Research Team for “Theory and Applications of Fractional Differential Equations”of Xiangtan University
The fractional calculus started more than three centuries ago. In the last decade, fractional calculus has been playing a very important role in various scientific fields. In fact, it has been recognized as one of the best tools to describe long-memory processes. Fractional-order models are interesting not only for engineers and physicists, but also for mathematicians. The most important among such models are those described by partial differential equations containing fractional derivatives. Their evolutions behave in a much more complex way than in the classical integer-order case and the study of the corresponding theory is a hugely demanding task. The research team for “Theory and Applications of Fractional Differential Equations” is devoted to studying the basic theory for fractional differential equations, fractional order modeling and numerical methods, and applying fractional calculus to some important problems in science and engineering. This team is mainly composed of Professors Yong Zhou, Chengfu Li, Yonghong Lan, and Dr. Lu Zhang, Li Peng, Jiawei He, Jingna Wang.
In the past years, the team carried out extensive academic exchanges and scientific cooperations with more than 20 overseas researchers including those in the United States, France, Australia, Spain, Italy, Slovakia, Belgium, Portugal, Turkey, India, Iran, Saudi Arabia and so on. In recent years, the group has undertaken more than 10 projects including National Natural Science Foundation, Specialized Research Fund for the Doctoral Program of Higher Education and Key Projects of Hunan Provincial Natural Science Foundation. The research team focused on studying the existence of homoclinic orbits for fractional Hamiltonian systems, well -posedness and regularity of the time fractional Navier-Stokes equations, Schrödinger equations and diffusion equations, and optimal control of fractional nonlinear systems. In particular, they solved the most important and key problems in the well posedness theory of fractional evolution equations.
The team leader Professor Yong Zhou serves on the editorial boards of several international mathematical journals. He has published 6 monographs and more than 200 papers in the journals such as Mathematische Annalen, Journal of Functional Analysis, Bulletin des Sciences Mathématiques, Comptes Rendus Mathématique and Nonlinear Dynamics, over 26 papers of which were included in ESI Highly Cited Papers. He was awarded the second prize of Natural Science of Ministry of Education and the second prize of Natural Science of Hunan province. Professor Yong Zhou won Highly Cited Researcher Award from Thomson Reuters in 2014, and was included in the list of Most Cited Chinese Researchers by Elsevier from 2014 to 2017.