Investigation of Fractional-Ordered Tumor-Immune Interaction Model via Fractional-Order Derivative

Abstract

Dynamical analysis of system of ordinary differential equations (ODEs) is an interesting topic among researchers and several tools have been discovered since so far to deal with its several other features. There are many built-in functions designed in MATLAB that researchers can use as a tool for the system of ODEs with integer order but in the similar systems have fractional-order derivative is a difficult task. Therefore, the purpose of this work is to use the Caputo fractional-order derivative to qualitatively analyze and then numerically simulate the tumor-immune system interaction model. Moreover, the Schauder fixed point theorem is used to establish the condition for the existence of at least one solution, while the Banach fixed point theorem is utilized to guarantee the existence of a unique solution. Moreover, the stability in the trajectories of considered system achieved with the aid of Ulam–Hyers (UH) stability. In addition, the numerical computations are performed using Variational Iteration Method (VIM) and the visualized results are shown using MATLAB.