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.

近几十年来已经提出了许多方法来表示出现在各种学术领域的某些复杂的全球问题的行为。这些问题之一是某些情况下表现出的多步行为。Abdon 和 Seda 设计了称为“分段算子”的新算子来处理此类问题。本文从分段导数的角度介绍了肿瘤-免疫-维生素模型的动力学。这里考虑的分段算子由经典算子和 Caputo 算子组成。借助不动点结果，给出了分段导数解的存在唯一性。在牛顿多项式的帮助下，为所检查的模型提出了一个数值方案。通过对不同分数阶的模拟，可以看到所获得的结果。