In this paper two numerical methods are used to study the non-linear fractional optimal control problem (FOCP) for the human immunodeficiency virus (HIV) model. The objective functional is based on a combination of maximizing benefit relied on uninfected cells count and minimizing the systemic cost of chemotherapy. The state equations are given as a system of fractional order differential equations (FODEs). The fractional derivatives are described in the Caputo sense. The Pontriagyn maximum principle (PMP) is used to obtain a necessary optimality condition for the FOCP. The optimality system is derived and we introduce an iterative optimal control method (IOCM) to solved it numerically, comparisons between IOCM and the generalized Euler method (GEM) are given. Numerical experiment is presented
to demonstrate the validity and applicability of the proposed technique. we can conclude that IOCM is preferable because the uninfected cells are increasing using the proposed method than GEM, moreover the infected cells are decreasing in better way than GEM. |
