Browsing by Author "Akman Yildiz, Tugba"

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Citation - WoS: 2
Citation - Scopus: 3
Analysis of mixed-order Caputo fractional system with nonlocal integral boundary condition
(Tubitak Scientific & Technological Research Council Turkey, 2018) Akman Yildiz, Tugba; Baleanu, Dumitru; Khodabakhshi, Neda; Baleanu, Dumitru; 56389; Matematik
This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.
Citation - WoS: 23
Citation - Scopus: 23
New observations on optimal cancer treatments for a fractional tumor growth model with and without singular kernel
(Pergamon-elsevier Science Ltd, 2018) Akman Yildiz, Tugba; Baleanu, Dumitru; Arshad, Sadia; Baleanu, Dumitru; 56389; Matematik
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.
Citation - WoS: 26
Citation - Scopus: 32
Optimal chemotherapy and immunotherapy schedules for a cancer-obesity model with Caputo time fractional derivative
(Wiley, 2018) Akman Yildiz, Tugba; Baleanu, Dumitru; Arshad, Sadia; Baleanu, Dumitru; 56389; Matematik
This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy and immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population and minimize the drug dose over a finite time interval. The constraint is a model including tumor cells, immune cells, fat cells, and chemotherapeutic and immunotherapeutic drug concentrations with the Caputo time fractional derivative. We investigate the existence and stability of the equilibrium points, namely, tumor-free equilibrium and coexisting equilibrium, analytically. We discretize the cancer-obesity model using the L1 method. Simulation results of the proposed model are presented to compare three different treatment strategies: chemotherapy, immunotherapy, and their combination. In addition, we investigate the effect of the differentiation order alpha and the value of the decay rate of the amount of chemotherapeutic drug to the value of the cost functional. We find out the optimal treatment schedule in case of chemotherapy and immunotherapy.