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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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/464 |
| _version_ | 1818019589290721280 |
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| author | Arsen Pskhu |
| author_facet | Arsen Pskhu |
| author_sort | Arsen Pskhu |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-14T07:54:20Z |
| format | Article |
| id | doaj.art-ed36603268994b058843ee6c76672470 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-14T07:54:20Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ed36603268994b058843ee6c766724702022-12-22T02:05:07ZengMDPI 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 |
| 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 |
| title | 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_short | 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 |
| 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 |