Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative
| dc.citation.epage | 177 | |
| dc.citation.issue | 11 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 166 | |
| dc.citation.volume | 1 | |
| dc.contributor.affiliation | Університет Хасана ІІ Касабланки | |
| dc.contributor.affiliation | Регіональний центр освіти і підготовки професій (CRMEF) | |
| dc.contributor.affiliation | Hassan II University of Casablanca | |
| dc.contributor.affiliation | Centre R´egional des M´etiers de l’Education et de la Formation (CRMEF) | |
| dc.contributor.author | Ассадікі, Ф. | |
| dc.contributor.author | Ель Юнуссі, М. | |
| dc.contributor.author | Хаттаф, К. | |
| dc.contributor.author | Юсфі, Н. | |
| dc.contributor.author | Assadiki, F. | |
| dc.contributor.author | El Younoussi, M. | |
| dc.contributor.author | Hattaf, K. | |
| dc.contributor.author | Yousfi, N. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-10-20T07:44:10Z | |
| dc.date.created | 2024-02-24 | |
| dc.date.issued | 2024-02-24 | |
| dc.description.abstract | У цій статті запропоновано та проаналізовано дробову модель «жертва-хижак» з узагальненою дробовою похідною Хаттафа (ДДХ). Доведено, що запропонована модель є екологічно та математично коректною. Крім того, показано, що ця модель має три точки рівноваги. Накінець, встановлено стійкість цих рівноваг. | |
| dc.description.abstract | In this paper, we propose and analyze a fractional prey–predator model with generalized Hattaf fractional (GHF) derivative. We prove that our proposed model is ecologically and mathematically well-posed. Furthermore, we show that our model has three equilibrium points. Finally, we establish the stability of these equilibria. | |
| dc.format.extent | 166-177 | |
| dc.format.pages | 12 | |
| dc.identifier.citation | Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative / F. Assadiki, M. El Younoussi, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 166–177. | |
| dc.identifier.citationen | Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative / F. Assadiki, M. El Younoussi, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 166–177. | |
| dc.identifier.doi | 10.23939/mmc2024.01.166 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/113776 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 11 (1), 2024 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 11 (1), 2024 | |
| dc.relation.references | [1] Lotka A. J. A Natural Population Norm I and II. Academy of Sciences, Washington (1913). | |
| dc.relation.references | [2] Volterra V. Fluctuations in the abundance of a species considered mathematically. Nature. 118, 558–560 (1926). | |
| dc.relation.references | [3] Kar T. K. Stability analysis of a prey–predator model incorporating a prey refuge. Communications in Nonlinear Science and Numerical Simulation. 10 (6), 681–691 (2005). | |
| dc.relation.references | [4] Garain K., Kumar U., Mandal P. S. Global dynamics in a Beddington–DeAngelis prey–predator model with density dependent death rate of predator. Differential Equations and Dynamical Systems. 29, 265–283 (2021). | |
| dc.relation.references | [5] Cheneke K. R., Rao K. P., Edessa G. K. Application of a new generalized fractional derivative and rank of control measures on cholera transmission dynamics. International Journal of Mathematics and Mathematical Sciences. 2021, 2104051 (2021). | |
| dc.relation.references | [6] Ghanbari B., Djilali S. Mathematical and numerical analysis of a three-species predator–prey model with herd behavior and time fractional-order derivative. Mathematical Methods in the Applied Sciences. 43 (4), 1736–1752 (2020). | |
| dc.relation.references | [7] Acay B., Bas E., Thabet A. Fractional economic models based on market equilibrium in the frame of different type kernels. Chaos, Solitons & Fractals. 130, 109438 (2020). | |
| dc.relation.references | [8] Bachraoui M., Hattaf K., Yousfi N. Spatiotemporal dynamics of fractional hepatitis B virus infection model with humoral and cellular immunity. BIOMAT 2020: Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells. 293–313 (2020). | |
| dc.relation.references | [9] Bachraoui M., Ichou M. A., Hattaf K., Yousfi N. Spatiotemporal dynamics of a fractional model for hepatitis B virus infection with cellular immunity. Mathematical Modelling of Natural Phenomena. 16, 5 (2021). | |
| dc.relation.references | [10] El Younoussi M., Hajhouji Z., Hattaf K., Yousfi N. A new fractional model for cancer therapy with M1 oncolytic virus. Complexity. 2021, 9934070 (2021). | |
| dc.relation.references | [11] Rasheed A., Shoaib Anwar M. Interplay of chemical reacting species in a fractional viscoelastic fluid flow. Journal of Molecular Liquids. 273, 576–588 (2019). | |
| dc.relation.references | [12] Ladaci S., Bensafia Y. Indirect fractional order pole assignment based adaptive control. Engineering Science and Technology, an International Journal. 19 (1), 518–530 (2016). | |
| dc.relation.references | [13] Ahmed E., El-Sayed A. M. A., El-Saka H. A. A. Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models. Journal of Mathematical Analysis and Applications. 325 (1), 542–553 (2007). | |
| dc.relation.references | [14] Javidi M., Nyamoradi N. Dynamic analysis of a fractional order prey–predator interaction with harvesting. Applied Mathematical Modelling. 37 (20–21), 8946–8956 (2013). | |
| dc.relation.references | [15] Ghaziani R. K., Alidousti J., Eshkaftaki A. B. Stability and dynamics of a fractional order Leslie–Gower prey–predator model. Applied Mathematical Modelling. 40 (3), 2075–2086 (2016). | |
| dc.relation.references | [16] Hattaf K. A new generalized definition of fractional derivative with non-singular kernel. Computation. 8 (2), 49 (2020). | |
| dc.relation.references | [17] Caputo M., Fabrizio M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications. 1, 73–85 (2015). | |
| dc.relation.references | [18] Atangana A., Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. Thermal Science. 20 (2), 763–769 (2016). | |
| dc.relation.references | [19] Al-Refai M. On weighted Atangana–Baleanu fractional operators. Advances in Difference Equations. 2020, 3 (2020). | |
| dc.relation.references | [20] Hattaf K. Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative. Mathematical Problems in Engineering. 2021, 8608447 (2021). | |
| dc.relation.references | [21] Hattaf K., Mohsen A. A., Al-Husseiny H. F. Gronwall inequality and existence of solutions for differential equations with generalized Hattaf fractional derivative. Journal of Mathematics and Computer Science. 27 (1), 18–27 (2022). | |
| dc.relation.references | [22] Zine H., Lotfi E. M., Torres D. F., Yousfi N. Taylor’s formula for generalized weighted fractional derivatives with nonsingular kernels. Axioms. 11 (5), 231 (2022). | |
| dc.relation.references | [23] Hattaf K. On the stability and numerical scheme of fractional differential equations with application to biology. Computation. 10 (6), 97 (2022). | |
| dc.relation.referencesen | [1] Lotka A. J. A Natural Population Norm I and II. Academy of Sciences, Washington (1913). | |
| dc.relation.referencesen | [2] Volterra V. Fluctuations in the abundance of a species considered mathematically. Nature. 118, 558–560 (1926). | |
| dc.relation.referencesen | [3] Kar T. K. Stability analysis of a prey–predator model incorporating a prey refuge. Communications in Nonlinear Science and Numerical Simulation. 10 (6), 681–691 (2005). | |
| dc.relation.referencesen | [4] Garain K., Kumar U., Mandal P. S. Global dynamics in a Beddington–DeAngelis prey–predator model with density dependent death rate of predator. Differential Equations and Dynamical Systems. 29, 265–283 (2021). | |
| dc.relation.referencesen | [5] Cheneke K. R., Rao K. P., Edessa G. K. Application of a new generalized fractional derivative and rank of control measures on cholera transmission dynamics. International Journal of Mathematics and Mathematical Sciences. 2021, 2104051 (2021). | |
| dc.relation.referencesen | [6] Ghanbari B., Djilali S. Mathematical and numerical analysis of a three-species predator–prey model with herd behavior and time fractional-order derivative. Mathematical Methods in the Applied Sciences. 43 (4), 1736–1752 (2020). | |
| dc.relation.referencesen | [7] Acay B., Bas E., Thabet A. Fractional economic models based on market equilibrium in the frame of different type kernels. Chaos, Solitons & Fractals. 130, 109438 (2020). | |
| dc.relation.referencesen | [8] Bachraoui M., Hattaf K., Yousfi N. Spatiotemporal dynamics of fractional hepatitis B virus infection model with humoral and cellular immunity. BIOMAT 2020: Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells. 293–313 (2020). | |
| dc.relation.referencesen | [9] Bachraoui M., Ichou M. A., Hattaf K., Yousfi N. Spatiotemporal dynamics of a fractional model for hepatitis B virus infection with cellular immunity. Mathematical Modelling of Natural Phenomena. 16, 5 (2021). | |
| dc.relation.referencesen | [10] El Younoussi M., Hajhouji Z., Hattaf K., Yousfi N. A new fractional model for cancer therapy with M1 oncolytic virus. Complexity. 2021, 9934070 (2021). | |
| dc.relation.referencesen | [11] Rasheed A., Shoaib Anwar M. Interplay of chemical reacting species in a fractional viscoelastic fluid flow. Journal of Molecular Liquids. 273, 576–588 (2019). | |
| dc.relation.referencesen | [12] Ladaci S., Bensafia Y. Indirect fractional order pole assignment based adaptive control. Engineering Science and Technology, an International Journal. 19 (1), 518–530 (2016). | |
| dc.relation.referencesen | [13] Ahmed E., El-Sayed A. M. A., El-Saka H. A. A. Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models. Journal of Mathematical Analysis and Applications. 325 (1), 542–553 (2007). | |
| dc.relation.referencesen | [14] Javidi M., Nyamoradi N. Dynamic analysis of a fractional order prey–predator interaction with harvesting. Applied Mathematical Modelling. 37 (20–21), 8946–8956 (2013). | |
| dc.relation.referencesen | [15] Ghaziani R. K., Alidousti J., Eshkaftaki A. B. Stability and dynamics of a fractional order Leslie–Gower prey–predator model. Applied Mathematical Modelling. 40 (3), 2075–2086 (2016). | |
| dc.relation.referencesen | [16] Hattaf K. A new generalized definition of fractional derivative with non-singular kernel. Computation. 8 (2), 49 (2020). | |
| dc.relation.referencesen | [17] Caputo M., Fabrizio M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications. 1, 73–85 (2015). | |
| dc.relation.referencesen | [18] Atangana A., Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. Thermal Science. 20 (2), 763–769 (2016). | |
| dc.relation.referencesen | [19] Al-Refai M. On weighted Atangana–Baleanu fractional operators. Advances in Difference Equations. 2020, 3 (2020). | |
| dc.relation.referencesen | [20] Hattaf K. Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative. Mathematical Problems in Engineering. 2021, 8608447 (2021). | |
| dc.relation.referencesen | [21] Hattaf K., Mohsen A. A., Al-Husseiny H. F. Gronwall inequality and existence of solutions for differential equations with generalized Hattaf fractional derivative. Journal of Mathematics and Computer Science. 27 (1), 18–27 (2022). | |
| dc.relation.referencesen | [22] Zine H., Lotfi E. M., Torres D. F., Yousfi N. Taylor’s formula for generalized weighted fractional derivatives with nonsingular kernels. Axioms. 11 (5), 231 (2022). | |
| dc.relation.referencesen | [23] Hattaf K. On the stability and numerical scheme of fractional differential equations with application to biology. Computation. 10 (6), 97 (2022). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2024 | |
| dc.subject | екологія | |
| dc.subject | математичне моделювання | |
| dc.subject | здобич–хижак | |
| dc.subject | дробова похідна Хаттафа | |
| dc.subject | функція Ляпунова | |
| dc.subject | стійкість | |
| dc.subject | ecology | |
| dc.subject | mathematical modeling | |
| dc.subject | prey–predator | |
| dc.subject | Hattaf fractional derivative | |
| dc.subject | Lyapunov function | |
| dc.subject | stability | |
| dc.title | Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative | |
| dc.title.alternative | Динаміка екологічної моделі “жертва–хижак” на основі узагальненої дробової похідної Хаттафа | |
| dc.type | Article |
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