Fractional-order dynamics appear in several problems in science and engineering such as viscoelastic materials, economics, continuum and statistical mechanics, solid mechanics, bioengineering, dynamics of interfaces between nanoparticles and substrates. Although the optimal control theory is an area in mathematics that has been under development for many years, the fractional optimal control theory is a very new area in mathematics. The control of systems with time delay has been of considerable concern. Delays can be occurred in various fields including chemical, biological, economics, and traortation systems. These systems and many physical systems are modeled by delay fractional differential equations. The delay fractional optimal control problem is an optimal control problem in which system dynamics are defined with delay fractional differential equations.
