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New observations on optimal cancer treatments for a fractional tumor growth model with and without singular kernel

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dc.contributor.author Akman Yıldız, Tuğba
dc.contributor.author Arshad, Sadia
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2020-03-18T13:48:20Z
dc.date.available 2020-03-18T13:48:20Z
dc.date.issued 2018-12
dc.identifier.citation Akman Yildiz, Tugba; Arshad, Sadia; Baleanu, Dumitru, "New observations on optimal cancer treatments for a fractional tumor growth model with and without singular kernel", Chaos Solitons & Fractals, Vol. 117, pp. 226-239, (2018). tr_TR
dc.identifier.issn 0960-0779
dc.identifier.uri http://hdl.handle.net/20.500.12416/2671
dc.description.abstract The aim of this study is to examine a fractional optimal control problem (FOCP) governed by a cancer-obesity model with and without singular kernel, separately. We propose a new model including the population of immune cells, tumor cells, normal cells, fat cells, chemotherapeutic and immunotherapeutic drug concentrations. Existence and stability of the tumor free equilibrium point and coexisting equilibrium point are investigated analytically. We obtain the numerical solution of the fractional cancer-obesity model using L1 formula. The aim behind the FOCP is to find the optimal doses of chemotherapeutic and immunotherapeutic drugs which minimize the difference between the number of tumor cells and normal cells. To do so, we insert some weight constants as the coefficients of tumor and normal cells in the cost functional so that normal cell population is larger compared to tumor burden. On the other hand, we investigate the effect of obesity to the choice and schedules of treatment strategies in case of low and high caloric diets. Moreover, we discuss the choice of the differentiation operator, namely operators with and without singular kernel. Lastly, some illustrative examples are shown to examine the impact of the fractional derivatives of different orders on cancer-obesity model and we observe the contribution of the cost functional to eradicate tumor burden and regenerate normal cell population. Our model predicts the negative effect of obesity on the health of patient and we show that the most efficient treatment choice to eradicate the tumor is to apply combined therapy together with low caloric diet. (C) 2018 Elsevier Ltd. All rights reserved. tr_TR
dc.language.iso eng tr_TR
dc.publisher Pergamon-Elsevier Science LTD tr_TR
dc.relation.isversionof 10.1016/j.chaos.2018.10.029 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Optimal Control tr_TR
dc.subject Chemotherapy tr_TR
dc.subject Immunotherapy tr_TR
dc.subject Obesity tr_TR
dc.subject Fractional Differential Equations tr_TR
dc.subject Nonsingular Kernel tr_TR
dc.subject Stability tr_TR
dc.title New observations on optimal cancer treatments for a fractional tumor growth model with and without singular kernel tr_TR
dc.type article tr_TR
dc.relation.journal Chaos Solitons & Fractals tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 117 tr_TR
dc.identifier.startpage 226 tr_TR
dc.identifier.endpage 239 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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