Numerical Treatment of Tumor‐Immune Interaction Model of Fractional Order Related to Lung Cancer via Chelyshkov Polynomials

ABSTRACT Cancer is an infectious disease that affects all organs of the body, especially the lungs, and without proper prevention and treatment, it is very fatal for humans. A more accurate mathematical model can help us control disease progression and treatment strategies. This disease is modeled with a nonlinear system of differential equations including four dependent variables, which are considered to be of fractional order in order to achieve more accurate results and better understanding. This article presents a numerical approach based on Chelyshkov polynomials and collocation idea to simulate the unknown variables of the fractional tumor‐immune interaction model. By estimating the parameters with well‐known Chelyshkov polynomials and after implementing the proposed method, the original system of differential equations is transformed into a nonlinear system of algebraic equations, which can be numerically solved via Newton‐Raphson idea. Some theoretical theorems related to the convergence order and error analysis are also discussed. Finally, we investigate the effect of the fractional order derivative on the behavior of tumor cells, active macrophage cells, macrophage cells, and the normal tissue. We also examine the effect of different parameters on the number of tumor cells to determine which parameters have a significant effect on these cells.