Specially invited expert: Tao Ran (Professor, Beijing Institute of Technology, China) ，Li Bingzhao (Professor, Beijing Institute of Technology, China) Since the theory and method of fractional Fourier domain signal processing have the unique characteristics of fractional domain, their related researches have been rapidly infiltrated from the early fields of mathematics, quantum mechanics and optical domain (optical image compression) to encryption, digital watermarking, communication, information security, medical imaging, radar and sonar and so on. According to the increasing demand of fractional Fourier theory in various fields, this special issue further studies the basic theory and application of fractional domain signal processing based on the existing theoretical results. The experts and scholars in this field are invited to elaborate on the latest research results and development trends to further promoting the synergistic development of relevant theories, technologies and applications. Through this topic, the aim is to grasp the research opportunities together, face the challenges of research and promote the progress and development of this field. The articles published include two reviews and twelve research papers.