癌症是全球死亡最主要的原因，预计到2020年将有约1000万人死于癌症，即每六个死亡事件中就有一个与癌症相关。乳腺癌、肺癌、结肠癌、直肠癌和前列腺癌是最常见的癌症类型。本文介绍了一种描述混合疗法（免疫疗法和化疗）下癌症治疗动力学的分数模型。癌症治疗的数学模型对于理解疾病的动态行为至关重要。分数模型考虑了免疫疗法和化疗在细胞种群水平上控制癌症生长。这些模型由一组分数微分方程（FDEs）组成。分数项由Caputo分数导数定义。通过使用Adams-Bashforth-Moulton方法对模型进行数值求解。所有分数模型的合理分数阶范围为β = 0.6至β = 0.9。给出了平衡点和稳定性分析。此外，证明了解的正性和有界性。此外，还提供了癌细胞、免疫疗法和化疗的图形表示，以了解癌症治疗的行为。最后，展示了一种曲线拟合过程，可以帮助医疗从业者治疗癌症患者。© 2023作者。IMR Press发表。

Cancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are the most prevalent types of cancer.In this work, fractional modeling is presented which describes the dynamics of cancer treatment with mixed therapies (immunotherapy and chemotherapy). Mathematical models of cancer treatment are important to understand the dynamical behavior of the disease. Fractional models are studied considering immunotherapy and chemotherapy to control cancer growth at the level of cell populations. The models consist of the system of fractional differential equations (FDEs). Fractional term is defined by Caputo fractional derivative. The models are solved numerically by using Adams-Bashforth-Moulton method.For all fractional models the reasonable range of fractional order is between β = 0.6 and β = 0.9. The equilibrium points and stability analysis are presented. Moreover, positivity and boundedness of the solution are proved. Furthermore, a graphical representation of cancerous cells, immunotherapy and chemotherapy is presented to understand the behaviour of cancer treatment.At the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.© 2023 The Author(s). Published by IMR Press.