IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923008093.html
   My bibliography  Save this article

Eliminating solution singularity of variably distributed-order time-fractional diffusion equation via strongly singular initial distribution

Author

Listed:
  • Zheng, Xiangcheng
  • Jia, Jinhong
  • Guo, Xu

Abstract

We investigate a distributed-order time-fractional diffusion equation with a time-dependent density function and its support. The well-posedness and regularity of the equation are analyzed. In particular, by proposing appropriate assumptions on the density function, which may lead to a strongly singular initial distribution instead of smooth distributions that are usually imposed in the literature, we prove smoothing properties of the solutions and eliminate their nonphysical initial singularities without affecting the memory and hereditary properties of the model, i.e. the current state of the model depends on its states at previous time instants, away from the initial time. The results generalize the solution theory of distributed-order equations and provide a model correction for problems that do not exhibit initial singularities.

Suggested Citation

  • Zheng, Xiangcheng & Jia, Jinhong & Guo, Xu, 2023. "Eliminating solution singularity of variably distributed-order time-fractional diffusion equation via strongly singular initial distribution," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
  • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923008093
    DOI: 10.1016/j.chaos.2023.113908
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923008093
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.113908?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. Alikhanov, Anatoly A., 2015. "Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 12-22.
    2. Zhang, Meihui & Jia, Jinhong & Zheng, Xiangcheng, 2023. "Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    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. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.
    2. Yang, Dongsheng & Yu, Yongguang & Wang, Hu & Ren, Guojian & Zhang, Xiaoli, 2024. "Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    3. Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Wang, Yuan-Ming & Wen, Xin, 2020. "A compact exponential difference method for multi-term time-fractional convection-reaction-diffusion problems with non-smooth solutions," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    5. Alikhanov, Anatoly A. & Huang, Chengming, 2021. "A high-order L2 type difference scheme for the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 411(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:chsofr:v:174:y:2023:i:c:s0960077923008093. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.