Abstract
This research presents a novel approach to address the complexities of heterogeneous lung cancer dynamics through the development of a Fractional-Order Model. Focusing on the optimization of combination therapy, the model integrates immunotherapy and targeted therapy with the specific aim of minimizing side effects. Notably, our approach incorporates a clever fusion of Proportional-Integral-Derivative (PID) feedback controls alongside the optimization process. Unlike previous studies, our model incorporates essential equations accounting for the interaction between regular and mutated cancer cells, delineates the dynamics between immune cells and mutated cancer cells, enhances immune cell cytotoxic activity, and elucidates the influence of genetic mutations on the spread of cancer cells. This refined model offers a comprehensive understanding of lung cancer progression, providing a valuable tool for the development of personalized and effective treatment strategies. the findings underscore the potential of the optimized treatment strategy in achieving key therapeutic goals, including primary tumor control, metastasis limitation, immune response enhancement, and controlled genetic mutations. The dynamic and adaptive nature of the treatment approach, coupled with economic considerations and memory effects, positions the research at the forefront of advancing precision and personalized cancer therapeutics.