he major goal of the this work is to present an optimal design of the Fractional-order Proportional-Derivative-Integral (FoPID) controller for the single-joint arm dynamics. For meeting this aim, the Particle Swarm Optimization (PSO) algorithm will be implement to tune the parameters of such controller. Six FoPID-controllers will be generated in accordance with two kinds of approaches (Continued Fraction Expansion (CFE) and Outstaloup’s approaches) for Laplacian operators, coupled with three fitness functions (IAE, ITAE, ITSE). These controllers will be competed to each other to determine which one can provide to the closed-loop system of the single-joint robot arm model a good rise time, short settling time, and an excellent overshoot. Keywords: Fractional-order model; Oustaloup approximation, Continued