Fractional-order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative. Such systems are said to have fractional dynamics. Integrals and derivatives of fractional orders are used to illustrate objects that can be described by power-law nonlocality, power-law long-range dependence, or fractal properties. FOS are advantageous in studying the behaviour of dynamical systems in electrochemistry, physics, viscoelasticity, biology, and chaotic systems. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in many subjects of the control theory, for example in stability, stabilization, controllability, observability, observer design, and fault estimation.

The application of control theory in fractional-order systems an important issue in many engineering applications. It is necessary to note that several physical systems are not truly modelled with integer-order differential equations. The reason is that their actual dynamics contain non-integer derivatives. So, in order to accurately describe these systems, the fractional-order differential equations have been introduced. Such systems are conventionally called fractional-order systems. Fractional-order systems with a fractional derivative between 0 and 1 correspond to an extension of the classical integer-order ones, so that a broader set of real systems could be covered. As examples: image processing, electromagnetic systems, and dielectric polarization have been modelled using the fractional-order calculus. Indeed, this subject covers also important applications in engineering areas such as bioengineering, viscoelasticity, electronics, robotics, control theory, and signal processing.

The aim of this Special Issue is to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problem of nonlinear systems. Topics of interest include state estimation for fractional-order systems including, for example, works on new results on the state estimation problem for fractional-order systems and robust observer scheme for a class of linear fractional systems. The problem of stabilization can be presented also, namely the feedback control scheme for fractional systems or the model-reference control problem. Furthermore, fault estimation for fractional nonlinear systems is one of the most important subjects, for example, the adaptive estimation strategy of component faults and actuator faults for fractional-order nonlinear systems, etc. We invite authors to contribute original research as well as review articles related to all aspects of this Special Issue.

Potential topics include but are not limited to the following:

• Stability analysis of fractional-order systems
• Controllability and observability of fractional-order systems
• State estimation of fractional-order systems
• Stabilization of fractional-order systems
• Fault estimation of fractional nonlinear systems
• Identification of continuous-time fractional models
• Design of robust fractional PI controller
• Modelling, identification, and control a robot system with fractional-order differential equations
• Field programmable gate array implementation
• Microprocessor implementation and applications
• Switched capacitor and integrated circuit design