Fractional calculus is a mathematical theory studying the properties and applications of any order of differential, and integral operators. It is an ancient and novel mathematical theory. Until the last twenty years, people began to apply fractional calculus theory to practical engineering. The main reason is that fractional calculus has no definite physical meaning, in practice, there is not a specific physical device to realize its infinite memory, and genetic characteristics. In the past decade, fractional calculus has become a hot research topic at home and abroad, and some scientists have successfully applied it to chaotic systems, electromagnetics, signal processing, viscoelasticity and genetic mechanics, mechanical engineering and robot control. Fractional calculus theory has been gradually applied in viscoelastic materials, biology, oscillation, turbulence, molecular diffusion, and material mechanics, and shows its broad engineering application prospects. Compared with the integer-order dynamical system, fractional-order dynamical systems have advantages. Firstly, the fractional-order system is the generalisation of the integer-order system, and the integer-order system is only a special case of fractional-order system, so the fractional-order system also has some properties of an integer-order system, such as transfer function, state equation description, etc. In addition, the fractional-order system has stronger memory, and is especially suitable for describing the memory, heredity, mechanical, and electrical properties of various materials. Furthermore, the fractional-order system is more stable and more objective to reveal, and describe the original phenomenon of nature. Moreover, the parameter adjustment of the fractional-order system controller is wider.

Recently, fractional-order systems have gained increasing interest. Fractional-order systems are related to the complexity and heredity of models, which can characterise the actual evolution process more adequately than integer-order systems, and provide a more abundant degree of freedom when we model real-world problems. Fractional phenomena would pose great challenges to the nonlinear dynamics analysis of fractional-order systems. The problems of analysis, and control of fractional-order systems deserve more investigation due to the growing demands for systems theory and control practice.

The aim of this Special Issue is to solicit original research articles investigating more effective, and innovative analysis methods, and easy-to-use tools for fractional-order systems. Submissions focussing on the potential and current applications of fractional calculus in science, and engineering are particularly encouraged. Review articles discussing the state of the art are also welcome.

Potential topics include but are not limited to the following:

• Fractional abstract cauchy problems
• Stability, and qualitative analysis of fractional-order systems
• Strategies, and algorithms in fractional-order control systems
• Modelling, analysis, simulation, and design of fractional-order controls
• Singular characteristics in fractional-order systems
• Hybrid properties in fractional-order systems
• Controllability of fractional diffusion equation
• Fractional derivative modelling of physical processes in complex media
• Fractional calculus applications in signal, and image processing
• Fractional calculus applications in science, and engineering