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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
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    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.
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