Fractional order modeling of prostate cancer with pulsed treatment and the impact of effector cell killing and cell competition.

This manuscript illustrates a fractional-order mathematical model for prostate cancer (PC) growth under pulsed treatment, incorporating the effects of effector cell killing and competition between androgen-dependent (AD) and androgen-independent (AI) PC cells. We establish the existence and uniqueness of solutions using fixed-point theorems (Leray-Schauder and Banach) and investigate Ulam-Hyers stability to assess the model's solution stability under the fractional order. Numerical results are obtained via the fractional Euler method for simulation of the model at various fractional orders. Graphical results illustrate the model's dynamics, and the impact of key parameters, including the effector cell killing rate and inter-cell competition, is investigated. These findings provide insights into the complex interplay between treatment, immune response, and cancer cell dynamics, potentially informing therapeutic strategies for PC.