Title: Fractional confusion: some of the things we have discovered about fractional order differential equations; some we haven’t and some that are still a complete enigma.

Abstract: The idea of a fractional derivative dates back to the final years of the seventeenth century. It had its rigorous mathematical foundations in the mid-nineteenth century and was a nearly complete theory by 1970. Work on physical models of diffusion over the last 50 years has indicated that traditional assumptions based on Einstein’s formulation of Brownian motion may not hold in general and instead of a Gaussian process and the heat equation being the basic building block, current thinking has taken this into the realm of fractional differential operators.

About the Speaker: Professor Rundell received his PhD in Mathematics 1974 from Glasgow University, under advisor David Colton. He has been a member of the Mathematics department at Texas A&M since 1974, including ten years as department head, was the director of NSF-DMS for 4 years and has done a great deal of other service for the mathematics profession. His main research interests throughout his career have involved inverse problems for ordinary and partial differential equations.