Fractional calculus increases their applications in system design and analysis problems because of providing more realistic modeling of real systems. Owing to computational complexity of fractional calculus, the computer-aided design and analysis methods are required for engineering applications of fractional order systems. This study presents a numerical method for parametric robust stabilization of fractional order systems by employing single-parameter perturbation. This method implements a fractional order perturbation strategy on the basis of brute-force search technique for system stabilization problems. In order to meet a predefined minimum argument root design specification, the proposed algorithm searches for a desired placement of the minimum argument characteristic root within the first Riemann sheet by performing iterative perturbations of the fractional order. This approach can provide a straightforward numerical solution for robust stabilization problems of fractional order systems by employing an order perturbation scheme. Moreover, a possible utilization of a fractional order derivative operator as a system stabilizer is theoretically discussed. Illustrative examples show the utilization of the proposed stabilization algorithms for computer-aided fractional order system design applications.