Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains
We construct the Green function of the first boundary-value problem for a diffusion-wave equation with fractional derivative with respect to the time variable. The Green function is sought in terms of a double-layer potential of the equation under consideration. We prove a jump relation and solve an...
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doaj-ed36603268994b058843ee6c766724702020-11-25T03:10:06ZengMDPI AGMathematics2227-73902020-03-018446410.3390/math8040464math8040464Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional DomainsArsen Pskhu0Institute of Applied Mathematics and Automation, Kabardin-Balkar Scientific Center of Russian Academy of Sciences, 89-A Shortanov Street, 360000 Nalchik, RussiaWe construct the Green function of the first boundary-value problem for a diffusion-wave equation with fractional derivative with respect to the time variable. The Green function is sought in terms of a double-layer potential of the equation under consideration. We prove a jump relation and solve an integral equation for an unknown density. Using the Green function, we give a solution of the first boundary-value problem in a multidimensional cylindrical domain. The fractional differentiation is given by the Dzhrbashyan−Nersesyan fractional differentiation operator. In particular, this covers the cases of equations with the Riemann−Liouville and Caputo derivatives.https://www.mdpi.com/2227-7390/8/4/464diffusion-wave equationboundary-value problemgreen functiondouble-layer potentialfractional derivativedzhrbashyan–nersesyan operator |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Arsen Pskhu |
spellingShingle |
Arsen Pskhu Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains Mathematics diffusion-wave equation boundary-value problem green function double-layer potential fractional derivative dzhrbashyan–nersesyan operator |
author_facet |
Arsen Pskhu |
author_sort |
Arsen Pskhu |
title |
Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains |
title_short |
Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains |
title_full |
Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains |
title_fullStr |
Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains |
title_full_unstemmed |
Green Functions of the First Boundary-Value Problem for a Fractional Diffusion—Wave Equation in Multidimensional Domains |
title_sort |
green functions of the first boundary-value problem for a fractional diffusion—wave equation in multidimensional domains |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2020-03-01 |
description |
We construct the Green function of the first boundary-value problem for a diffusion-wave equation with fractional derivative with respect to the time variable. The Green function is sought in terms of a double-layer potential of the equation under consideration. We prove a jump relation and solve an integral equation for an unknown density. Using the Green function, we give a solution of the first boundary-value problem in a multidimensional cylindrical domain. The fractional differentiation is given by the Dzhrbashyan−Nersesyan fractional differentiation operator. In particular, this covers the cases of equations with the Riemann−Liouville and Caputo derivatives. |
topic |
diffusion-wave equation boundary-value problem green function double-layer potential fractional derivative dzhrbashyan–nersesyan operator |
url |
https://www.mdpi.com/2227-7390/8/4/464 |
work_keys_str_mv |
AT arsenpskhu greenfunctionsofthefirstboundaryvalueproblemforafractionaldiffusionwaveequationinmultidimensionaldomains |
_version_ |
1724660511808684032 |