Regularization for a fractional sideways heat equation

Chen, 2010, Fractional diffusion equations by the Kansa method, Computers and Mathematics with Applications, 59, 1614, 10.1016/j.camwa.2009.08.004 Yu, 1998, Numerical research on the coherent structure in the viscoelastic second-order mixing layers, Applied Mathematics and Mechanics, 19, 671 Laskin, 2002, Fractional Levy motion and its application to network traffic modeling, Computer Networks, 40, 363, 10.1016/S1389-1286(02)00300-6 Scher, 1975, Anomalous transit-time dispersion in amorphous, Physical Review B, 12, 2455, 10.1103/PhysRevB.12.2455 Szabo, 2000, A model for longitudinal and shear wave propagation in viscoelastic media, Journal of the Acoustical Society of America, 107, 2437, 10.1121/1.428630 Gorenflo, 2002, Discrete random walk models for space–time fractional diffusion, Chemical Physics, 284, 521, 10.1016/S0301-0104(02)00714-0 Metzler, 2000, The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, 339, 1, 10.1016/S0370-1573(00)00070-3 Sokolov, 2002, Fractional kinetics, Physics Today, 55, 48, 10.1063/1.1535007 Mendes, 2009, A fractional calculus interpretation of the fractional volatility model, Nonlinear Dynamics, 55, 395, 10.1007/s11071-008-9372-0 Hadamard, 1953 Hon, 2008, A computational method for inverse free boundary determination problem, International Journal for Numerical Methods in Engineering, 73, 1291, 10.1002/nme.2122 Cheng, 2009, Uniqueness in an inverse problem for one-dimensional fractional diffusion equation, Inverse Problems, 16, 115002, 10.1088/0266-5611/25/11/115002 Zheng, 2010, Spectral regularization method for a Cauchy problem of the time fractional advection–dispersion equation, Journal of Computational and Applied Mathematics, 233, 2631, 10.1016/j.cam.2009.11.009 Bondarenko, 2009, Numerical methods for solving inverse problems for time fractional diffusion equation with variable coefficient, Journal of Inverse and Ill-Posed Problems, 17, 419, 10.1515/JIIP.2009.028 Murio, 2007, Stable numerical solution of a fractional-diffusion inverse heat conduction problem, Computers & Mathematics with Applications, 53, 1492, 10.1016/j.camwa.2006.05.027 Hon, 2004, A fundamental solution method for inverse heat conduction problem, Engineering Analysis with Boundary Elements, 28, 489, 10.1016/S0955-7997(03)00102-4 Hon, 2005, The method of fundamental solutions for solving multidimensional inverse heat conduction problems, Computer Modeling in Engineering & Sciences, 7, 119 Berntsson, 1999, A spectral method for solving the sideways heat equation, Inverse Problems, 15, 891, 10.1088/0266-5611/15/4/305 Podlubny, 1999 Eldén, 2000, Wavelet and Fourier methods for solving the sideways heat equation, SIAM Journal on Scientific Computing, 21, 2187, 10.1137/S1064827597331394 Seidman, 1990, An ‘optimal filtering’ method for the sideways heat equation, Inverse Problems, 6, 681, 10.1088/0266-5611/6/4/013 Tautenhahn, 1998, Optimality for ill-posed problems under general source conditions, Numerical Functional Analysis and Optimization, 19, 377, 10.1080/01630569808816834