IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v384y2020ics0096300320303350.html

Simultaneous identification of three parameters in a time-fractional diffusion-wave equation by a part of boundary Cauchy data

Author

Listed:
  • Xian, Jun
  • Yan, Xiong-bin
  • Wei, Ting

Abstract

This paper is devoted to determine the fractional order, the initial flux speed and the boundary Neumann data simultaneously in a one-dimensional time-fractional diffusion-wave equation from part boundary Cauchy observation data. We prove the uniqueness result for this inverse problem by using a new result for the Mittag-Leffler function and Laplace transform combining with analytic continuation. Then we use the iterative regularizing ensemble Kalman method in Bayesian framework to solve the inverse problem numerically. And four numerical examples are provided to show the effectiveness and stability of the proposed algorithm.

Suggested Citation

  • Xian, Jun & Yan, Xiong-bin & Wei, Ting, 2020. "Simultaneous identification of three parameters in a time-fractional diffusion-wave equation by a part of boundary Cauchy data," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    • Handle: RePEc:eee:apmaco:v:384:y:2020:i:c:s0096300320303350
    DOI: 10.1016/j.amc.2020.125382
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320303350
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125382?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    2. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    3. Ruan, Zhousheng & Zhang, Wen & Wang, Zewen, 2018. "Simultaneous inversion of the fractional order and the space-dependent source term for the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 365-379.
    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. Hou, Mimi & Xi, Xuan-Xuan & Zhou, Xian-Feng, 2021. "Boundary control of a fractional reaction-diffusion equation coupled with fractional ordinary differential equations with delay," Applied Mathematics and Computation, Elsevier, vol. 406(C).

    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. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    2. Alqhtani, Manal & Owolabi, Kolade M. & Saad, Khaled M. & Pindza, Edson, 2022. "Efficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Yang, Fan & Fu, Chu-Li & Li, Xiao-Xiao, 2018. "The method of simplified Tikhonov regularization for a time-fractional inverse diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 219-234.
    4. Marseguerra, Marzio & Zoia, Andrea, 2008. "Pre-asymptotic corrections to fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2668-2674.
    5. Staccioli, Jacopo & Napoletano, Mauro, 2021. "An agent-based model of intra-day financial markets dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 331-348.
    6. Wei, T. & Li, Y.S., 2018. "Identifying a diffusion coefficient in a time-fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 77-95.
    7. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    8. Berardi, Luca & Serva, Maurizio, 2005. "Time and foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 403-412.
    9. Zhigang Hu & Wenbin Liu & Jiaying Liu, 2014. "Existence of Solutions of Fractional Differential Equation with p‐Laplacian Operator at Resonance," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    10. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.
    11. Allaberen Ashyralyev & Yagub A. Sharifov, 2012. "Existence and Uniqueness of Solutions for the System of Nonlinear Fractional Differential Equations with Nonlocal and Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    12. Scalas, Enrico & Viles, Noèlia, 2014. "A functional limit theorem for stochastic integrals driven by a time-changed symmetric α-stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 385-410.
    13. Cen, Zhongdi & Le, Anbo & Xu, Aimin, 2017. "A robust numerical method for a fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 445-452.
    14. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
    15. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    16. Marseguerra, M. & Zoia, A., 2008. "Monte Carlo evaluation of FADE approach to anomalous kinetics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 345-357.
    17. Wael W. Mohammed & Meshari Alesemi & Sahar Albosaily & Naveed Iqbal & M. El-Morshedy, 2021. "The Exact Solutions of Stochastic Fractional-Space Kuramoto-Sivashinsky Equation by Using ( G ′ G )-Expansion Method," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
    18. Cappellini, Alessandro & Ferraris, Gianluigi, 2007. "Waiting Times in Simulated Stock Markets," MPRA Paper 7324, University Library of Munich, Germany.
    19. Kashfi Sadabad, Mahnaz & Jodayree Akbarfam, Aliasghar, 2021. "An efficient numerical method for estimating eigenvalues and eigenfunctions of fractional Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 547-569.
    20. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:384:y:2020:i:c:s0096300320303350. 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.