Numerical approximation with Newton polynomial for the solution of a tumor growth model including fractional differential operators

Öz

In this study, a mathematical model about tumor growth is handled and this model is modified with new differential and integral operators. Numerical method with Newton polynomial which is introduced by Atangana and Seda is used for numerical solution of this model. Also numerical simulations are presented to show the accuracy and the effectiveness of the method.

Anahtar Kelimeler

• numerical method
• fractional derivative and integral
• tumor growth model

Kesirli diferansiyel operatörler içeren bir tümör büyüme modelinin çözümü için yeni nümerik yaklaşım

Öz

Bu çalışmada, tümör büyüme ile ilgili bir matematiksel model ele alıyoruz ve bu modeli yeni diferansyel ve integral operatörlerle modifiye ediyoruz. Bu modelin nümerik çözümü için Atangana ve Seda tarafından tanıtılan Newton polinomuna sahip yeni bir nümerik metot kullanılır. Ayrıca metodun etkinliğini ve doğruluğunu görmek için nümerik simülasyon sunuyoruz.

Anahtar Kelimeler

• : Yeni nümerik metot
• kesirli türev ve integral
• tümör büyüme modeli

Kaynakça

1. Alkahtani BST., 2020. A new numerical scheme based on Newton polynomial with application to fractional nonlinear differential equations, Alexandria Engineering Journal.
2. Atangana A., Baleanu D., 2016. New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Thermal Science, 20, 2, 763-769.
3. Atangana A., Araz I.S., 2020. New numerical method for ordinary differential equations: Newton polynomial, Journal of Computational and Applied Mathematics, (2020), 372.
4. Barillot E, Calzone L, Hupe P, Vert J-P, Zinovyev A, 2013. Computational systems biology of cancer. Boca Raton: CRC Press.
5. Caputo M , Fabrizio M . A new definition of fractional derivative without singu- lar kernel. Prog Fract Differ Appl 2015;1(2):73–85 .
6. Kim Y, Magdalena AS, Othmer HG, 2007. A hybrid model for tumor spheroid growth in vitro I: theoretical development and early results. Math Models Methods Appl Sci., 17:1773–98.
7. Mekkaoui T., Atangana A., 2017. New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models, European Physical Journal Plus, 132: 444.
8. Owolabi KM, Atangana A., 2020. Numerical methods for fractional differentiation, Springer Series in Computational Mathematics, 54 , Springer.

9. Subaşı M., İğret Araz S. 2019. Numerical Regularization of Optimal Control for the Coefficient Function in a Wave Equation, Iranian Journal of Science and Technology, Transactions A: Science, 1-9.
10. Subaşı M. 2004. A Variational method of optimal control problems for nonlinear Schrödinger equation. Numerical Methods for Partial Differential Equations, 20(1), 82-89.
11. Watanabe Y., Dahlman E., Hui S., 2016. A mathematical model of tumor growth and its response to single irradiation, Theoretical Biology and Medical Modeling, 13:6.