Analyzing chaotic systems with multi-step methods: Theory and simulations
Identifying and analyzing fixed points plays a crucial role in chaos theory for grasping the system behavior and advancing the understanding of its fundamental mechanics. This study explores new chaotic nonlinear integro-differential systems with four variables, employing Caputo–Fabrizio and Atangan...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824014145 |
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| author | Meriem Mansouria Belhamiti Zoubir Dahmani Jehad Alzabut D.K. Almutairi Hasib Khan |
| author_facet | Meriem Mansouria Belhamiti Zoubir Dahmani Jehad Alzabut D.K. Almutairi Hasib Khan |
| author_sort | Meriem Mansouria Belhamiti |
| collection | DOAJ |
| description | Identifying and analyzing fixed points plays a crucial role in chaos theory for grasping the system behavior and advancing the understanding of its fundamental mechanics. This study explores new chaotic nonlinear integro-differential systems with four variables, employing Caputo–Fabrizio and Atangana–Baleanu derivatives. We confirm the presence and reliability of solutions and offer a real-life example. Additionally, we implement the suggested multi-step techniques on different nonlinear chaotic systems to demonstrate their accuracy. |
| format | Article |
| id | doaj-art-19ce72a6bdd946058f5db049b11edd57 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-19ce72a6bdd946058f5db049b11edd572025-02-07T04:46:58ZengElsevierAlexandria Engineering Journal1110-01682025-02-01113516534Analyzing chaotic systems with multi-step methods: Theory and simulationsMeriem Mansouria Belhamiti0Zoubir Dahmani1Jehad Alzabut2D.K. Almutairi3Hasib Khan4Laboratory LMPA, Faculty of Exact Sciences and Informatics, University of Mostaganem, AlgeriaLaboratory LMPA, Faculty of Exact Sciences and Informatics, University of Mostaganem, AlgeriaDepartment of Mathematics and Science, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Turkiye; Center for Research and Innovation, Asia International University, Yangiobod MFY, G’ijduvon street, House 74, Bukhara, Uzbekistan; Corresponding author at: Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Turkiye.Department of Mathematics, College of Science Al-Zulf, Majmaah University, 11952 Al-Majmaah, Saudi ArabiaDepartment of Mathematics and Science, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics, Shaheed Benazir Bhutto University, Dir(U), 18000, Khyber Pakhtunkhwa, PakistanIdentifying and analyzing fixed points plays a crucial role in chaos theory for grasping the system behavior and advancing the understanding of its fundamental mechanics. This study explores new chaotic nonlinear integro-differential systems with four variables, employing Caputo–Fabrizio and Atangana–Baleanu derivatives. We confirm the presence and reliability of solutions and offer a real-life example. Additionally, we implement the suggested multi-step techniques on different nonlinear chaotic systems to demonstrate their accuracy.http://www.sciencedirect.com/science/article/pii/S1110016824014145Caputo–Fabrizio derivativeAtangana–Baleanu derivativeFixed point theoremUlam–Hyers stabilityThree-step Adams–Bashforth scheme |
| spellingShingle | Meriem Mansouria Belhamiti Zoubir Dahmani Jehad Alzabut D.K. Almutairi Hasib Khan Analyzing chaotic systems with multi-step methods: Theory and simulations Alexandria Engineering Journal Caputo–Fabrizio derivative Atangana–Baleanu derivative Fixed point theorem Ulam–Hyers stability Three-step Adams–Bashforth scheme |
| title | Analyzing chaotic systems with multi-step methods: Theory and simulations |
| title_full | Analyzing chaotic systems with multi-step methods: Theory and simulations |
| title_fullStr | Analyzing chaotic systems with multi-step methods: Theory and simulations |
| title_full_unstemmed | Analyzing chaotic systems with multi-step methods: Theory and simulations |
| title_short | Analyzing chaotic systems with multi-step methods: Theory and simulations |
| title_sort | analyzing chaotic systems with multi step methods theory and simulations |
| topic | Caputo–Fabrizio derivative Atangana–Baleanu derivative Fixed point theorem Ulam–Hyers stability Three-step Adams–Bashforth scheme |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824014145 |
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