| Dynamics of Variable-Order Cancer Model; Numerical Approach |
| Paper ID : 1080-ISCHU |
| Authors |
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Obida Hassan Abbas *1, Salma Asaad Mohammed Shatta2, Doha Mahmoud Abdel-Twaab3 1Graduate student department of mathematics, faculty of science Helwan university 2T.A at Mathematics department, faculty of Science, Helwan university, Cairo, Egypt. 3Lecturer at department of mathematics, faculty of science Helwan university |
| Abstract |
| Recently, a mathematical model has proven to be valuable in understating the dynamics of the spread of tumor cells inside the human body and determining its future behavior. Cancer and immune cells have a complex nature and produce chaotic behavior when they are simulated. In this talk, the dynamics of variable-order Cancer Model [1] is presented. The variable-order fractional derivatives are defined in the Caputo sense [2]. Moreover, the parameters of the proposed model are dependent on the variable-order fractional. The basic reproduction number of the model is derived. Linear stability of different equilibrium points is analyzed. Bifurcations and properties of the proposed model are studied analytically and numerically. Two numerical methods are introduced to study the proposed model. These methods are the generalized Euler’s method (GEM) [3], and the generalized fourth order Runge-Kutta method (GRK4M) [3]. Numerical simulations show that the generalized fourth order Runge-Kutta method can be applied to solve such variable-order fractional chaotic. Finally, comparative studies and numerical simulations are implemented. References: [1] MEHMET ITIK and STEPHEN P. BANKS. Chaos in a three-dimensional cancer model. International Journal of Bifurcation and Chaos, 20(01):71–79, 2010. [2] Dina Tavares, Ricardo Almeida, and Delfim FM Torres. Caputo derivatives of fractional variable order: numerical approximations. Communications in Nonlinear Science and Numerical Simulation, 35:69–87, 2016. [3] Constantin Milici, Jose Tenreiro Machado, and Gheorghe Draganescu. Application of the Euler and Runge–Kutta generalized methods for fde and symbolic packages in the analysis of some fractional attractors. International Journal of Nonlinear Sciences and Numerical Simulation, 21(2):159–170, 2020. [4] Nasser Sweilam, Seham Al-Mekhlafi, and Salma Shatta. Optimal bang- bang control for variable-order dengue virus; numerical studies. Journal of Advanced Research, 32, 04 2021. |
| Keywords |
| Chaotic system; Bifurcations; Fixed point theorems; Variable-order fractional derivatives; Generalized Euler’s method; Generalized fourth order Runge-Kutta method. |
| Status: Abstract Accepted (Poster Presentation) |