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Numerical Analysis Seminar

Date: December 12, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 506A

Speaker: Prof. Kai Diethelm, Technische University at Braunschweig, Germany

  

Title: On the Principle of ``Fractionalization'' in Mathematical Modeling

Abstract: Traditional mathematical models for many phenomena in various different fields of science and engineering are based on the use of classical differential equations, i.e. on equations containing integer order derivatives. These models are usually well understood from an analytic point of view, in particular regarding the qualitative behavior of their solutions. The availability of such information is important for evaluating whether the mathematical model really reflects the actual properties that the process in question has, and thus for showing that the set of equations is indeed a suitable model for the concrete process. In many cases, it has been observed that a generalization of the classical models obtained by replacing the integer order derivative(s) by a derivative of fractional (i.e., non-integer) order leads to better quantitative agreement between the mathematical model and experimental data, but the knowledge about qualitative properties is frequently lacking. Thus, the question whether the fractional order model is in fact able to correctly reproduce the behavior that the underlying process must exhibit frequently remains unanswered. In this talk, specific examples from the life sciences are used to demonstrate potential approaches to handle such issues and point out possible pitfalls in this ``fractionalization'' procedure for differential equation based mathematical models. Parts of the work described in this presentation are based on results of the project READEX that has received funding from the European Union's Horizon 2020 research and innovation program under Grant Agreement No.\ 671657.