Complexity is a challenging notion for theoretical modelling, technical analysis, and numerical simulation in physics and mathematics, as well as many other fields, as highly correlated nonlinear phenomena, evolving over a large range of timescales and length-scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be it physical, biological, or financial, and technological complex systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods.

Using these methods predictive tools have been developed for a number of applications, from explaining economic growth in the extensive area of complexity economics, to predicting mechanisms of drug delivery of pharmaceutical compounds in the living organisms. Regarding the techniques for highlighting the complex character of studied systems, a pertinent suggestion could be fractal analysis, highlighting the fractal dimension and the measurement of lacunarity, both locally, on small areas, and on the entire surface/volume of the studied sample.

The aim of this Special Issue is to highlight here papers that show modelling, simulation, and applications of fractional order derivatives or fractional calculus. This has recently become an increasingly popular subject, with an impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to a certain objective presented above are especially welcome subjects. Likewise, we hope to attract review articles, which describe the current state of the art in complexity theory.

Potential topics include but are not limited to the following:

• Nonlinear dynamics in biological complex systems
• Complexity diagnosis in extensive financial data by time-series method
• Fractal analysis of fracture surfaces in materials testing
• Nonlinear processes in plasma complex structures
• Spatiotemporal fractal-type behaviours in field theory
• Structure models that contain re-occurring patterns in nuclear physics and medicine
• Pattern predictions in environmental sciences and biometric studies of plant morphology
• New algorithms to solve classical problems in the area of fractional order derivatives
• Fractional-dynamic analogues of standard models by using fractional calculus