IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v206y2023icp636-663.html
   My bibliography  Save this article

On spectral polar fractional Laplacian

Author

Listed:
  • Ansari, Alireza
  • Derakhshan, Mohammad Hossein

Abstract

In this paper, we introduce the fractional Sturm–Liouville operators and present the polar fractional Laplacian as a particular case of these operators. We also consider the distributed order space–time fractional diffusion equation involving the polar fractional Laplacian and propose three approaches for studying this problem on the circle and ring domains. First, we apply the integral transforms as the analytical methods to get the solution in terms of the Laplace-type integrals using the Titchmarsh theorem. Second, we use the finite difference method for discretization of the space variable and employ the matrix transfer technique to obtain a system of the distributed order fractional equations. For this system, we modify the Putzer’s algorithm and get the solution in terms of the eigenvalues of discretization matrix. Third, we employ the backward Euler numerical method for discretization of the time variable and find the corresponding error bound. Moreover, we compare and verify the approximate solutions with the exact solutions in analytical form.

Suggested Citation

  • Ansari, Alireza & Derakhshan, Mohammad Hossein, 2023. "On spectral polar fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 636-663.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:636-663
    DOI: 10.1016/j.matcom.2022.12.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004955
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.12.008?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. Azamat Dzarakhohov & Yuri Luchko & Elina Shishkina, 2021. "Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator," Mathematics, MDPI, vol. 9(13), pages 1-18, June.
    2. Boyadjiev, Lyubomir & Luchko, Yuri, 2017. "Mellin integral transform approach to analyze the multidimensional diffusion-wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 127-134.
    3. Yuri Luchko, 2017. "On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation," Mathematics, MDPI, vol. 5(4), pages 1-16, December.
    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. Marasi, H.R. & Derakhshan, M.H. & Ghuraibawi, Amer A. & Kumar, Pushpendra, 2024. "A novel method based on fractional order Gegenbauer wavelet operational matrix for the solutions of the multi-term time-fractional telegraph equation of distributed order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 405-424.
    2. Derakhshan, Mohammad Hossein & Rezaei, Hamid & Marasi, Hamid Reza, 2023. "An efficient numerical method for the distributed order time-fractional diffusion equation with error analysis and stability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 315-333.
    3. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2024. "Time–space fractional Euler–Poisson–Darboux equation with Bessel fractional derivative in infinite and finite domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 383-402.

    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. Awad, Emad & Sandev, Trifce & Metzler, Ralf & Chechkin, Aleksei, 2021. "Closed-form multi-dimensional solutions and asymptotic behaviors for subdiffusive processes with crossovers: I. Retarding case," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Yuri Luchko, 2017. "On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation," Mathematics, MDPI, vol. 5(4), pages 1-16, December.
    3. Francesco Mainardi & Armando Consiglio, 2020. "The Wright Functions of the Second Kind in Mathematical Physics," Mathematics, MDPI, vol. 8(6), pages 1-26, June.
    4. Emilia Bazhlekova & Ivan Bazhlekov, 2019. "Subordination Approach to Space-Time Fractional Diffusion," Mathematics, MDPI, vol. 7(5), pages 1-12, May.
    5. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.
    6. Yuri Luchko, 2019. "Some Schemata for Applications of the Integral Transforms of Mathematical Physics," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
    7. repec:eur:ejfejr:65 is not listed on IDEAS

    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:matcom:v:206:y:2023:i:c:p:636-663. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.