报告题目： Modelling with Fractional Calculus
报告人： Dr. Christopher Angstmann，University of New South Wales
In recent years there has been great interest in developing models involving fractional derivatives in many branches of science and engineering. The use of fractional derivatives allows for the inclusion of a non-locality in the models. This non-locality has allowed for the development of models that fit a variety of phenomena that are not easily modelled with simple integer-order differential equations such as anomalous diffusion, and chronic infections. The use of fractional-order derivatives is of course not without its drawbacks. For example as the models are non-local, the numeric approximation of the solutions are much more onerous to produce. Another issue that often arises is the physical meaning of the parameters in such models and a general loss of modelling intuition.
Some of the issues that arise in modelling with fractional-order derivatives can be circumvented by constructing the models via stochastic processes. The most simple example of this can be seen with the derivation of the fractional diffusion equation from a continuous time random walk. In general, semi-Markov process such as the continuous time random walk can serve as a prototypical basis for the construction of models involving fractional-order derivatives. The stochastic models can also help us understand the applicability of fractional derivatives used in modelling.
In this talk I will highlight many of the recent advances in modelling with fractional-order derivatives from stochastic processes, focusing on time-fractional models of anomalous diffusion and fractional-order compartment models.
Dr. Christopher Angstmann is an Applied Mathematician from the University of New South Wales, Sydney, Australia. He has a diverse academic background obtaining a PhD in Theoretical Physics as well as a Master degree in Actuarial Science. Much of his research could broadly be placed in the categories of complex dynamical systems and stochastic modelling. He is keenly interested in the connections between stochastic processes and fractional calculus. He has published influential academic papers in famous international journals including SIAM Journal on Applied Mathematics.