1. Aubert, G., Kornprobst, P.:Mathematical Problems in Image Processing:Partial Diferential Equations and the Calculus of Variations, vol. 147. Springer, Berlin (2006) 2. Brunner, H., Han, H., Yin, D.:Artifcial boundary conditions and fnite diference approximations for a time-fractional difusion-wave equation on a two-dimensional unbounded spatial domain. J. Comput. Phys. 276, 541-562 (2014) 3. Burden, R., Faires, J.D.:Numerical Analysis, 9th edn. Brooks/Cole, Boston (2011) 4. Cao, J., Li, C., Chen, Y.:High-order approximation to Caputo derivatives and Caputo-type advectiondifusion equations (II). Fract. Calc. Appl. Anal. 18, 735-761 (2015) 5. Cao, J., Xu, C., Wang, Z.:A high order fnite diference/spectral approximations to the time fractional difusion equations. Adv. Mater. Res. 875, 781785 (2014) 6. Cao, W., Zeng, F., Zhang, Z., Karniadakis, G.E.:Implicit-explicit diference schemes for nonlinear fractional diferential equations with nonsmooth solutions. SIAM J. Sci. Comput. 38(5), A3070-A3093 (2016) 7. Cui, M.:Compact fnite diference method for the fractional difusion equation. J. Comput. Phys. 228, 7792-7804 (2009) 8. Deng, W.H., Hesthaven, J.S.:Local discontinuous Galerkin methods for fractional difusion equations. Math. Model. Numer. Anal. 47, 1845-1864 (2013) 9. Deng, W.H., Hesthaven, J.S.:Local discontinuous Galerkin methods for fractional ordinary diferential equations. BIT 55(4), 967-985 (2015) 10. Diethelm, K.:The Analysis of Fractional Diferential Equations. Springer, Berlin (2010) 11. Dimitrov, Y.:Three-point approximation for Caputo fractional derivative. Commun. Appl. Math. Comput. 31(4), 413-442 (2017) 12. Gao, G.H., Sun, Z.Z., Zhang, H.W.:A new fractional numerical diferentiation formula to approximate the Caputo fractional derivative and its applications. J. Comput. Phys. 259, 33-50 (2014) 13. Gonzalez, R., Woods, R.:Digital Image Processing, 2nd edn. Prentice Hall, New York (2001) 14. Guo, Z., Sun, J., Zhang, D., Wu, B.:Adaptive Perona-Malik model based on the variable exponent for image denoising. IEEE Trans. Image Process. 21, 958-967 (2012) 15. Jain, A.K.:Fundamentals of Digital Image Processing. Prentice Hall, Englewood Clifs (1989) 16. Langlands, T., Henry, B.:The accuracy and stability of an implicit solution method for the fractional difusion equation. J. Comput. Phys. 205, 719-736 (2005) 17. Lee, S.H., Seo, J.K.:Noise removal with Gauss curvature-driven difusion. IEEE Trans. Image Process. 14, 904-909 (2005) 18. Li, C., Chen, A., Ye, J.:Numerical approaches to fractional calculus and fractional ordinary diferential equation. J. Comput. Phys. 230, 3352-3368 (2011) 19. Lin, Y., Xu, C.:Finite diference/spectral approximations for the time-fractional difusion equation. J. Comput. Phys. 225, 1533-1552 (2007) 20. Lv, C., Xu, C.:Error analysis of a high order method for time-fractional difusion equations. SIAM J. Sci. Comput. 38, A2699-A2724 (2016) 21. Meerschaert, M., Tadjeran, C.:Finite diference approximations for fractional advection-dispersion fow equations. J. Comput. Appl. Math. 172, 65-77 (2004) 22. Perona, P., Malik, J.:Scale-space and edge detection using an isotropic difusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629-639 (1990) 23. Podlubny, I.:Fractional Diferential Equations. Academic Press, San Diego (1999) 24. Roop, J.P.:Computational aspect of FEM approximation of fractional advection dispersion equation on bounded domains in R2. J. Comput. Appl. Math. 193(1), 243-268 (2006) 25. Sun, Z.Z., Wu, X.:A fully discrete diference scheme for a difusion-wave system. Appl. Numer. Math. 56, 193-209 (2006) 26. Xu, Q., Hesthaven, J.S.:Discontinuous Galerkin method for fractional convection-difusion equations. SIAM J. Numer. Anal. 52(1), 405-423 (2014) 27. Yeganeh, S., Mokhtari, R., Hesthaven, J.S.:Space-dependent source determination in a time-fractional difusion equation using a local discontinuous Galerkin method. BIT Numer. Math. 57(3), 685-707 (2017) 28. Zhuang, P., Gu, Y.T., Liu, F., Turner, I., Yarlagadda, P.K.D.V.:Time-dependent fractional advectiondifusion equations by an implicit MLS meshless method. Int. J. Numer. Methods Eng. 88, 1346-1362 (2011) |