报告题目：Fractional Derivatives and Their Applications
摘要：Considerable progress has been made in the area of Fractional Derivatives and Their Applications in the last two decades. Fractional Calculus is now being used in almost every field of science, engineering, and applied mathematics. However, many researchers still remain unaware of this field, and very few universities offer courses in this area at the graduate level and almost none at the undergraduate level. When people hear about the fractional derivatives, they often ask: What is a fractional derivative? Are there applications of this field? What are those applications? Is this subject very difficult? In this talk, I will introduce the concept of fractional derivatives and present several of its applications. I plan to formulate the following problems: The Tautochrone, Flow through a channel, Model of a disk brake, Lossy RC transmission line, Model of a real capacitor, Elastic bar on a viscoelastic surface, Shear stress in a fluid, and Motion of a plate in a Newtonian fluid. I will discuss application of fractional derivatives in modeling of disk brakes in detail, and compare analytical and numerical results for the problem. I will also demonstrate that one can use the tools and the techniques developed in this field without much knowledge of mathematics behind the subject. To demonstrate this, I will introduce a simulink half-order integrator block and discuss its applications in fractional integration of a function. I will also discuss the solution of a fractional differential equation and fractional order control. I will present some statistical data to show the growth of this field in the last three decades. I will also discuss current research areas where Fractional Calculus is being applied and used to unify fundamental laws. 报告人简介：Dr. Agrawal graduated and got his Ph.D. degree from University of Illinois at Chicago in 1984. Now he is a full professor in the Department of Mechanical Engineering and Energy Processes at Southern Illinois University, Carbondale, IL, USA. Since 1997, Professor Agrawal has been actively involved and promoting in the area of Fractional Derivatives and Their Applications. He has made significant contributions to the field including: Formulation of fractional variational calculus and fractional Euler-Lagrange equations, Deterministic and stochastic analysis of fractional dynamic and fractional optimal control systems, and analytical and numerical tools and techniques for fractional systems. Dr. Agrawal has been a plenary keynote speaker and invited speaker at several symposia, conferences, and universities. He has received various awards for his contributions in the field of Fractional Derivatives. In 2003, he organized the First Symposium on Fractional Derivatives and Their Applications in Chicago. This symposium was the first symposium to bring together at one place many people from different fields (engineering, science, economics and finance, mathematics, bioengineering, etc.) working on the application of Fractional Derivatives. In 2004, Professor Agrawal led a US team in a US-French collaboration on Fractional Derivatives and Their Applications. One of his works was recently called the Agrawal Principle by some experts in the field. Along with Prof. Tenreiro Machado and Dr. Sabatier, Professor Agrawal has co-edited a special issue of Nonlinear Dynamics and a book on Recent Advances in Fractional Calculus. Dr. Agrawal has published over 100 papers, and Google shows that the total citation are over 6000. Currently, Professor Agrawal is an associate editor of the Journal of Computational and Nonlinear Dynamics and the Indian Journal of Theoretical Physics. He is also a member of the editorial board of the International Journal of Differential Equations and Fractional Dynamic Systems.