Innovative techniques to chaotic dynamics and kinetic differ-integral equations
In this work, we analyse advancements in chaotic modelling by applying a modified version of the Atangana-Baleanu Caputo (MABC) fractional derivative operator (FDO) with respect to another function within a mathematical model (MMd). We employ an iterative method and fixed-point theory to verify the...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Mathematical and Computer Modelling of Dynamical Systems |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/13873954.2025.2490515 |
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| author | Ahsan Mehmood Zhi-Guo Liu Muhammad Samraiz Fuat Usta Sama Arjika |
| author_facet | Ahsan Mehmood Zhi-Guo Liu Muhammad Samraiz Fuat Usta Sama Arjika |
| author_sort | Ahsan Mehmood |
| collection | DOAJ |
| description | In this work, we analyse advancements in chaotic modelling by applying a modified version of the Atangana-Baleanu Caputo (MABC) fractional derivative operator (FDO) with respect to another function within a mathematical model (MMd). We employ an iterative method and fixed-point theory to verify the existence of a unique solution for this model. Additionally, due to the high non-linearity of the problem, we apply an appropriate numerical scheme to solve this system of equations computationally. Graphical representations illustrate the convergence of solutions within the chaotic model. To test the versatility of the modified Atangana-Baleanu Riemann (MABR) FDO, we generalize a kinetic differ-integral equation and compute its solution. The main contribution of our research is the construction of a chaotic model with the MABC FDO and a non-local, nonlinear kernel. Utilizing advanced numerical methods, we transform the non-local kernel into its local counterpart in order to obtain efficient and accurate solutions. |
| format | Article |
| id | doaj-art-d06b1b950c9d4a5e975bb1b98fb5f63f |
| institution | OA Journals |
| issn | 1387-3954 1744-5051 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Mathematical and Computer Modelling of Dynamical Systems |
| spelling | doaj-art-d06b1b950c9d4a5e975bb1b98fb5f63f2025-08-20T01:49:20ZengTaylor & Francis GroupMathematical and Computer Modelling of Dynamical Systems1387-39541744-50512025-12-0131110.1080/13873954.2025.2490515Innovative techniques to chaotic dynamics and kinetic differ-integral equationsAhsan Mehmood0Zhi-Guo Liu1Muhammad Samraiz2Fuat Usta3Sama Arjika4School of Mathematical Sciences and Shanghai Key Labortary PMMP, East China Normal University, Shanghai, ChinaSchool of Mathematical Sciences and Shanghai Key Labortary PMMP, East China Normal University, Shanghai, ChinaDepartment of Mathematics, University of Sargodha, Sargodha, PakistanDepartment of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, TürkiyeDepartment of Fundamental Sciences, University of Agadez, Agadez, NigarIn this work, we analyse advancements in chaotic modelling by applying a modified version of the Atangana-Baleanu Caputo (MABC) fractional derivative operator (FDO) with respect to another function within a mathematical model (MMd). We employ an iterative method and fixed-point theory to verify the existence of a unique solution for this model. Additionally, due to the high non-linearity of the problem, we apply an appropriate numerical scheme to solve this system of equations computationally. Graphical representations illustrate the convergence of solutions within the chaotic model. To test the versatility of the modified Atangana-Baleanu Riemann (MABR) FDO, we generalize a kinetic differ-integral equation and compute its solution. The main contribution of our research is the construction of a chaotic model with the MABC FDO and a non-local, nonlinear kernel. Utilizing advanced numerical methods, we transform the non-local kernel into its local counterpart in order to obtain efficient and accurate solutions.https://www.tandfonline.com/doi/10.1080/13873954.2025.2490515Extended fractional derivativechaotic modelfractional kinetic differ-integral equation |
| spellingShingle | Ahsan Mehmood Zhi-Guo Liu Muhammad Samraiz Fuat Usta Sama Arjika Innovative techniques to chaotic dynamics and kinetic differ-integral equations Mathematical and Computer Modelling of Dynamical Systems Extended fractional derivative chaotic model fractional kinetic differ-integral equation |
| title | Innovative techniques to chaotic dynamics and kinetic differ-integral equations |
| title_full | Innovative techniques to chaotic dynamics and kinetic differ-integral equations |
| title_fullStr | Innovative techniques to chaotic dynamics and kinetic differ-integral equations |
| title_full_unstemmed | Innovative techniques to chaotic dynamics and kinetic differ-integral equations |
| title_short | Innovative techniques to chaotic dynamics and kinetic differ-integral equations |
| title_sort | innovative techniques to chaotic dynamics and kinetic differ integral equations |
| topic | Extended fractional derivative chaotic model fractional kinetic differ-integral equation |
| url | https://www.tandfonline.com/doi/10.1080/13873954.2025.2490515 |
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