The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann-Liouville partial derivative
The paper is devoted to the first boundary-value problem in a rectangular domain for a differential equation with the singular Bessel operator acting with respect to a spatial variable and the Riemann-Liouville fractional differentiation operator acting with respect to a time variable. An explic...
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Samara State Technical University
2021-01-01
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Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
Online Access: | http://mi.mathnet.ru/vsgtu1820 |
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doaj-77fd4ca775c04b9d8965f2156a41017a2021-08-12T18:42:06ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812021-01-0125224125610.14498/vsgtu1820The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann-Liouville partial derivativeFatima Gidovna Khushtova0Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Centre of RAS, Nal'chik, 360000, Russian Federation The paper is devoted to the first boundary-value problem in a rectangular domain for a differential equation with the singular Bessel operator acting with respect to a spatial variable and the Riemann-Liouville fractional differentiation operator acting with respect to a time variable. An explicit representation of the solution is constructed. The uniqueness of the solution is proved in the class of functions satisfying the Hölder condition with respect to the time variable. When the order of the fractional derivative is equal to unity, and the Bessel operator has no singularity, the studied equation coincides with the heat equation and the obtained results coincide with well-known corresponding classical results.http://mi.mathnet.ru/vsgtu1820 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Fatima Gidovna Khushtova |
spellingShingle |
Fatima Gidovna Khushtova The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann-Liouville partial derivative Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
author_facet |
Fatima Gidovna Khushtova |
author_sort |
Fatima Gidovna Khushtova |
title |
The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann-Liouville partial derivative |
title_short |
The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann-Liouville partial derivative |
title_full |
The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann-Liouville partial derivative |
title_fullStr |
The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann-Liouville partial derivative |
title_full_unstemmed |
The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann-Liouville partial derivative |
title_sort |
first boundary value problem in a rectangular domain for a differential equation with the bessel operator and the riemann-liouville partial derivative |
publisher |
Samara State Technical University |
series |
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
issn |
1991-8615 2310-7081 |
publishDate |
2021-01-01 |
description |
The paper is devoted to the first boundary-value problem in a rectangular domain for a differential equation with the singular Bessel operator acting with respect to a spatial variable and the Riemann-Liouville fractional differentiation operator acting with respect to a time variable.
An explicit representation of the solution is constructed.
The uniqueness of the solution is proved in the class of functions satisfying the Hölder condition with respect to the time variable.
When the order of the fractional derivative is equal to unity, and the Bessel operator has no singularity, the studied equation coincides with the heat equation and the obtained results coincide with well-known corresponding classical results. |
url |
http://mi.mathnet.ru/vsgtu1820 |
work_keys_str_mv |
AT fatimagidovnakhushtova thefirstboundaryvalueprobleminarectangulardomainforadifferentialequationwiththebesseloperatorandtheriemannliouvillepartialderivative AT fatimagidovnakhushtova firstboundaryvalueprobleminarectangulardomainforadifferentialequationwiththebesseloperatorandtheriemannliouvillepartialderivative |
_version_ |
1721209295461154816 |