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Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source

Author

Listed:
  • Fan Yang

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, China)

  • Ping Fan

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, China)

  • Xiao-Xiao Li

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, China)

  • Xin-Yi Ma

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, China)

Abstract

In present paper, we deal with a backward diffusion problem for a time-fractional diffusion problem with a nonlinear source in a strip domain. We all know this nonlinear problem is severely ill-posed, i.e., the solution does not depend continuously on the measurable data. Therefore, we use the Fourier truncation regularization method to solve this problem. Under an a priori hypothesis and an a priori regularization parameter selection rule, we obtain the convergence error estimates between the regular solution and the exact solution at 0 ≤ x < 1 .

Suggested Citation

  • 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, MDPI, vol. 7(9), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:865-:d:268639
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    References listed on IDEAS

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    1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    2. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
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    Cited by:

    1. Fan Yang & Qu Pu & Xiao-Xiao Li & Dun-Gang Li, 2019. "The Truncation Regularization Method for Identifying the Initial Value on Non-Homogeneous Time-Fractional Diffusion-Wave Equations," Mathematics, MDPI, vol. 7(11), pages 1-21, October.

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