團隊負責人周勇教授

團隊主要成員

獲獎證書和專著

分數階微積分始于三百多年前。近十年來，分數階微積分在許多學科領域發揮了非常重要的作用，已被公認為描述長記憶過程的最好工具之一。分數階模型不僅使工程師和物理學家感興趣，而且對于數學家來說也是有趣的。在這些模型中，包含分數導數的偏微分方程所描述的模型是非常重要的，它們的性質比經典的整數階方程更為復雜，其理論研究是一項非常艱巨的任務。湘潭大學“分數微分方程理論及其應用”研究團隊致力于分數微分方程的基本理論、分數階建模和數值方法的研究，并將分數階微積分應用于科學和工程中的一些重要問題。該團隊由周勇教授負責，主要成員有李成福教授、蘭永紅教授、張璐博士、彭麗博士、何家維、王靜娜等。

近年來，該團隊與20余個國家和地區的研究人員有著廣泛的學術合作；團隊承擔了國家自然科學基金項目7項、教育部博士點基金項目2項、湖南省自然科學基金重點項目等科研項目；主要研究領域包括分數哈密頓系統同宿軌的存在性，時間分數Navier-Stokes方程、Schr?dinger方程和擴散方程的適定性和正則性，分數非線性系統的最優控制。特別是他們解決了分數發展方程適定性理論中最核心和關鍵的問題。

團隊負責人周勇教授是多個國際數學雜志的編委和客座編委，已出版學術專著（英文）6部；在Mathematische Annalen，Journal of Functional Analysis，Bulletin des Sciences Mathématique，Comptes Rendus Mathématique，Nonlinear Dynamics等重要學術期刊上發表論文200余篇，其中26篇論文被列入ESI 高被引論文（Highly Cited Papers）；獲得教育部自然科學二等獎和湖南省自然科學二等獎。周勇教授于2014年獲得湯森路透（Thomson Reuters）高被引科學家獎， 2014－2017年連續四年入選愛思唯爾（Elsevier）中國高被引學者。

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, Schr?dinger 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.