| Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives |
| Paper ID : 1047-ISCHU |
| Authors |
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Aya Ahmed Mahmoud *1, Nasser Hassan sweilam2, Seham Almikhlafi3, Emad aboeldahab4 1mathematical department, faculty of science, Helwan university, Cairo, Egypt 2Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt. 3Mathematics Department, Faculty of Education, Sana'a University, Yemen 4Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt |
| Abstract |
| In this paper, two crossover hybrid variable order derivatives of the cancer model are developed. Grunwald Letnikov approximation is used to approximate the hybrid variable order fractional operator [1]. The existence, uniqueness, and stability of the proposed model are discussed. Adams Bashfourth's fifth step method with a hybrid variable order fractional operator is developed to study the proposed models [2], [3]. Comparative studies with generalized fifth order Runge Kutta method are given. Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented. 1- Sweilam, N.H.; Al-Ajami, T.M., Legendre spectral-collocation method for solving some types of fractional optimal control problems. J Adv Res 2015, 6(3), 393–403. 2- de Pillis, L.G.; Radunskaya, A., The dynamics of an optimally controlled tumor model: A case study. Math. Comput. Model 2003, 37, 1221–1244. 3- Kuznetsov, V.A.; Knott, G.D., Modeling tumor regrowth and immunotherapy. Math. Comput. Model. 2001, 33(12-13), 1275–1287. |
| Keywords |
| Cancer diseases; Hybrid variable-order fractional derivatives; Adams Bashfourth fifth step; Generalized fifth order Runge-Kutta method. |
| Status: Abstract Accepted (Poster Presentation) |