Globally, aging is a serious problem that can cause conditions such as movement disorders, stroke, and loss of mobility. Spinal cord Injury (SCI) is also one of the main causes of mobility disorders among human beings. Physical therapy is significantly used to help people with some mobility disorders that need the involvement of a nurse or physiotherapist. Therefore, it is desired to develop a rehabilitation robotic exoskeleton that can help people to regain their movement capabilities and it will also limit the need for a physiotherapist or nurse. For designing an exoskeleton system, an efficient control strategy is an essential requirement. Here, a closed-loop fractional-order-proportional integral-derivative (FO-PID) scheme is employed for a leg robotic rehabilitation exoskeleton (RRE) plant. A nature-based Grey wolf optimization (GWO) is explored for getting the best control values for a closed-loop FO-PID scheme. Apart from this, an external disturbance has been induced in the closed-loop system to observe the performance. The resulting values are compared with its integer counterpart controller.