A Fractional-Order Model of Breast Cancer, Approximate Solutions, and a Control Strategy

Breast cancer is one of the leading causes of cancer-related mortality among women worldwide. Therefore, the collection of patient data, the simulation of breast cancer, and the analysis of tumor dynamics are critically important. To that end, the development of efficient numerical methods or the improvement of existing computational algorithms is essential. In this study, a pseudo-spectral method based on shifted Jacobi polynomials is proposed. Furthermore, a control strategy based on the Lagrange multiplier approach is incorporated to improve the performance of the proposed model. The existence and uniqueness of the solution to the differential equation are proved using the Leray–Schauder fixed-point theorem. Additionally, upper bounds for the residual functions are derived in a weighted function space, and a sensitivity analysis is conducted to determine the influence of the model parameters on the tumor dynamics. The numerical results demonstrate the effectiveness of the proposed approach. Furthermore, the results confirm a significant reduction in the tumor radius, indicating the potential of the control strategy to suppress breast cancer growth.