Investigating Pancreatic Cancer Dynamics Through Fractional Modeling With Caputo Derivative

This research investigates the interplay among pancreatic cancer cells (PCCs), pancreatic stellate cells (PSC), effector cells, and both tumor-suppressing and tumor-promoting cytokines to better understand the dynamics of pancreatic cancer. Using the Caputo fractional derivative, the traditional model is transformed into a fractional-order framework while maintaining dimensional consistency in its equations. The study examines equilibrium points, with a specific focus on the tumor-free and high-tumor state, to evaluate local stability. The fixed-point theorem is applied to confirm the existence and uniqueness of solutions, and global stability is established through the Hyers–Ulam–Rassias method. Numerical simulations, carried out using the zwo-step Adams-Bashforth method across various fractional orders, unveil the system's complex behaviors. These results contribute to a deeper understanding of pancreatic cancer dynamics and provide meaningful insights into its underlying mechanisms.