven two-phase fluid systems by using a lattice boltzmann phase-field model, International Journal for Numerical Methods in Fluids, vol.60, issue.2, pp.203-225, 2009.

A. Fakhari and M. Rahimian, Phase-field modeling by the method of lattice boltzmann equations, Phys. Rev. E, vol.81, p.36707, 2010.

J. Zhou, P. Haygarth, P. J. Withers, C. Macleod, P. Falloon et al., Lattice boltzmann method for the fractional advection-diffusion equation, Phys. Rev. E, vol.93, p.43310, 2016.

P. Bhatnagar, E. Gross, and M. Krook, A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems, Physical Review, vol.94, issue.3, pp.511-536, 1954.

S. Walsh and M. Saar, Macroscale lattice-boltzmann methods for low peclet number solute and heat transport in heterogeneous porous media, Water Resources Research, vol.46, issue.W07517, pp.1-15, 2010.

A. Cartalade, A. Younsi, and M. Plapp, Lattice boltzmann simulations of 3d crystal growth: Numerical schemes for a phase-field model with anti-trapping current, Computers & Mathematics with Applications, vol.71, issue.9, pp.1784-1798, 2016.
URL : https://hal.archives-ouvertes.fr/cea-01806375

A. Younsi and A. Cartalade, On anisotropy function in crystal growth simulations using lattice boltzmann equation, Journal of Computational Physics, vol.325, pp.1-21, 2016.
URL : https://hal.archives-ouvertes.fr/cea-01806166

P. Lallemand and L. Luo, Theory of the lattice boltzmann method: Dispersion, dissipation, isotropy, galilean invariance, and stability, Physical Review E, vol.61, issue.6, pp.6546-6562, 2000.

D. Humières, I. Ginzburg, M. Krafczyk, P. Lallemand, and L. Luo, Multiple-relaxation-time lattice boltzmann models in three dimensions, Phil. Trans. R. Soc. Lond. A, vol.360, pp.437-451, 2002.

K. Diethelm, N. Ford, A. Freed, and Y. Luchko, Algorithms for the fractional calculus: A selection of numerical methods, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.6-8, pp.743-773, 2005.

H. Risken, The Fokker-Planck Equation, 1984.

R. Weron, On the chambers-mallows-stuck method for simulating skewed stable random variables, Statistics & Probability Letters, vol.28, issue.2, pp.113-114, 1996.

P. Patie and T. Simon, Intertwining certain fractional derivatives, Potential Analysis, vol.36, pp.569-587, 2012.

Z. Chen, M. Meerschaert, and E. Nane, Space-time fractional diffusion on bounded domains, Journal of Mathematical Analysis and Applications, vol.393, issue.2, pp.479-488, 2012.

N. Burch and R. Lehoucq, Continuous-time random walks on bounded domains, Phys. Rev. E, vol.83, p.12105, 2011.

Q. Du, Z. Huang, and R. Lehoucq, Nonlocal convection-diffusion volume-constrained problems and jump processes, Discrete and Continuous Dynamical Systems -Series B, vol.19, issue.2, pp.373-389, 2014.

B. Baeumer, T. Luks, and M. Meerschaert, Space-time fractional dirichlet problems, under review

B. Baeumer, M. Kovács, M. Meerschaert, R. Schilling, and P. Straka, Reflected spectrally negative stable processes and their governing equations, Transactions of the American Mathematical Society, vol.368, issue.1, pp.227-248, 2016.

N. Krepysheva, L. D. Pietro, and M. Néel, Fractional diffusion and reflective boundary condition, Physica A: Statistical Mechanics and its Applications, vol.368, issue.2, pp.355-361, 2006.

J. Cushman and T. Ginn, Fractional advection-dispersion equation: A classical mass balance with convolution-fickian flux, Water Resource Research, vol.36, pp.3763-3766, 2000.

N. Cusimano, K. Burrage, I. Turner, and D. Kay, On reflecting boundary conditions for space-fractional equations on a finite interval: Proof of the matrix transfer technique, Applied Mathematical Modelling, vol.42, pp.554-565, 2017.