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Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative

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  • Songshu Liu

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

Abstract

This research determines an unknown source term in the fractional diffusion equation with the Riemann–Liouville derivative. This problem is ill-posed. Conditional stability for the inverse source problem can be given. Further, a fractional Tikhonov regularization method was applied to regularize the inverse source problem. In the theoretical results, we propose a priori and a posteriori regularization parameter choice rules and obtain the convergence estimates.

Suggested Citation

  • Songshu Liu, 2022. "Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3213-:d:907451
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    References listed on IDEAS

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    1. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    2. Ma, Yong-Ki & Prakash, P. & Deiveegan, A., 2018. "Generalized Tikhonov methods for an inverse source problem of the time-fractional diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 39-48.
    3. Xiong, Xiangtuan & Xue, Xuemin, 2019. "A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 292-303.
    4. Zheng, Guang-Hui & Zhang, Quan-Guo, 2018. "Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 37-47.
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