Stability and BI-RADS 4 subcategories mitigate on cancer risk dynamics with fractional operators: A case study analysis

In this paper, we present a mathematical model to lower the probability of breast cancer risk of the Breast Imaging Reporting and Data Systems (BI-RADS) 4 subcategories with the fractal fractional operator. This method improves evaluation quality, creates straightforward concepts for the early detection of breast cancer, and outcomes can be tracked easily by using BI-RADS-4 subcategories data at the Near East University Hospital. It uses the Banach fixed point theorem for nonlinear functional analysis and confirms the boundedness and uniqueness of solutions. Sensitivity analysis was performed on model parameters, and advanced numerical techniques were used to develop solutions. Also, this reveals disease-free and endemic equilibrium points, indicating local and global asymptotic stability. Chaos control was used in the regulated for linear responses approach to bring the system to stabilize according to its points of equilibrium. The growing procedure yields more effective and similar outcomes than the rotting technique, which happens quickly in the lowest fractional orders. Using Lagrange polynomial insight into the fractal-fractional operator, we conducted simulations and presented a comparative analysis in graphical form with classical and non-integer derivatives. The comparison of integer and non-integer results highlighted the importance of accurate fractional parameters in simulation. Moreover, it suggests that fractional operator-included mathematical models can help reveal more significant decisions on managing such real-life problems. Numerical simulations reveal absorption features for the fractal-fractional derivative with a generalized Mittag-Leffler kernel. The approximation solution approach allows for different order and dimension between 0 and 1, with outcomes changing for different fractional and fractal orders. It was determined that early diagnosis, quitting smoking, higher lactation rates, and ongoing care can reduce cancer risk. Our findings are critical for researchers, policymakers, and health care practitioners in combating and preventing breast cancer, contributing to worldwide public health initiatives. • The (BI-RADS) is intended to standardize reporting on breast imaging. • Model was tested on 42 BI-RADS 4 patients at NEU Hospital, demonstrating converging characteristics. • It uses the Banach fixed point theorem for nonlinear functional analysis. • Disease-free and endemic equilibrium points, indicating local and global asymptotic stability. • Sensitivity analysis is performed, and advanced numerical techniques are used to develop solutions.