A novel fractional computational neural framework for analyzing cancer model under chemotherapy drug

In this study, a novel Caputo fractional-order model is proposed to represent the complex interactions among stem cells, effector cells, and tumor cells, considering both scenarios of chemotherapy. Furthermore, the proposed model, which incorporates treatment with effective chemotherapy, is thoroughly examined. The necessary properties, including the positivity and equilibrium points, as well as the local asymptotic stability analysis, are investigated. Additionally, the existence and uniqueness of solutions for the proposed model are thoroughly analyzed. We perform a thorough assessment of the solutions produced by the deep neural network by comparing them against established benchmarks and carefully analyzing them through testing, validation, training, error distribution analysis, and regression analysis. The temporal concentration pattern of stem, effector and tumor cells as well as chemotherapy drugs are examined. It is noted that chemotherapy leads to a decrease in tumor cell density over time, which extends the period required to achieve equilibrium. The decay rates of stem cells and tumor cells are recognized as essential elements affecting cancer dynamics. Furthermore, the integration of fractional orders is found to be important for precisely depicting the concentrations of cancer cells.