IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p2086-d449236.html
   My bibliography  Save this article

Fractional Diffusion–Wave Equation with Application in Electrodynamics

Author

Listed:
  • Arsen Pskhu

    (Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of Russian Academy of Sciences, 89-A Shortanov Street, 360000 Nalchik, Russia)

  • Sergo Rekhviashvili

    (Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of Russian Academy of Sciences, 89-A Shortanov Street, 360000 Nalchik, Russia)

Abstract

We consider a diffusion–wave equation with fractional derivative with respect to the time variable, defined on infinite interval, and with the starting point at minus infinity. For this equation, we solve an asympotic boundary value problem without initial conditions, construct a representation of its solution, find out sufficient conditions providing solvability and solution uniqueness, and give some applications in fractional electrodynamics.

Suggested Citation

  • Arsen Pskhu & Sergo Rekhviashvili, 2020. "Fractional Diffusion–Wave Equation with Application in Electrodynamics," Mathematics, MDPI, vol. 8(11), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2086-:d:449236
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/2086/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/2086/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    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. Ertuğrul Karaçuha & Vasil Tabatadze & Kamil Karaçuha & Nisa Özge Önal & Esra Ergün, 2020. "Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    2. Monica Aureliana Petcu & Liliana Ionescu-Feleaga & Bogdan-Ștefan Ionescu & Dumitru-Florin Moise, 2023. "A Decade for the Mathematics : Bibliometric Analysis of Mathematical Modeling in Economics, Ecology, and Environment," Mathematics, MDPI, vol. 11(2), pages 1-30, January.
    3. Arsen Pskhu, 2020. "Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains," Mathematics, MDPI, vol. 8(4), pages 1-15, March.
    4. İbrahim Avcı & Nazim I. Mahmudov, 2020. "Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    5. Bazán Navarro, Ciro Eduardo & Benazic Tomé, Renato Mario, 2024. "Qualitative behavior in a fractional order IS-LM-AS macroeconomic model with stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 425-443.
    6. Shi, Jianping & He, Ke & Fang, Hui, 2022. "Chaos, Hopf bifurcation and control of a fractional-order delay financial system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 348-364.
    7. Hou, Jie & Ma, Zhiying & Ying, Shihui & Li, Ying, 2024. "HNS: An efficient hermite neural solver for solving time-fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    8. Turkyilmazoglu, Mustafa & Altanji, Mohamed, 2023. "Fractional models of falling object with linear and quadratic frictional forces considering Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    9. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    10. Inés Tejado & Emiliano Pérez & Duarte Valério, 2020. "Fractional Derivatives for Economic Growth Modelling of the Group of Twenty: Application to Prediction," Mathematics, MDPI, vol. 8(1), pages 1-21, January.
    11. Kyriaki Tsilika, 2023. "Exploring the Contributions to Mathematical Economics: A Bibliometric Analysis Using Bibliometrix and VOSviewer," Mathematics, MDPI, vol. 11(22), pages 1-21, November.
    12. Ohud Almutairi & Adem Kılıçman, 2020. "Integral Inequalities for s -Convexity via Generalized Fractional Integrals on Fractal Sets," Mathematics, MDPI, vol. 8(1), pages 1-11, January.
    13. Vasily E. Tarasov, 2020. "Non-Linear Macroeconomic Models of Growth with Memory," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
    14. Wang, Bo & Liu, Jinping & Alassafi, Madini O. & Alsaadi, Fawaz E. & Jahanshahi, Hadi & Bekiros, Stelios, 2022. "Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    15. Vasily E. Tarasov, 2020. "Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 8(5), pages 1-3, April.
    16. Vasily E. Tarasov, 2024. "General Fractional Economic Dynamics with Memory," Mathematics, MDPI, vol. 12(15), pages 1-24, August.
    17. Borin, Daniel, 2024. "Caputo fractional standard map: Scaling invariance analyses," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    18. José A. Tenreiro Machado & Maria Eugénia Mata & António M. Lopes, 2020. "Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    19. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.

    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:8:y:2020:i:11:p:2086-:d:449236. 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.