In recent times, the application of fractional mathematics helps in modeling the mechanical and electrical properties of real systems. Fractional integrals and derivatives have found full attention in the control of dynamical systems when the controlled system and the controller is described by a set of fractional order differential equations. This paper elaborates the ability of grey wolf optimization (GWO) in optimizing the fractional order proportional integral derivative (FOPID) controller parameters to control the exhaust temperature of a gas turbine (GT). The maintenance and operation of GTs at optimum performance with minimum fuel stroke ratio is mandatory in the electricity production sector. The obtained results of the optimum values of FOPID based exhaust temperature controller are compared with those attained using the optimum values of the current existing 265 MW simple cycle, actual single-shaft heavy duty GT. The attained results are impressive in terms of enhancing the dynamic performance and decreasing the response time.