On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative
We aim to study a unique solvability of a boundary-value problem for a time-fractional diffusion equation involving the Prabhakar fractional derivative in a Caputo sense in a bounded domain. We use the method of separation of variables and in time-variable, we obtain the Cauchy problem for...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2023-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2023-111-3/04.pdf |
| _version_ | 1797636649570533376 |
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| author | E.T. Karimov A. Hasanov |
| author_facet | E.T. Karimov A. Hasanov |
| author_sort | E.T. Karimov |
| collection | DOAJ |
| description | We aim to study a unique solvability of a boundary-value problem for a time-fractional diffusion equation involving the Prabhakar fractional derivative in a Caputo sense in a bounded domain. We use the method of separation of variables and in time-variable, we obtain the Cauchy problem for a fractional differential equation with the Prabhakar derivative. Solution of this Cauchy problem we represent via Mittag-Leffler type function of two variables. Using the new integral representation of this two-variable Mittag-Leffler type function, we obtained the required estimate, which allows us to prove uniform convergence of the infinite series form of the solution for the considered problem. |
| first_indexed | 2024-03-11T12:37:05Z |
| format | Article |
| id | doaj.art-e043badc852143e6b4954737339196c2 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-11T12:37:05Z |
| publishDate | 2023-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-e043badc852143e6b4954737339196c22023-11-05T16:09:12ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-09-011113394610.31489/2023M3/39-46On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivativeE.T. KarimovA. Hasanov We aim to study a unique solvability of a boundary-value problem for a time-fractional diffusion equation involving the Prabhakar fractional derivative in a Caputo sense in a bounded domain. We use the method of separation of variables and in time-variable, we obtain the Cauchy problem for a fractional differential equation with the Prabhakar derivative. Solution of this Cauchy problem we represent via Mittag-Leffler type function of two variables. Using the new integral representation of this two-variable Mittag-Leffler type function, we obtained the required estimate, which allows us to prove uniform convergence of the infinite series form of the solution for the considered problem.https://mathematics-vestnik.ksu.kz/apart/2023-111-3/04.pdf |
| spellingShingle | E.T. Karimov A. Hasanov On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative Қарағанды университетінің хабаршысы. Математика сериясы |
| title | On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative |
| title_full | On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative |
| title_fullStr | On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative |
| title_full_unstemmed | On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative |
| title_short | On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative |
| title_sort | on a boundary value problem in a bounded domain for a time fractional diffusion equation with the prabhakar fractional derivative |
| url | https://mathematics-vestnik.ksu.kz/apart/2023-111-3/04.pdf |
| work_keys_str_mv | AT etkarimov onaboundaryvalueprobleminaboundeddomainforatimefractionaldiffusionequationwiththeprabhakarfractionalderivative AT ahasanov onaboundaryvalueprobleminaboundeddomainforatimefractionaldiffusionequationwiththeprabhakarfractionalderivative |