Fractional optimal control of breast cancer dynamics using Caputo derivatives: modeling, analysis, and numerical investigation

Abstract In this paper, we present a fractional-order mathematical model for breast cancer dynamics that incorporates memory effects through Caputo fractional derivatives. The model describes the interactions among tumor cells, immune cells, and healthy host cells under the influence of two therapeutic interventions representing chemotherapy and immunotherapy. An optimal control problem is formulated to minimize tumor burden while balancing treatment costs. We establish fundamental mathematical properties of the model, including positivity, boundedness, and existence and uniqueness of solutions. Necessary optimality conditions are derived using the fractional Pontryagin Maximum Principle. A numerical solution…

• BU
  Beni-Suef University