STUDY ON THE DYNAMICS OF A PIECEWISE TUMOR-IMMUNE INTERACTION MODEL

Many approaches have been proposed in recent decades to represent the behaviors of certain complicated global problems appearing in a variety of academic domains. One of these issues is the multi-step behavior that some situations exhibit. Abdon and Seda devised new operators known as piecewise operators to deal with such problems. This paper presents the dynamics of the tumor-immune-vitamins model in the sense of a piecewise derivative. The piecewise operator considered here is composed of classical and Caputo operators. The existence and uniqueness of the solution with a piecewise derivative are presented with the aid of fixed point results. With the help of the Newton polynomial, a numerical scheme is presented for the examined model. The attained results are visualized through simulations for different fractional orders.

Automated summary

This paper presents a new operator for dealing with multi-step behaviors in complicated global problems and investigates the dynamics of the tumor-immune-vitamins model using piecewise derivatives. The existence and uniqueness of solutions with piecewise derivatives are established, and a numerical scheme using Newton polynomials is proposed. Visualizations of the results for different fractional orders are provided through simulations.