Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives

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dc.contributor.authorMaroua Amel Boubekeur
dc.contributor.authorİrem Akbulut Arik
dc.contributor.authorSeda İğret Araz
dc.date.accessioned2025-04-17T07:30:12Z
dc.date.available2025-04-17T07:30:12Z
dc.date.issued2025-01-01
dc.departmentFakülteler, Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü
dc.description.abstractThis 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.
dc.identifier.citationBoubekeur, M. A., Arik, İ. A., & Araz, S. I. (2025). Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives. Open Physics, 23(1), 20250134.
dc.identifier.doi10.1515/phys-2025-0134
dc.identifier.issn2391-5471
dc.identifier.issue1
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1515/phys-2025-0134
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8622
dc.identifier.volume23
dc.identifier.wos001455355900001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.institutionauthorİğret Araz, Seda
dc.institutionauthorid0000-0002-7698-0709
dc.language.isoen
dc.publisherWalter de Gruyter GmbH
dc.relation.ispartofOpen Physics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectmemristor system
dc.subjectpiecewise memductance function
dc.subjectfractal-fractional derivatives
dc.subjectKrasnoselskii-Krein uniqueness theorem
dc.titleTheoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives
dc.typejournal-article
oaire.citation.issue1
oaire.citation.volume23

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