Browsing by Author "Yildiz, Tugba Akman"

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Citation Count: Yildiz, Tugba Akman...et al. (2020). "New aspects of time fractional optimal control problems within operators with nonsingular kernel", Discrete and Continuous Dynamical Systems-Series S, Vol. 13, No.3, pp.407-428.
New aspects of time fractional optimal control problems within operators with nonsingular kernel
(2020) Yildiz, Tugba Akman; Jajarmi, Amin; Yildiz, Burak; Baleanu, Dumitru; 56389
This paper deals with a new formulation of time fractional optimal control problems governed by Caputo-Fabrizio (CF) fractional derivative. The optimality system for this problem is derived, which contains the forward and backward fractional differential equations in the sense of CF. These equations are then expressed in terms of Volterra integrals and also solved by a new numerical scheme based on approximating the Volterra integrals. The linear rate of convergence for this method is also justified theoretically. We present three illustrative examples to show the performance of this method. These examples also test the contribution of using CF derivative for dynamical constraints and we observe the efficiency of this new approach compared to the classical version of fractional operators.
Citation Count: Arshad, Sadia...et al. (2020). "THE ROLE OF OBESITY IN FRACTIONAL ORDER TUMOR-IMMUNE MODEL", University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, Vol. 82, no. 2, pp. 181-196.
THE ROLE OF OBESITY IN FRACTIONAL ORDER TUMOR-IMMUNE MODEL
(2020) Arshad, Sadia; Yildiz, Tugba Akman; Baleanu, Dumitru; Tang, Yifa; 56389
This work investigates the tumor-obesity model via a fractional operator to analyze the interactions between cancer and obesity, since fractional derivatives capture the long formation of cancerous tumor cells that might takes years to develop. It is known that fat cells enhance the development of cancerous tumor cells. To examine how the immune system is influenced due to fat cells, interactions of four types of cell population, namely tumor cells, immune cells, normal cells and fat cells are examined. We investigate the equilibrium points and discuss their stability analytically. Numerical simulations are carried out to verify the analytical results, demonstrating that a low fat diet results in a smaller tumor burden as compared to a high-caloric diet.