The method of simplified Tikhonov regularization for a time-fractional inverse diffusion problem
Tài liệu tham khảo
Barkai, 2000, From continuous time random walks to the fractional Fokker-Planck equation, Phys. Rev. E, 61, 132, 10.1103/PhysRevE.61.132
Blumen, 1989, Transport aspects in anomalous diffusion, Levy Walks, 40, 3964
Carasso, 1982, Determining surface temperature from interior observations, SIAM J. Appl. Math., 42, 558, 10.1137/0142040
Chaves, 1998, A fractional diffusion equation to descrive levy flights, Phys. Lett. A, 239, 13, 10.1016/S0375-9601(97)00947-X
Cheng, 2007, A modified Tikhonov regularization method for a spherically symmetric three-dimensional inverse heat conduction problem, Math. Comput. Simulation, 75, 97, 10.1016/j.matcom.2006.09.005
Cheng, 2009, Uniqueness in an inverse problem for one-dimensional fractional diffusion equation, Inverse Problems, 16, 115002, 10.1088/0266-5611/25/11/115002
Engl, 1996
Feng, 2011, A regularization method for solving the Cauchy problem for the Helmholtz equation, Appl. Math. Model., 35, 3301, 10.1016/j.apm.2011.01.021
Fu, 2004, Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation, J. Comput. Appl. Math., 167, 449, 10.1016/j.cam.2003.10.011
Kirsch, 1996
Liu, 2010, A backward problem for the time-fractional diffusion equation, Appl. Anal., 89, 1769, 10.1080/00036810903479731
Metzler, 2000, Boundary value problems for fractional diffusion equations, Physica A, 278, 107, 10.1016/S0378-4371(99)00503-8
Murio, 2007, Stable numerical solution of a fractional-diffusion inverse heat conduction problem, Comput. Math. Appl., 53, 1492, 10.1016/j.camwa.2006.05.027
Murio, 2008, Time fractional IHCP with Caputo fractional derivatives, Comput. Math. Appl., 56, 2371, 10.1016/j.camwa.2008.05.015
Podlubny, 1999
Qian, 2010, Optimal modified method for a fractional-diffusion inverse heat conduction problem, Inverse Probl. Sci. Eng., 18, 521, 10.1080/17415971003624348
Raberto, 2002, Waiting-times and returns in high-frequency financial data: an empirical study, Physica A, 314, 749, 10.1016/S0378-4371(02)01048-8
Wang, 2013, Two regularization methods to identify a space-dependent source for the time-fractional diffusion equation, Appl. Numer. Math., 68, 39, 10.1016/j.apnum.2013.01.001
Xiong, 2012, An inverse problem for a fractional diffusion equation, J. Comput. Appl. Math., 236, 4474, 10.1016/j.cam.2012.04.019
Yang, 2010, A simplified Tikhonov regularization method for determining the heat source, Appl. Math. Model., 34, 3286, 10.1016/j.apm.2010.02.020
Yang, 2015, The quasi-reversibility regularization method for identifying the unknown source for time fractional diffusion equation, Appl. Math. Model., 39, 1500, 10.1016/j.apm.2014.08.010
Yang, 2014, A mollification regularization method for unknown source in time-fractional diffusion equation, Int. J. Comput. Math., 91, 516, 10.1080/00207160.2013.851787
Zhang, 2013, An optimal regularization method for space-fractional backward diffusion problem, Math. Comput. Simulation, 92, 14, 10.1016/j.matcom.2013.04.008
Zhang, 2013, Identifying an unknown source in time-fractional diffusion equation by a truncation method, Appl. Math. Comput., 219, 5972
Zheng, 2010, Spectral regularization method for the time fractional inverse advection–dispersion equation, Math. Comput. Simulation, 81, 37, 10.1016/j.matcom.2010.06.017
Zheng, 2010, Two regularization methods for solving a Riesz-Feller space-fractional backward diffusion problem, Inverse Problems, 26, 115017, 10.1088/0266-5611/26/11/115017
Zheng, 2011, A new regularization method for solving a time-fractional inverse diffusion problem, J. Math. Anal. Appl., 378, 418, 10.1016/j.jmaa.2011.01.067
Zheng, 2012, A new regularization method for a Cauchy problem of the time fractional diffusion equation, Adv. Comput. Math., 36, 377, 10.1007/s10444-011-9206-3