An Investigation on an Optimal Control Problem with a Fractional Constraint in the Riemann-Liouville Sense

Abstract

Abstract. This work, deals with a fractional optimal control problem (in the Riemann-Liouville sense). An analytic description of an initial value appears in the constraint of the optimal control problem is presented and some sufficient and necessary conditions for the given initial value is obtained. Making use of an auxiliary variable together with the optimal control law, the given problem is converted into a system of ordinary integro-differential equations. Then using the Adomian decomposition method, an approximate solution is illustrated.

Analysis of a fractional order mathematical model for tuberculosis with optimal control

“…The results show that the fractional-order model can describe more complex dynamical processes than the integer model, and can easily include memory effects that exist in the real world. In recent years, more and more scholars studied the optimal control of fractional order, for example [27,28,29,30]. The aim of this paper is to investigate the best control methods to minimize the number of active, infectious and latent TB patients, taking into account the cost of treating TB patients.…”