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Reconstruction of a space-dependent source in the inexact order time-fractional diffusion equation

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  • Trong, Dang Duc
  • Hai, Dinh Nguyen Duy
  • Minh, Nguyen Dang

Abstract

An inverse problem to recover a space-dependent factor of a source term in the inexact order time-fractional diffusion equation from final data is considered. The problem arises in many applications, but it is in general ill-posed. The ill-posedness is since small errors in the input data cause large errors in the output solution. To overcome this instability we propose the stable approximation solution via a general modified quasi-boundary value regularization method. Order optimal convergence rates for the worst case error of the method are derived under the usual source condition by using an a-priori and an a-posteriori regularization parameter choice rules, respectively. Finally, several numerical examples are provided to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Trong, Dang Duc & Hai, Dinh Nguyen Duy & Minh, Nguyen Dang, 2020. "Reconstruction of a space-dependent source in the inexact order time-fractional diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301260
    DOI: 10.1016/j.chaos.2020.109724
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    References listed on IDEAS

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    1. Trong, Dang Duc & Hai, Dinh Nguyen Duy & Minh, Nguyen Dang, 2019. "Optimal regularization for an unknown source of space-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 184-206.
    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.
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