In our research article, the mathematical model of fractional non-linear cancer dynamical system with the interaction of tumor cells, immune, and drugs reaction systems is taken in $\mathcal{ABC}$ derivative sense of fractional order. Qualitative results including existence and uniqueness has been analyzed by applying some theorems of fixed point theory. The approximate results for the considered system are obtained by numerical method due to Adams-Bashforth $\left(\mathcal{AB}\right)$ in non-integer order. Simulation of the Obtained iterative scheme are then drawn against the real data for different non-integer order. The suitability of the proposed model for our results are applied to study dynamics of tumor cells which help in investigating the dynamical interaction among tumor cells, immune cells and drugs reaction of the disease.

在我们的研究文章中，采用了具有肿瘤细胞，免疫和药物反应系统相互作用的分数非线性癌症动力系统的数学模型。 $\mathcal{美国广播公司}$分数阶的导数意义。通过应用定点理论的一些定理，分析了包括存在性和唯一性在内的定性结果。由于Adams-Bashforth，通过数值方法获得了所考虑系统的近似结果。$（\mathcal{AB}）$以非整数顺序。然后针对不同的非整数顺序，针对实际数据绘制获得的迭代方案的仿真。所提出的模型对我们的结果的适用性被用于研究肿瘤细胞的动力学，这有助于研究肿瘤细胞，免疫细胞和疾病药物反应之间的动力学相互作用。