Fractional order dynamics in breast cancer control: a Caputo perspective

In this study, we present a novel fractional-order framework to model the dynamics of breast cancer, incorporating the Liouville–Caputo fractional derivative to capture memory effects inherent in biological systems. The model describes tumor progression and its regulation through chemotherapy within a fractional calculus setting, introducing three control variables-monoclonal antibody drugs, a ketogenic diet, and z-control to influence system behavior. The existence and uniqueness of solutions are rigorously established via Sadovskii's fixed-point theorem, while global stability is examined using Hyers–Ulam stability criteria. Numerical validation is carried out using a predictor–corrector method, and graphical simulations demonstrate the improved accuracy and realism of the fractional-order model compared to its integer-order counterpart. This framework offers a robust theoretical basis for improving breast cancer treatment strategies and has the potential to inform future clinical decision making.