Examining of a tumor system with Caputo derivative

Abstract

Tumor diseases have killed many people around the world for centuries. For this purpose, a lot of scientists have analyzed immune system’s cells in order to cope with tumor growths in living beings. For this reason, we examine a system reflecting the relationship between immune system and tumor growth in this study. This system is handled with the traditional Caputo fractional derivative. We give stability analysis of equilibrium points and solution properties of this system. Then, the conditions about the existence and uniqueness of the solution for this system are clear. In conclusion, we solve this fractional system benefiting from Grünwald-Letnikov scheme.