Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 91Citation - Scopus: 111A New Intervention Strategy for an Hiv/Aids Transmission by a General Fractional Modeling and an Optimal Control Approach(Pergamon-elsevier Science Ltd, 2023) Hasanabadi, Manijeh; Vaziri, Asadollah Mahmoudzadeh; Jajarmi, Amin; Baleanu, Dumitru; Mahmoudzadeh Vaziri, AsadollahThis study proposes a new mathematical model in a generalized fractional framework for the investigation of an HIV/AIDS transmission dynamics. An auxiliary parameter further prevents the fractional equations from mismatching in the dimension. In order to analyze the general model, the non-negativity of the solution and the stability of the equilibrium points are examined. The model is also implemented by a powerful numerical scheme based on the quadrature rules and the repeated Trapezoidal method; as well, the error discussion and the convergence analysis are established. In addition, an efficient intervention strategy is developed and examined based on the optimal control theories in terms of optimality necessary conditions. Real-life clinical observations from Cape Verde Islands show that the new fractional model outperforms the classical one with ordinary time-derivatives, and enhances the modeling output compared to the previous fractional mathematical results. Further, numerical simulations demonstrate that the proposed optimal control measure leads to a significant reduction in the disease spread. As a result, the general fractional model offers a degree-of-freedom, an efficient tool which is helpful to illustrate the fundamental features of the disease transmission and to increase the efficiency of the proposed treatment strategy.Article Citation - WoS: 27Citation - Scopus: 28New Observations on Optimal Cancer Treatments for a Fractional Tumor Growth Model With and Without Singular Kernel(Pergamon-elsevier Science Ltd, 2018) Arshad, Sadia; Baleanu, Dumitru; Akman Yildiz, TugbaThe 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.Article Citation - WoS: 20Citation - Scopus: 23A Numerical Scheme for Two-Dimensional Optimal Control Problems With Memory Effect(Pergamon-elsevier Science Ltd, 2010) Defterli, OzlemA new formulation for multi-dimensional fractional optimal control problems is presented in this article. The fractional derivatives which are coming from the formulation of the problem are defined in the Riemann-Liouville sense. Some terminal conditions are imposed on the state and control variables whose dimensions need not be the same. A numerical scheme is described by using the Grunwald-Letnikov definition to approximate the Riemann-Liouville Fractional Derivatives. The set of fractional differential equations, which are obtained after the discretization of the time domain, are solved within the Grunwald-Letnikov approximation to obtain the state and the control variable numerically. A two-dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme. (C) 2009 Elsevier Ltd. All rights reserved.