Existence, uniqueness and synchronization of a fractional tumor growth model in discrete time with numerical results
Jehad Alzabut, R. Dhineshbabu, A. George Maria Selvam, J. F. Gómez‐Aguilar, Hasib Khan
Abstract
A mathematical model of discrete fractional equations with initial condition is constructed to study the tumor-immune interactions in this research. The model is a system of two nonlinear difference equations in the sense of Caputo fractional operator. The applications of Banach’s and Leray-Schauder’s fixed point theorems are used to analyze the existence results for the proposed model. Additionally, we developed several kinds of Ulam’s stability results for the suggested model. The tumor-immune fractional map’s dynamic behavior is numerical analyzed for some special cases. Further, adaptive control law is proposed to stabilize the fractional map and a control scheme is introduced to enhance the synchronization of the fractional model.