Examining of a tumor system with Caputo derivative

Year 2023, Volume: 25 Issue: 1, 37 - 48, 16.01.2023

Esmehan Uçar

https://doi.org/10.25092/baunfbed.1113646

Abstract

Cancer is a disease that many people are exposed to, which results in the recovery of some and the death of others. For this reason, A system reflecting the relationship between immune system and tumor growth in this study is examined. This system is handled with the traditional Caputo fractional derivative. The stability analysis of equilibrium points and solution properties of this system is searched. Then, the conditions about the existence and uniqueness of the solution for this system are given. In conclusion, the fractional system is solved benefiting from Grünwald-Letnikov scheme.

Keywords

Caputo derivative, mathematical modeling, numerical solution.

Tümör sisteminin Caputo türev ile incelenmesi

Abstract

Birçok insanın maruz kaldığı kanser, bazı hastaların iyileşmesi bazılarının ölmesi ile sonuçlanan bir hastalıktır. Bu nedenle bu çalışmada bağışıklık sistemi ile tümör büyümesi arasındaki ilişkiyi yansıtan bir sistem inceliyoruz. Söz konusu sistem, Caputo kesirli türevi ile ele alınacaktır. Bu sistemin denge noktalarının kararlılık analizini ve çözüm özelliklerini vereceğiz. Daha sonra bu sistem için çözüm özellikleri belirtilecektir. Son olarak, bu kesirli sistemi Grünwald-Letnikov nümerik metodunu kullanarak çözeceğiz.

Keywords

Caputo derivative, mathematical modeling, numerical solution

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