Modeling and optimal analysis of lung cancer cell growth and apoptosis with fractional-order dynamics

This study explores the application of fractional-order calculus in modeling lung cancer cell growth dynamics, emphasizing its advantages over traditional integer-order models. Conventional models often fail to capture the complexities of tumor behavior, such as memory effects and long-range interactions. The fractional-order logistic equation provides a more sophisticated framework that integrates intrinsic growth rates and environmental constraints, enabling a nuanced analysis of tumor progression and treatment responses. A key component of this research involves deriving a Laplace domain representation to assess transfer function characteristics, which aids in evaluating stability and response across various frequency domains. An improved fractional-order model was developed to illustrate the interplay between cancer proliferation and immune response mechanisms. The optimization of critical parameters, including the fractional-order ultimate growth rate, has been achieved using a genetic algorithm (GA) optimization. The main findings of this work include the potential of fractional-order modeling to understand, analyze, and determine treatment strategies, ultimately advancing the understanding of cancer dynamics and improving patient outcomes in oncology. Here, it shows the application of fractional-order dynamics to determine the effective treatment procedure concerning all complex parameters involved. This research contributes to the growing body of knowledge on sophisticated mathematical frameworks in cancer research, facilitating the development of tailored therapeutic interventions based on individual patient profiles.