IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v349y2019icp292-303.html
   My bibliography  Save this article

A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation

Author

Listed:
  • Xiong, Xiangtuan
  • Xue, Xuemin

Abstract

In this paper, we are concerned with an inverse source problem for the time-fractional diffusion equation with variable coefficients in a general bounded domain. The problem is mildly ill-posed. A new fractional Tikhonov method is proposed. We discuss the a-priori regularization parameter choice rule and the a-posteriori regularization parameter choice rule, and prove the corresponding convergence estimates. Numerical experiments are conducted for illustrating effectiveness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:292-303
    DOI: 10.1016/j.amc.2018.12.063
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031831124X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.12.063?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Virginia Kiryakova & Jordanka Paneva-Konovska, 2024. "Going Next after “A Guide to Special Functions in Fractional Calculus”: A Discussion Survey," Mathematics, MDPI, vol. 12(2), pages 1-39, January.
    2. Edgardo Alvarez & Carlos Lizama, 2020. "The Super-Diffusive Singular Perturbation Problem," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    3. Sweilam, N.H. & El-Sakout, D.M. & Muttardi, M.M., 2020. "Numerical study for time fractional stochastic semi linear advection diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Ravi Agarwal & Snezhana Hristova & Donal O’Regan & Peter Kopanov, 2020. "p -Moment Mittag–Leffler Stability of Riemann–Liouville Fractional Differential Equations with Random Impulses," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    5. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    6. Rakesh K. Parmar, 2015. "A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus," Mathematics, MDPI, vol. 3(4), pages 1-14, November.
    7. Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.
    8. Angstmann, C.N. & Henry, B.I. & Jacobs, B.A. & McGann, A.V., 2017. "A time-fractional generalised advection equation from a stochastic process," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 175-183.
    9. Soma Dhar & Lipi B. Mahanta & Kishore Kumar Das, 2019. "Formulation Of The Simple Markovian Model Using Fractional Calculus Approach And Its Application To Analysis Of Queue Behaviour Of Severe Patients," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 117-129, March.
    10. Saif Eddin Jabari & Nikolaos M. Freris & Deepthi Mary Dilip, 2020. "Sparse Travel Time Estimation from Streaming Data," Transportation Science, INFORMS, vol. 54(1), pages 1-20, January.
    11. Katarzyna Górska & Andrzej Horzela, 2021. "Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character," Mathematics, MDPI, vol. 9(5), pages 1-13, February.
    12. Slawomir Blasiak, 2021. "Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach," Energies, MDPI, vol. 14(17), pages 1-13, September.
    13. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
    14. Goswami, Koushik, 2021. "Work fluctuations in a generalized Gaussian active bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    15. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model," Mathematics, MDPI, vol. 9(7), pages 1-34, March.
    16. Virginia Kiryakova, 2021. "A Guide to Special Functions in Fractional Calculus," Mathematics, MDPI, vol. 9(1), pages 1-40, January.
    17. Murat A. Sultanov & Durdimurod K. Durdiev & Askar A. Rahmonov, 2021. "Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    18. Kassim, Mohammed D. & Tatar, Nasser-eddine, 2021. "Nonlinear fractional distributed Halanay inequality and application to neural network systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    19. Jessica Mendiola-Fuentes & Eugenio Guerrero-Ruiz & Juan Rosales-García, 2024. "Multivariate Mittag-Leffler Solution for a Forced Fractional-Order Harmonic Oscillator," Mathematics, MDPI, vol. 12(10), pages 1-11, May.
    20. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:292-303. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.