The study and characterization of non-linear systems has been mostly addressed using integer-derivative operators. However, the use of operators, both derivative and integrative, of non-integer order has received increasing attention in recent years. The use of this type of operator gives its name to fractional calculus, with numerous examples of its application in the area of nonlinear systems. One of the main differences between systems based on classical calculus (integer-order) and fractional-order calculus is that fractional operators can model memory and hereditary properties.

Examples of remarkable contributions in the study of fractional-order chaotic systems have been developed in systems that present the coexistence of attractors. These investigations range from systems without equilibrium points, systems based on memristors, and multi-scroll systems to systems capable of presenting families of attractors with coexisting bistable solutions. From the point of view of the hidden attractors, there are also interesting results shown in well-known systems, such as Lorenz, Chua, and Chen systems, among others. Furthermore, theoretical analysis of fractional order systems also exhibits notable insights where the stability has been studied in linear time-invariant fractional-order systems involving different derivative methods.

This Special Issue aims to provide a platform for state-of-the-art achievements about the dynamical behavior of fractional-order complex systems with a wide range of behaviors such as multistability or hidden attractors, among many others, and explore the potential engineering applications of this kind of systems. Original research and review articles are both welcome.

Potential topics include but are not limited to the following:

• Chaos theory, chaotic systems, and fractional-order complex systems
• Fractional order chaotic systems
• Numerical simulations and methods for fractional-order complex systems
• Multistability in fractional-order systems
• Design of fractional-order chaotic systems
• Design of fractional-order chaotic circuits
• Extreme events in fractional-order non-linear systems
• Emergent behaviors in complex networks based on fractional-order systems
• Synchronization of fractional-order systems
• Fractional-order chaos-based security applications
• Chaos and fractional-order neural networks
• Chaos in physical, chemical, and biological inspired fractional-order systems
• Fractal behavior in fractional-order systems