Work

Dynamic Analysis of a Fractional Breast Cancer Model with Incommensurate Orders and Optimal Control

Year: 2025

Type: article

Abstract: This paper constructs a fundamental mathematical model to depict the therapeutic effects of two drugs on breast cancer patients. The model is described by fractional order differential equations with two control variables. Two scenarios are considered: the constant control and the optimal control. For the constant control scenario, the existence and uniqueness of the solution of the system are proved by using the fixed point theorem and combining with the Caputo–Fabrizio fractional derivative; then, the sufficient conditions for the existence and stability of the system’s equilibriums are derived. For the optimal control scenario, the optimal control solution is obtained by using the Pontryagin’s maximum principle. To further validate the effectiveness of the theoretical results, numerical simulations were conducted. The results show that the parameters have significant sensitivity to the dynamic behavior of the system.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9060371

Authors: Yanling Zhao, Ruiqing Shi

Institution: Shanxi Normal University

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $3,258