Optimal control for cancer treatment mathematical model using Atangana–Baleanu–Caputo fractional derivative

Abstract

Abstract In this work, optimal control for a fractional-order nonlinear mathematical model of cancer treatment is presented. The suggested model is determined by a system of eighteen fractional differential equations. The fractional derivative is defined in the Atangana–Baleanu Caputo sense. Necessary conditions for the control problem are derived. Two control variables are suggested to minimize the number of cancer cells. Two numerical methods are used for simulating the proposed optimal system. The methods are the iterative optimal control method and the nonstandard two-step Lagrange interpolation method. In order to validate the theoretical results, numerical simulations and comparative studies are given.

Keywords

• Fractional-order derivatives
• Mathematical cancer models
• Anti-angiogenic therapy
• Immunotherapy
• Iterative optimal control method
• The nonstandard two-step Lagrange interpolation method