[1] G. K. Ananth Grama, Anshul Gupta, V. Kumar, Introduction to Parallel Computing. 2nd Ed., Addison-Wesley (2003). Google Scholar

[2] K. Asanovic, R. Bodik, J. Demmel, T. Keaveny, K. Keutzer, J. Kubiatowicz, N. Morgan, D. Patterson, K. Sen, J. Wawrzynek, et al., A view of the parallel computing landscape. Communications of the ACM
52 (2009), 56–67. http://dx.doi.org/10.1145/1562764.1562783CrossrefWeb of ScienceGoogle Scholar

[3] K. Burrage, N. Hale, D. Kay, An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. SIAM J. on Scientific Computing
34 (2012), 2145–2172. http://dx.doi.org/10.1137/110847007CrossrefWeb of ScienceGoogle Scholar

[4] B. Catanzaro, N. Sundaram, K. Keutzer, Fast support vector machine training and classification on graphics processors. In: Proc. 25th Internat. Conf. on Machine Learning ACM (2008), 104–111. Google Scholar

[5] J. Chen, F. Liu, Analysis of stability and convergence of numerical approximation for the Riesz fractional reaction-dispersion equation (in Chinese). J. of Xiamen University (Natural Science)
45 (2006), 466–469. Google Scholar

[6] J. Chen, F. Liu, Stability and convergence of an implicit difference approximation for the space Riesz fractional reaction-dispersion equation. Numerical Mathematics, A Journal of Chinese Universities (EN Ser.)
16 (2007), 253. Google Scholar

[7] J. Chen, F. Liu, I. Turner, V. Anh, The fundamental and numerical solutions of the Riesz space fractional reaction-dispersion equation. ANZIAM J.
50 (2008), 45–57. http://dx.doi.org/10.1017/S1446181108000333CrossrefWeb of ScienceGoogle Scholar

[8] G. Colomer, R. Borrell, F. Trias, I. Rodrguez, Parallel algorithms for sn transport sweeps. J. of Computational Physics
232 (2012), 118–135. http://dx.doi.org/10.1016/j.jcp.2012.07.009Web of ScienceCrossrefGoogle Scholar

[9] C. Dhaigude, V. Nikam, Solution of fractional partial differential equations using iterative method. Fract. Calc. Appl. Anal.
15, No 4 (2012), 684–699; DOI: 10.2478/s13540-012-0046-8; at http://link.springer.com/journal/13540. CrossrefGoogle Scholar

[10] K. Diethelm, An efficient parallel algorithm for the numerical solution of fractional differential equations. Fract. Calc. Appl. Anal.
14, No 3 (2011), 475–490; DOI: 10.2478/s13540-011-0029-1; at http://link.springer.com/journal/13540. CrossrefGoogle Scholar

[11] N. Ford, J. Xiao, Y. Yan, A finite element method for time fractional partial differential equations. Fract. Calc. Appl. Anal.
14, No 3 (2011), 454–474; DOI: 10.2478/s13540-011-0028-2; at http://link.springer.com/journal/13540. CrossrefGoogle Scholar

[12] G. hua Gao, Z. zhong Sun, Y. nan Zhang, A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions. J. of Computational Physics
231 (2012), 2865–2879. http://dx.doi.org/10.1016/j.jcp.2011.12.028CrossrefWeb of ScienceGoogle Scholar

[13] C. Gong, J. Liu, L. Chi, H. Huang, J. Fang, Z. Gong, GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method. J. of Computational Physics
230 (2011), 6010–6022. http://dx.doi.org/10.1016/j.jcp.2011.04.010Web of ScienceGoogle Scholar

[14] C. Gong, J. Liu, H. Huang, Z. Gong, Particle transport with unstructured grid on GPU. Computer Physics Communications
183 (2012), 588–593. http://dx.doi.org/10.1016/j.cpc.2011.12.002CrossrefWeb of ScienceGoogle Scholar

[15] R. Gorenflo, F. Mainardi, Approximation of lévy-feller diffusion by random walk. J. for Analysis and its Applications
18 (1999), 231–246. Google Scholar

[16] H. Hejazi, T. Moroney, F. Liu, A finite volume method for solving the two-sided time-space fractional advection-dispersion equation. In: Proc. FDA’12 — 5th Symposium on Fractional Differentiation and Its Applications, Hohai University, 2012. Google Scholar

[17] J. T. Katsikadelis, The BEM for numerical solution of partial fractional differential equations. Comput. Math. Appl.
62 (2011), 891–901. http://dx.doi.org/10.1016/j.camwa.2011.04.001CrossrefGoogle Scholar

[18] D. J. Kerbyson, M. Lang, S. Pakin, Adapting wave-front algorithms to efficiently utilize systems with deep communication hierarchies. Parallel Computing
37 (2011), 550–561. http://dx.doi.org/10.1016/j.parco.2011.02.008CrossrefWeb of ScienceGoogle Scholar

[19] M. Köpf, C. Corinth, O. Haferkamp, T. Nonnenmacher, Anomalous diffusion of water in biological tissues. Biophysical Journal
70 (1996), 2950–2958. http://dx.doi.org/10.1016/S0006-3495(96)79865-XCrossrefGoogle Scholar

[20] C. Li, F. Zeng, F. Liu, Spectral approximations to the fractional integral and derivative. Fract. Calc. Appl. Anal.
15, No 3 (2012), 383–406; DOI: 10.2478/s13540-012-0028-x; at http://link.springer.com/journal/13540. CrossrefGoogle Scholar

[21] J. Lima, R. C. de Souza, The fractional Fourier transform over finite fields. Signal Processing
92 (2012), 465–476. http://dx.doi.org/10.1016/j.sigpro.2011.08.010CrossrefGoogle Scholar

[22] S. Lu, F. Molz, G. Fix, Possible problems of scale dependency in applications of the three-dimensional fractional advection-dispersion equation to natural porous media. Water Resour. Res.
38 (2002), 1165. Google Scholar

[23] M. Meerschaert, C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations. J. of Computational and Applied Mathematics
172 (2004), 65–77. http://dx.doi.org/10.1016/j.cam.2004.01.033CrossrefGoogle Scholar

[24] M. Meerschaert, C. Tadjeran, Finite difference approximations for twosided space-fractional partial differential equations. Applied Numerical Mathematics
56 (2006), 80–90. http://dx.doi.org/10.1016/j.apnum.2005.02.008Web of ScienceCrossrefGoogle Scholar

[25] K. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley & Sons, New York (1993). Google Scholar

[26] Y. nan Zhang, Z. zhong Sun, Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation. J. of Computational Physics
230 (2011), 8713–8728. http://dx.doi.org/10.1016/j.jcp.2011.08.020CrossrefWeb of ScienceGoogle Scholar

[27] N. Ozdemir, D. Avci, B. Iskender, The numerical solutions of a two-dimensional space-time Riesz-Caputo fractional diffusion equation. Intern. J. of Optimization and Control: Theories & Applications (IJOCTA)
1, (2011), 17–26. http://dx.doi.org/10.11121/ijocta.01.2011.0028Google Scholar

[28] H.-K. Pang, H.-W. Sun, Multigrid method for fractional diffusion equations. J. of Computational Physics
231 (2012), 693–703. http://dx.doi.org/10.1016/j.jcp.2011.10.005CrossrefGoogle Scholar

[29] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA (1999). Google Scholar

[30] S. Samko, A. Kilbas, O. Maričev, Fractional Integrals and Derivatives, Gordon and Breach Science Publ., Yverdon (1993). Google Scholar

[31] M. Snir, S. W. Otto, D. W. Walker, J. Dongarra, S. Huss-Lederman, MPI: The Complete Reference, MIT Press, Cambridge, MA — USA (1995). Google Scholar

[32] C. Tadjeran, M. M. Meerschaert, H.-P. Scheffler, A second-order accurate numerical approximation for the fractional diffusion equation. J. of Computational Physics
213 (2006), 205–213. http://dx.doi.org/10.1016/j.jcp.2005.08.008CrossrefGoogle Scholar

[33] Y. Xu, Z. He, The short memory principle for solving abel differential equation of fractional order. Computers & Mathematics with Applications
62 (2011), 4796–4805. http://dx.doi.org/10.1016/j.camwa.2011.10.071CrossrefWeb of ScienceGoogle Scholar

[34] S. B. Yuste, J. Quintana-Murillo, A finite difference method with nonuniform timesteps for fractional diffusion equations. Computer Physics Communications
183 (2012), 2594–2600. http://dx.doi.org/10.1016/j.cpc.2012.07.011CrossrefWeb of ScienceGoogle Scholar

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