With the continuous improvement of information system performance, increasing mathematical methods have been applied to practical applications to achieve excellent results. Among them, fractional methods (including fractional calculus, fractional Fourier analysis, and the linear canonical transform) are becoming increasingly important in the field of mathematics and the applied mathematical community. The theory and method of fractional domain analysis can further describe the dynamic process of signal transformation from time domain to frequency domain, which opens a new way for non-stationary signal analysis and processing research. Fractional methods are ideal for dealing with problems encountered in engineering fields such as radar, communications, and sonar as they provide new ideas, algorithms, and insights compared to classical integral methods.

Although these new kinds of fractional methods have many advantages, due to the unpredictable uncertainty of the transmitted signal in practical engineering applications and the influence of various disturbances and noises on the transmission process, there are still some key problems to be solved. At the same time, there are many practical limitations in engineering such as sampling and filtering in the field of multi-dimensional signals, which are also a major challenge for fraction theory.

The aim of this Special Issue is to focus on the recent achievements and future challenges for the theory and applications of fractional methods in engineering. Original research and review articles are welcomed.

Potential topics include but are not limited to the following:

• Discretization algorithm, sampling, uncertainty principles, and other basic theories related to the fractional methods
• New results of fractional methods associated with the quaternion transform, octonion transform and Clifford algebra
• New results of fractional methods associated with compressed sensing, graph signal processing and quantum information technology
• Applications of the fractional methods in Radar, medical image, communications, navigations and optics system
• Hyers-Ulam-Rassias stability on fractional operators over function spaces
• Metaheuristic algorithms associated with the fractional methods