Theoretical and numerical aspects for the longtime behavior of nonlinear delay time Caputo fractional reaction–diffusion equations
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Theoretical and numerical aspects for the longtime behavior of nonlinear delay time Caputo fractional reaction–diffusion equations
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| Автор |
Hendy, A. S.
Zaky, M. A. Van, Bockstal, K. |
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| Тематика |
CONTRACTIVITY
ENERGY ESTIMATES SPECTRAL METHOD STABILITY TIME DELAY TIME FRACTIONAL REACTION–DIFFUSION EQUATIONS DIFFUSION NONLINEAR EQUATIONS NUMERICAL METHODS PARTIAL DIFFERENTIAL EQUATIONS TIME DELAY TIMING CIRCUITS ASYMPTOTICS CONTRACTIVITY ENERGY ESTIMATES FRACTIONAL REACTIONS LONG TIME BEHAVIOR REACTION DIFFUSION EQUATIONS SPECTRAL METHODS THEORETICAL ASPECTS TIME FRACTIONAL REACTION–DIFFUSION EQUATION TIME-DELAYS ASYMPTOTIC STABILITY |
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| Описание |
In this paper, we investigate the longtime behavior of time fractional reaction–diffusion equations with delay. The governing partial differential equation generalizes the Hutchinson, the Mackey–Glass and the Nicholson’s blowflies equations. Energy estimates, asymptotic stability and asymptotic contractivity of the problem are proved. The finite difference technique is used to discretize the time-fractional Caputo derivative, and the spectral Galerkin approach is used for the spatial approximation. Additionally, the ability to preserve asymptotic contractivity and stability rates can be proved for the numerical solution similarly as for the true solution. Finally, some numerical experiments are performed to confirm our findings. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.
National Research Centre, NRC; Russian Science Foundation, RSF: 22-21-00075; Bijzonder Onderzoeksfonds UGent, BOF: 01M01021 This study was supported financially by the RSF grant, project 22-21-00075, the National Research Centre of Egypt (NRC), and the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021). The authors are grateful to the handling editor and the anonymous referees for their constructive feedback and helpful suggestions, which highly improved the paper. A. S. Hendy wishes to acknowledge the support of the RSF grant, project 22-21-00075. M. A. Zaky wishes to acknowledge the financial support of the National Research Centre of Egypt (NRC). K. Van Bockstal is supported by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021). |
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| Дата |
2024-04-05T16:17:27Z
2024-04-05T16:17:27Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Hendy, AS, Zaky, MA & Van Bockstal, K 2023, 'Theoretical and numerical aspects for the longtime behavior of nonlinear delay time Caputo fractional reaction–diffusion equations', Nonlinear Dynamics, Том. 111, № 4, стр. 3525-3537. https://doi.org/10.1007/s11071-022-07982-7
Hendy, A. S., Zaky, M. A., & Van Bockstal, K. (2023). Theoretical and numerical aspects for the longtime behavior of nonlinear delay time Caputo fractional reaction–diffusion equations. Nonlinear Dynamics, 111(4), 3525-3537. https://doi.org/10.1007/s11071-022-07982-7 0924-090X Final All Open Access, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85141392945&doi=10.1007%2fs11071-022-07982-7&partnerID=40&md5=d4ce61d4968a08bf49a1c648cad9f6c1 https://biblio.ugent.be/publication/01GP0M62T2DJWYJRFK32RNZ4HY/file/01GP0MK8S7RF3MAMYMW5GCB838.pdf http://elar.urfu.ru/handle/10995/130270 10.1007/s11071-022-07982-7 85141392945 000878949400007 |
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| Язык |
en
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//22-21-00075
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Springer Science and Business Media B.V.
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| Источник |
Nonlinear Dynamics
Nonlinear Dynamics |
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