Optimal Control for Fractional Order Dynamics of Tumor Growth

Abstract

This paper concerns the analysis and optimal control of fractional order model of tumor cells and the body’s immunological response using Atangana-Baleanu-Caputo derivative fractional operator. The model consists of spawning cells (S), reposing cells (R) and tumor cell (T) where we have used the Hattaf-Yousfi functional response for the activation of the reposing cells in the presence of tumor cells. We investigate the model’s existence and stability and present numerical results using a modified predict-evaluate-correct-evaluate (PECE) method of Adams-Bashforth-Moulton. We also study the Fractional optimal control problem (FOCP) in order to minimize tumor cell density. The Fractional Pontryagin maximum principle (FPMP) is used to characterize the fractional optimal control problem and we implement the forward-backward PECE method to determine the extremals of the problem. We study the optimal control dynamics of tumor growth via several numerical simulations.