Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives
This research deals with the theoretical and numerical investigations of a memristor system with memductance function. Stability, dissipativity, and Lyapunov exponents are extensively investigated and the chaotic tendencies of the system are studied in depth. The memristor model, where a piecewise m...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-03-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2025-0134 |
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| author | Boubekeur Maroua Amel Arik İrem Akbulut Araz Seda Igret |
| author_facet | Boubekeur Maroua Amel Arik İrem Akbulut Araz Seda Igret |
| author_sort | Boubekeur Maroua Amel |
| collection | DOAJ |
| description | This research deals with the theoretical and numerical investigations of a memristor system with memductance function. Stability, dissipativity, and Lyapunov exponents are extensively investigated and the chaotic tendencies of the system are studied in depth. The memristor model, where a piecewise memductance function is incorporated, is modified with fractal–fractional derivatives with exponential decay, power law, and Mittag–Leffler kernels, which provide powerful tools for modeling complex systems with memory effects, long-range interactions, and fractal-like behavior. Employing the Krasnoselskii–Krein uniqueness theorem and the fixed point theorem, the existence and uniqueness of the solutions of the model including fractal–fractional derivatives with the Mittag–Leffler kernel are proven. The fractal–fractional derivative model is solved numerically using the Lagrange polynomial approach, and the chaotic tendencies of the system are exhibited through numerical simulations. The findings indicated that the memristor model with fractal–fractional derivatives was observed to exhibit chaotic behavior. |
| format | Article |
| id | doaj-art-8c1d2e84826c43adad0781df8ce6e85c |
| institution | DOAJ |
| issn | 2391-5471 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj-art-8c1d2e84826c43adad0781df8ce6e85c2025-08-20T03:17:35ZengDe GruyterOpen Physics2391-54712025-03-0123122402283510.1515/phys-2025-0134Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivativesBoubekeur Maroua Amel0Arik İrem Akbulut1Araz Seda Igret2Department of Mathematics and Computer Science, University of Mostaganem, Mostaganem, AlgeriaDepartment of Mathematic Education, Faculty of Education, Siirt University, Siirt, TurkeyDepartment of Mathematic Education, Faculty of Education, Siirt University, Siirt, TurkeyThis research deals with the theoretical and numerical investigations of a memristor system with memductance function. Stability, dissipativity, and Lyapunov exponents are extensively investigated and the chaotic tendencies of the system are studied in depth. The memristor model, where a piecewise memductance function is incorporated, is modified with fractal–fractional derivatives with exponential decay, power law, and Mittag–Leffler kernels, which provide powerful tools for modeling complex systems with memory effects, long-range interactions, and fractal-like behavior. Employing the Krasnoselskii–Krein uniqueness theorem and the fixed point theorem, the existence and uniqueness of the solutions of the model including fractal–fractional derivatives with the Mittag–Leffler kernel are proven. The fractal–fractional derivative model is solved numerically using the Lagrange polynomial approach, and the chaotic tendencies of the system are exhibited through numerical simulations. The findings indicated that the memristor model with fractal–fractional derivatives was observed to exhibit chaotic behavior.https://doi.org/10.1515/phys-2025-0134memristor systempiecewise memductance functionfractal–fractional derivativeskrasnoselskii–krein uniqueness theorem |
| spellingShingle | Boubekeur Maroua Amel Arik İrem Akbulut Araz Seda Igret Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives Open Physics memristor system piecewise memductance function fractal–fractional derivatives krasnoselskii–krein uniqueness theorem |
| title | Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives |
| title_full | Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives |
| title_fullStr | Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives |
| title_full_unstemmed | Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives |
| title_short | Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives |
| title_sort | theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal fractional derivatives |
| topic | memristor system piecewise memductance function fractal–fractional derivatives krasnoselskii–krein uniqueness theorem |
| url | https://doi.org/10.1515/phys-2025-0134 |
| work_keys_str_mv | AT boubekeurmarouaamel theoreticalandnumericalinvestigationofamemristorsystemwithapiecewisememductanceunderfractalfractionalderivatives AT arikiremakbulut theoreticalandnumericalinvestigationofamemristorsystemwithapiecewisememductanceunderfractalfractionalderivatives AT arazsedaigret theoreticalandnumericalinvestigationofamemristorsystemwithapiecewisememductanceunderfractalfractionalderivatives |