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

Murat A. Sultanov, Durdimurod K. Durdiev and Askar A. Rahmonov
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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

Mathematics, 2021, vol. 9, issue 17, 1-12

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.

Keywords: time-fractional equation; Fox function; Hankel transform; Laplace operator; Green function; exact solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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