Fractional calculus (FC) was originally proposed by Guillaume de l'Hôpital, and in 1890, Oliver Heaviside created the first practical use of fractional differential operators in electrical transmission line analysis. Due to the lack of physical explanation, FC was not wellreceived by the engineering and scientific communities. The beauty of this domain is that, unlike integer order (IO) derivatives and integrals, which follow a point property, fractional order (FO) ones provide generalisation of the point property.This thesis focuses on robotic systems that are unstable and difficult to manage, such as a pendulum on a cart system. The management of 2-D gantry crane systems is of the utmost importance in businesses that deal with the transfer of big loads; these systems are often operated by humans, who rely on their own abilities and knowledge to move the huge objects, which may lead to serious mishaps. In order to construct the controller without resorting to the hit-and