A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments
A novel crossover model for monkeypox disease that incorporates Ψ-Caputo fractional derivatives is presented here, where we use a simple nonstandard kernel function Ψ(t). We can be obtained the Caputo and Caputo–Katugampola derivatives as special cases from the proposed derivative. The crossover dyn...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824011748 |
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| author | N.H. Sweilam S.M. Al-Mekhlafi W.S. Abdel Kareem G. Alqurishi |
| author_facet | N.H. Sweilam S.M. Al-Mekhlafi W.S. Abdel Kareem G. Alqurishi |
| author_sort | N.H. Sweilam |
| collection | DOAJ |
| description | A novel crossover model for monkeypox disease that incorporates Ψ-Caputo fractional derivatives is presented here, where we use a simple nonstandard kernel function Ψ(t). We can be obtained the Caputo and Caputo–Katugampola derivatives as special cases from the proposed derivative. The crossover dynamics model defines four alternative models: fractal fractional order, fractional order, variable order, and fractional stochastic derivatives driven by fractional Brownian motion over four time intervals. The Ψ-nonstandard finite difference method is designed to solve fractal fractional order, fractional order, and variable order mathematical models. Also, the nonstandard modified Euler Maruyama method is used to study the fractional stochastic model. A comparison between Ψ-nonstandard finite difference method and Ψ-standard finite difference method is presented. Moreover, numerous numerical tests and comparisons with real data were conducted to validate the methods’ efficacy and support the theoretical conclusions. |
| format | Article |
| id | doaj-art-f7a78cf423d44445b81b7735f3bcf67e |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-f7a78cf423d44445b81b7735f3bcf67e2025-01-18T05:03:34ZengElsevierAlexandria Engineering Journal1110-01682025-01-01111181193A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatmentsN.H. Sweilam0S.M. Al-Mekhlafi1W.S. Abdel Kareem2G. Alqurishi3Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt; Corresponding author.Department of Mathematics, Faculty of Education, Sana’a University, Yemen; Department of Engineering Mathematics and Physics, Future University in Egypt, EgyptDepartment of Mathematics, Faculty of Science, Suez University, Suez, EgyptDepartment of Mathematics, Faculty of Science, Suez University, Suez, EgyptA novel crossover model for monkeypox disease that incorporates Ψ-Caputo fractional derivatives is presented here, where we use a simple nonstandard kernel function Ψ(t). We can be obtained the Caputo and Caputo–Katugampola derivatives as special cases from the proposed derivative. The crossover dynamics model defines four alternative models: fractal fractional order, fractional order, variable order, and fractional stochastic derivatives driven by fractional Brownian motion over four time intervals. The Ψ-nonstandard finite difference method is designed to solve fractal fractional order, fractional order, and variable order mathematical models. Also, the nonstandard modified Euler Maruyama method is used to study the fractional stochastic model. A comparison between Ψ-nonstandard finite difference method and Ψ-standard finite difference method is presented. Moreover, numerous numerical tests and comparisons with real data were conducted to validate the methods’ efficacy and support the theoretical conclusions.http://www.sciencedirect.com/science/article/pii/S1110016824011748Crossover model for monkeypox diseasePsi-nonstandard finite difference methodNonstandard modified Euler Maruyama method |
| spellingShingle | N.H. Sweilam S.M. Al-Mekhlafi W.S. Abdel Kareem G. Alqurishi A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments Alexandria Engineering Journal Crossover model for monkeypox disease Psi-nonstandard finite difference method Nonstandard modified Euler Maruyama method |
| title | A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments |
| title_full | A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments |
| title_fullStr | A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments |
| title_full_unstemmed | A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments |
| title_short | A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments |
| title_sort | new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the ψ caputo derivative numerical treatments |
| topic | Crossover model for monkeypox disease Psi-nonstandard finite difference method Nonstandard modified Euler Maruyama method |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824011748 |
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