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Simultaneous identification of the unknown source term and initial value for the time fractional diffusion equation with local and nonlocal operators

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  • Qiao, Li
  • Yang, Fan
  • Li, Xiaoxiao

Abstract

In this paper, the problem of simultaneously identifying the unknown source term and initial value for the time fractional diffusion equation with local and nonlocal operators is studied. We prove the problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the measurable data. A fractional Tikhonov regularization method is proposed to solve the inverse problem. Moreover, based on a-priori bound assumption and a-priori, a-posteriori regularization parameter choice rules, we derive the convergence estimates. Finally, we provide several numerical examples to show the effectiveness of the proposed method.

Suggested Citation

  • Qiao, Li & Yang, Fan & Li, Xiaoxiao, 2024. "Simultaneous identification of the unknown source term and initial value for the time fractional diffusion equation with local and nonlocal operators," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011536
    DOI: 10.1016/j.chaos.2024.115601
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    References listed on IDEAS

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    1. Guo, Tian Liang & Zhang, KanJian, 2015. "Impulsive fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 581-590.
    2. S. Li, Y. & Wei, T., 2018. "An inverse time-dependent source problem for a time–space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 257-271.
    3. Zhang, Z.Q. & Wei, T., 2013. "An optimal regularization method for space-fractional backward diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 14-27.
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