IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i3p254-d213158.html
   My bibliography  Save this article

Some Schemata for Applications of the Integral Transforms of Mathematical Physics

Author

Listed:
  • Yuri Luchko

    (Department of Mathematics, Physics, and Chemistry, Beuth University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany)

Abstract

In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.

Suggested Citation

  • Yuri Luchko, 2019. "Some Schemata for Applications of the Integral Transforms of Mathematical Physics," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:254-:d:213158
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/3/254/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/3/254/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2023. "On spectral polar fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 636-663.
    5. Emilia Bazhlekova & Ivan Bazhlekov, 2019. "Subordination Approach to Space-Time Fractional Diffusion," Mathematics, MDPI, vol. 7(5), pages 1-12, May.
    6. 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:gam:jmathe:v:7:y:2019:i:3:p:254-:d:213158. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.