Dynamic Fractional-Order Computational Modeling of Lung Cancer: A Hybrid Biomechanical–Therapy Framework

Innovative computational biomechanics approaches are required to optimize the fractional dynamical behavior of non-small-cell lung cancer (NSCLC) systems, still one of the leading causes of cancer-related mortality globally. This study presents a comprehensive fractional-order computational dynamical system describing the biomechanical interactions among tumor cells, cytotoxic CD8⁺ T lymphocytes, and dendritic cells. The model is formulated in terms of a set of nonlinear differential equations, and the memory effect and anomalous biological processes are introduced through the complex transform of He. The equilibrium and stability analysis have provided important critical values, such as a basic reproduction number that controls the persistence or elimination of the tumor. The model of treatment is a hybrid system, which entails continuous immune tumor interactions and discrete therapeutic events. Computer modeling shows that in cases of early surgical intervention with subsequent periodic chemotherapy; the size of the tumor burden is decreased as well as the immune response is boosted. The results highlight the potential of mathematical modeling to enhance our comprehension of tumor–immune–therapy dynamics in NSCLC and to guide customized treatment planning.