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Articles

The inverse source problem for time-fractional diffusion equation: stability analysis and regularization

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Pages 969-996 | Received 27 Aug 2013, Accepted 12 Sep 2014, Published online: 16 Oct 2014

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Fan Yang, Qiaoxi Sun & Xiaoxiao Li. (2022) Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator. Acta Mathematica Scientia 42:4, pages 1485-1518.
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Caixuan Ren, Xinchi Huang & Masahiro Yamamoto. (2021) Conditional stability for an inverse coefficient problem of a weakly coupled time-fractional diffusion system with half order by Carleman estimate. Journal of Inverse and Ill-posed Problems 29:5, pages 635-651.
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Dinh Nguyen Duy Hai. (2021) Filter Regularization Method for a Nonlinear Riesz-Feller Space-Fractional Backward Diffusion Problem with Temporally Dependent Thermal Conductivity. Fractional Calculus and Applied Analysis 24:4, pages 1112-1129.
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Khaled M. Furati, Kassem Mustapha, Ibrahim O. Sarumi & Olaniyi S. Iyiola. (2021) Inverse source in two-parameter anomalous diffusion, numerical algorithms, and simulations over graded time meshes. Computational and Applied Mathematics 40:1.
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Fan Yang, Yan Zhang & Xiao-Xiao Li. (2019) Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation. Numerical Algorithms 83:4, pages 1509-1530.
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Xiaoliang Cheng, Lele Yuan & Kewei Liang. (2020) Inverse source problem for a distributed-order time fractional diffusion equation. Journal of Inverse and Ill-posed Problems 28:1, pages 17-32.
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Fan Yang, Ni Wang, Xiao-Xiao Li & Can-Yun Huang. (2019) A quasi-boundary regularization method for identifying the initial value of time-fractional diffusion equation on spherically symmetric domain. Journal of Inverse and Ill-posed Problems 27:5, pages 609-621.
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Fan Yang, Ping Fan, Xiao-Xiao Li & Xin-Yi Ma. (2019) Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source. Mathematics 7:9, pages 865.
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Fan Yang, Ping Fan & Xiao-Xiao Li. (2019) Fourier Truncation Regularization Method for a Three-Dimensional Cauchy Problem of the Modified Helmholtz Equation with Perturbed Wave Number. Mathematics 7:8, pages 705.
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Dang Duc Trong, Dinh Nguyen Duy Hai & Nguyen Dang Minh. (2019) Optimal regularization for an unknown source of space-fractional diffusion equation. Applied Mathematics and Computation 349, pages 184-206.
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Zhousheng Ruan, Sen Zhang & Wen Zhang. (2019) Numerical solution of time-dependent component with sparse structure of source term for a time fractional diffusion equation. Computers & Mathematics with Applications 77:5, pages 1408-1422.
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Atsushi Kawamoto. (2018) Lipschitz stability estimates in inverse source problems for a fractional diffusion equation of half order in time by Carleman estimates. Journal of Inverse and Ill-posed Problems 26:5, pages 647-672.
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Xiangtuan Xiong, E. Zhuang, Xuemin Xue & Zhi Qian. (2018) A regularization framework for mildly ill-posed problems connected with pseudo-differential operator. Journal of Computational and Applied Mathematics 341, pages 1-11.
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Fan Yang, Xiao Liu, Xiao-Xiao Li & Cheng-Ye Ma. (2017) Landweber iterative regularization method for identifying the unknown source of the time-fractional diffusion equation. Advances in Difference Equations 2017:1.
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Khaled M. Furati, Olaniyi S. Iyiola & Kassem Mustapha. (2017) An inverse source problem for a two-parameter anomalous diffusion with local time datum. Computers & Mathematics with Applications 73:6, pages 1008-1015.
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Qian Zhan & Hui Wei. (2016) An analytical approach to reconstruct the initial distribution of a sub-diffusion model with time-fractional derivative. Optik 127:21, pages 10238-10246.
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