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

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

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 s...

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Bibliographic Details
Main Authors: Murat A. Sultanov, Durdimurod K. Durdiev, Askar A. Rahmonov
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Mathematics
Subjects:
time-fractional equation
Fox function
Hankel transform
Laplace operator
Green function
exact solution
Online Access:https://www.mdpi.com/2227-7390/9/17/2052
Description
Summary: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 <i>H</i>-functions and the convolution theorem.
ISSN:2227-7390

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