报告题目：A New Theory of Fractional Calculus and Fractional Differential Equations and Their Numerical Methods

主讲人：凤小兵教授

单位：美国田纳西大学

时间：7月10日10:00

地点：学院二楼会议室

摘要：In this talk, I shall first discuss recent developments in weak fractional calculus and fractional Sobolev spaces based on a new weak fractional derivative concept which is a natural generalization of integer order weak derivatives and helps to unify multiple existing fractional derivative concepts. I shall then introduce a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. This new framework/theory is based on the theory of weak fractional derivatives and their associated fractional order Sobolev spaces. It leads to new types of fractional differential equations, including new one-side fractional Laplace operators and future value problems. Finally, I shall also briefly introduce some new finite element (and DG) methods for approximating the weak fractional derivatives and the solutions of fractional calculus of variations problems and their associated fractional differential equations.

简介：凤小兵，美国田纳西大学(The University of Tennessee)数学终身教授，现任数学系系主任(Department Head)。1983年和1985年分别获西安交大计算数学学士和硕士学位，1992年获美国普度大学（Purdue University）应用和计算数学博学位,师从Jim Douglas Jr.教授。凤小兵教授长期从事线性，特别是非线性确定和随机偏微分方程及其数值解法与算法的研究，并取得了一系列国际领先的成果。在SIAM Review, SIAM J. Numerical Analysis, Mathematics of Computation, Numerische Mathematik, SIAM J. Mathematical Analysis, Transaction of AMS, Calculus of Variation and PDEs等国际一流专业学术期刊上发表论120余篇。