Fractional-Order Control: Bibliometric Analysis and Performance Evaluation

The development of fractional-order control has been derived from the mathematical generalization of classical calculus and has become an important tool in the modeling and control of dynamical systems with memory and hereditary effects. In spite of the rapid development of this area of control theory and applications, the overall scientific development, structure, and engineering relevance of fractional-order control remain insufficiently understood. In this paper, we address this problem by combining large-scale bibliometric analysis with representative controller performance studies. A total of 6482 publications indexed in the Web of Science database during the period 2010–2026 are analyzed. The bibliometric results indicate that fractional-order control is an increasingly connected global research field with strong roots in fractional calculus, advanced control theory, and growing interdisciplinary links with applied mathematics, automation, and computer science. To further illustrate controller level behavior, representative simulations are performed on a fractional-order time-delay process and an uncertain nonlinear system. For the fractional-order time-delay process, a well-tuned PID controller is compared with a realizable FOPID controller implemented through Oustaloup recursive approximation. The results show that the FOPID controller improves several performance measures, including overshoot, settling time, control energy, total variation, and sensitivity peak, while the comparison is interpreted as a performance trade-off rather than universal superiority. For the uncertain nonlinear system, fractional-order sliding mode control produces smoother control action and substantially reduces chattering. By combining bibliometric mapping with representative performance evaluation, this paper provides a comprehensive overview of fractional-order control as a globally active and practically relevant discipline in control engineering.