Theoretical and numerical analysis of fractal fractional model of tumor-immune interaction with two different kernels

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dc.authoridAhmad, Shabir/0000-0002-5610-6248
dc.authoridUllah, Aman/0000-0003-4021-3599
dc.contributor.authorAhmad, Shabir
dc.contributor.authorUllah, Aman
dc.contributor.authorAkgu, Ali
dc.contributor.authorBaleanu, Dumitru
dc.date.accessioned2024-12-24T19:25:11Z
dc.date.available2024-12-24T19:25:11Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractFractal fractional operators in Caputo and Caputo-Fabrizio sense are being used in this manuscript to explore the interaction between the immune system and cancer cells. The tumour-immune model has been investigated numerically and theoretically by the singular and nonsingular fractal fractional operators. Via fixed point theorems, the existence and uniqueness of the model under the Caputo fractal fractional operator have been demonstrated. Using the fixed point theory, the existence of a unique solution has been derived under the Caputo-Fabrizio case. Through nonlinear analysis, the Ulam-Hyres stability of the model has been derived. For the singular and nonsingular fractal fractional operators, numerical results have been developed by Lagrangian-piece wise interpolation. We simulate the numerical results for the various sets of fractional and fractal orders to describe the relationship between immune and cancer cells under the novel operators with two different kernels. We compared the dynamics of the tumor-immune model using a power law and an exponential-decay kernel to explore that the nonsingular fractal fractional operator provides better dynamics for the considered model. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University
dc.identifier.doi10.1016/j.aej.2021.10.065
dc.identifier.endpage5752
dc.identifier.issn1110-0168
dc.identifier.issn2090-2670
dc.identifier.issue7
dc.identifier.scopus2-s2.0-85121754384
dc.identifier.scopusqualityQ1
dc.identifier.startpage5735
dc.identifier.urihttps://doi.org/10.1016/j.aej.2021.10.065
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6308
dc.identifier.volume61
dc.identifier.wosWOS:000744591500007
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofAlexandria Engineering Journal
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectFractal fractional operator
dc.subjectUlam-Hyres stability
dc.subjectExponential-decay kernel
dc.titleTheoretical and numerical analysis of fractal fractional model of tumor-immune interaction with two different kernels
dc.typeArticle

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