Stability estimate and the modified regularization method for a Cauchy problem of the fractional diffusion equation
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[1] T. Szabo,et al. A model for longitudinal and shear wave propagation in viscoelastic media , 2000, The Journal of the Acoustical Society of America.
[2] A. N. Tikhonov,et al. Solutions of ill-posed problems , 1977 .
[3] Fredrik Berntsson,et al. Wavelet and Fourier Methods for Solving the Sideways Heat Equation , 1999, SIAM J. Sci. Comput..
[4] Masahiro Yamamoto,et al. LETTER TO THE EDITOR: One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization , 2000 .
[5] Hans-Peter Scheffler,et al. Stochastic solution of space-time fractional diffusion equations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.
[6] Naomichi Hatano,et al. Aerosol migration near Chernobyl : Long-term data and modeling , 1998 .
[7] Fredrik Berntsson,et al. A spectral method for solving the sideways heat equation , 1999 .
[8] Ting Wei,et al. Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation , 2001 .
[9] J. Bouchaud,et al. Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , 1990 .
[10] George M. Zaslavsky,et al. Fractional kinetic equation for Hamiltonian chaos , 1994 .
[11] E. Montroll,et al. Anomalous transit-time dispersion in amorphous solids , 1975 .
[12] Xiang Xu,et al. Carleman estimate for a fractional diffusion equation with half order and application , 2011 .
[13] Peter Richmond,et al. Waiting time distributions in financial markets , 2002 .
[14] Brian Clark,et al. Physics in Oil Exploration , 2002 .
[15] Chu-Li Fu,et al. Regularization strategies for a two-dimensional inverse heat conduction problem , 2007 .
[16] L. Gelhar,et al. Field study of dispersion in a heterogeneous aquifer: 2. Spatial moments analysis , 1992 .
[17] Barkai,et al. From continuous time random walks to the fractional fokker-planck equation , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[18] Diego A. Murio,et al. Implicit finite difference approximation for time fractional diffusion equations , 2008, Comput. Math. Appl..
[19] I. Podlubny. Fractional differential equations , 1998 .
[20] A. Chaves,et al. A fractional diffusion equation to describe Lévy flights , 1998 .
[21] Enrico Scalas,et al. Waiting-times and returns in high-frequency financial data: an empirical study , 2002, cond-mat/0203596.
[22] Xiang-Tuan Xiong,et al. An optimal method for fractional heat conduction problem backward in time , 2012 .
[23] T. Wei,et al. A new regularization method for a Cauchy problem of the time fractional diffusion equation , 2012, Adv. Comput. Math..
[24] R. Gorenflo,et al. Discrete random walk models for space-time fractional diffusion , 2002, cond-mat/0702072.
[25] Boris Baeumer,et al. Particle tracking for time-fractional diffusion. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.
[26] Y. Hon,et al. The method of fundamental solution for solving multidimensional inverse heat conduction problems , 2005 .
[27] H. Engl,et al. Regularization of Inverse Problems , 1996 .
[28] M. Meerschaert,et al. Fractional vector calculus for fractional advection–dispersion , 2006 .
[29] D. S. Ivaschenko,et al. Numerical methods for solving inverse problems for time fractional diffusion equation with variable coefficient , 2009 .
[30] J. Klafter,et al. The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .
[31] T. Wei,et al. Spectral regularization method for a Cauchy problem of the time fractional advection-dispersion equation , 2010, J. Comput. Appl. Math..
[32] J. Hadamard,et al. Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .
[33] Masahiro Yamamoto,et al. Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation , 2009 .
[34] J. Klafter,et al. Transport aspects in anomalous diffusion: Lévy walks. , 1989, Physical review. A, General physics.
[35] Diego A. Murio,et al. Stable numerical solution of a fractional-diffusion inverse heat conduction problem , 2007, Comput. Math. Appl..