On a semilinear fractional reaction-diffusion equation with nonlocal conditions
In the present paper, a nonlocal problem for semilinear fractional diffusion equations with Riemann-Liouville derivative is investigated. By applying Banach fixed point theorem combined with some techniques on Mittag-Leffler functions, we establish some results on the existence, uniqueness, and regu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-12-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016821002465 |
| _version_ | 1819094154725031936 |
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| author | Tran Ngoc Thach Devendra Kumar Nguyen Hoang Luc Nguyen Duc Phuong |
| author_facet | Tran Ngoc Thach Devendra Kumar Nguyen Hoang Luc Nguyen Duc Phuong |
| author_sort | Tran Ngoc Thach |
| collection | DOAJ |
| description | In the present paper, a nonlocal problem for semilinear fractional diffusion equations with Riemann-Liouville derivative is investigated. By applying Banach fixed point theorem combined with some techniques on Mittag-Leffler functions, we establish some results on the existence, uniqueness, and regularity of the mild solutions of our problem in some suitable spaces. In addition, we show that the convergence of mild solution as the parameter tends to zero and present some numerical examples to illustrate the proposed method. |
| first_indexed | 2024-12-21T23:22:54Z |
| format | Article |
| id | doaj.art-5dcc5eb4b6964aafa185b5653fdd390c |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-21T23:22:54Z |
| publishDate | 2021-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-5dcc5eb4b6964aafa185b5653fdd390c2022-12-21T18:46:45ZengElsevierAlexandria Engineering Journal1110-01682021-12-0160655115520On a semilinear fractional reaction-diffusion equation with nonlocal conditionsTran Ngoc Thach0Devendra Kumar1Nguyen Hoang Luc2Nguyen Duc Phuong3Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet NamDepartment of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, IndiaDivision of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Viet NamFaculty of Fundamental Science, Industrial University of Ho Chi Minh City, Viet Nam; Corresponding author.In the present paper, a nonlocal problem for semilinear fractional diffusion equations with Riemann-Liouville derivative is investigated. By applying Banach fixed point theorem combined with some techniques on Mittag-Leffler functions, we establish some results on the existence, uniqueness, and regularity of the mild solutions of our problem in some suitable spaces. In addition, we show that the convergence of mild solution as the parameter tends to zero and present some numerical examples to illustrate the proposed method.http://www.sciencedirect.com/science/article/pii/S1110016821002465Fractional reaction-diffusion equationRegularityExistenceConvergence estimate |
| spellingShingle | Tran Ngoc Thach Devendra Kumar Nguyen Hoang Luc Nguyen Duc Phuong On a semilinear fractional reaction-diffusion equation with nonlocal conditions Alexandria Engineering Journal Fractional reaction-diffusion equation Regularity Existence Convergence estimate |
| title | On a semilinear fractional reaction-diffusion equation with nonlocal conditions |
| title_full | On a semilinear fractional reaction-diffusion equation with nonlocal conditions |
| title_fullStr | On a semilinear fractional reaction-diffusion equation with nonlocal conditions |
| title_full_unstemmed | On a semilinear fractional reaction-diffusion equation with nonlocal conditions |
| title_short | On a semilinear fractional reaction-diffusion equation with nonlocal conditions |
| title_sort | on a semilinear fractional reaction diffusion equation with nonlocal conditions |
| topic | Fractional reaction-diffusion equation Regularity Existence Convergence estimate |
| url | http://www.sciencedirect.com/science/article/pii/S1110016821002465 |
| work_keys_str_mv | AT tranngocthach onasemilinearfractionalreactiondiffusionequationwithnonlocalconditions AT devendrakumar onasemilinearfractionalreactiondiffusionequationwithnonlocalconditions AT nguyenhoangluc onasemilinearfractionalreactiondiffusionequationwithnonlocalconditions AT nguyenducphuong onasemilinearfractionalreactiondiffusionequationwithnonlocalconditions |