Mathematical Framework for Modeling Tumor Growth in Cancer Patients Using Fractional Derivatives

Tumor growth in cancer patients is a characteristic feature of the disease, characterized by abnormal cell division, often resulting in lumps or masses. These tumors can be benign or malignant, with malignant tumors exhibiting unbridled growth and metastasis. Understanding tumor growth mechanisms is crucial for developing effective treatments like surgery, chemotherapy, radiation, and targeted therapies. This study uses the reduced differential transform technique (RDTM) to analyze two cancer tumor simulations in the Caputo sense. The primary model describes the dynamic between chemotherapy medications, cancer cells, healthy cells, and immune cells. The additional framework analyzes scenarios where the cancer cell death rate K varies based on cell number, time, or location. The solutions are calculated using Mathematica software, producing innovative series results for different gamma values. The study validates the method’s use for analyzing chemotherapy’s side effects, as it boosts immunity against some malignancies by reducing the number of tumor cells proportional to the cancer cell killing ratel.