Chaos and proportional integral derivative (PID) control on cancer dynamics with fractal fractional operator

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dc.contributor.authorMuhammad Farman
dc.contributor.authorKottakkaran Sooppy Nisar
dc.contributor.authorKhadija Jamil
dc.contributor.authorAli Akgül
dc.contributor.authorAceng Sambas
dc.contributor.authorMustafa Bayram
dc.contributor.authorMustafa Habib
dc.contributor.authorMurad Khan Hassani
dc.date.accessioned2025-05-27T07:35:09Z
dc.date.available2025-05-27T07:35:09Z
dc.date.issued2025-06
dc.departmentFakülteler, Fen-Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractThis study presents a cancer dynamics model incorporating a fractal-fractional operator with a Mittag-Leffler kernel to capture complex interactions among cancer cells, tumor suppressor cells, immune cells, and oncolytic viruses. The model aims to enhance understanding of tumor-immune dynamics and improve treatment strategies. The existence and uniqueness of the solution are established using fixed point theory under the Lipschitz condition. Lyapunov stability of the system is also analyzed in the context of the fractal-fractional operator. To address chaotic behavior in cancer progression, chaos and Proportional-Integral-Derivative (PID) control techniques are implemented. These control methods effectively stabilize the system and regulate treatment administration. Numerical simulations illustrate the influence of fractional-order derivatives on tumor suppression and immune response, confirming the model's effectiveness in reflecting real-world cancer dynamics.
dc.identifier.citationFarman, M., Nisar, K. S., Jamil, K., Akgül, A., Sambas, A., Bayram, M., ... & Hassani, M. K. (2025). Chaos and Proportional Integral Derivative (PID) Control on Cancer Dynamics with Fractal fractional Operator. Results in Engineering, 105052.
dc.identifier.doi10.1016/j.rineng.2025.105052
dc.identifier.issn2590-1230
dc.identifier.scopus2-s2.0-105004985840
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.rineng.2025.105052
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8680
dc.identifier.volume26
dc.identifier.wosqualityQ1
dc.indekslendigikaynakScopus
dc.institutionauthorAkgül, Ali
dc.institutionauthorid0000-0001-9832-1424
dc.language.isoen
dc.publisherElsevier BV
dc.relation.ispartofResults in Engineering
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectCancer model
dc.subjectChaos control
dc.subjectMittag-Leffler kernel
dc.subjectPID control
dc.titleChaos and proportional integral derivative (PID) control on cancer dynamics with fractal fractional operator
dc.typejournal-article
oaire.citation.volume26

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