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Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation

Author

Listed:
  • Murat A. Sultanov

    (Department of Mathematics, Faculty of Natural Science, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 160200, Kazakhstan)

  • Durdimurod K. Durdiev

    (Bukhara Branch of the Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Bukhara 100170, Uzbekistan)

  • Askar A. Rahmonov

    (Department of Mathematics, Bukhara State University, Bukhara 200114, Uzbekistan)

Abstract

In this work, an explicit solution of the initial-boundary value problem for a multidimensional time-fractional differential equation is constructed. The possibility of obtaining this equation from an integro-differential wave equation with a Mittag–Leffler–type memory kernel is shown. An explicit solution to the problem under consideration is obtained using the Laplace and Fourier transforms, the properties of the Fox H -functions and the convolution theorem.

Suggested Citation

  • Murat A. Sultanov & Durdimurod K. Durdiev & Askar A. Rahmonov, 2021. "Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2052-:d:622075
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    References listed on IDEAS

    as
    1. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Economic interpretation of fractional derivatives," Papers 1712.09575, arXiv.org.
    2. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
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