IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v12y2020i1p74.html
   My bibliography  Save this article

Determination of Time-Dependent Coefficients in Time-Fractional Diffusion Equations by Variational Iteration Method

Author

Listed:
  • Mimi Li
  • Gongsheng Li
  • Zhiyuan Li
  • Xianzheng Jia

Abstract

Inverse problems of determining time-dependent coefficients in partial differential equations are difficult to deal with in general cases. The variational iteration method is introduced to determine the time-dependent coefficient in the fractional diffusion equation as well as the solution of the forward problem. By utilizing the additional condition and the property of the fractional derivative, an expression of the unknown is derived by which a nonlinear dynamical differential equation is obtained. The variational iteration method is applied to solve the nonlinear system and the time-dependent coefficient can be reconstructed in a semi-analytical form. Such method can give explicit expression of the solution in the meaning of approximation, or exact solution to the inverse problem in some cases. Several examples are presented to demonstrate feasibility and effectiveness of the proposed method for inverse time-dependent coefficient problems in the fractional diffusion equations.

Suggested Citation

  • Mimi Li & Gongsheng Li & Zhiyuan Li & Xianzheng Jia, 2020. "Determination of Time-Dependent Coefficients in Time-Fractional Diffusion Equations by Variational Iteration Method," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(1), pages 1-74, February.
    • Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:1:p:74
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/download/0/0/41953/43625
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/0/41953
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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)

    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. 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).

    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    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:ibn:jmrjnl:v:12:y:2020:i:1:p:74. 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: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    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.