A wide variety of processes in engineering and applied science exhibit a behaviour that cannot be modelled by classical methods, motivating and inspiring research on extended mathematical tools. In particular, partial and ordinary differential equations with derivatives of fractional order have attracted considerable attention in recent years. From the theoretical point of view they result in the modelling of physical phenomena and applications such as viscoelasticity, ground water flows, boundary layer theory, granular flows, dynamics of cold atoms in optical lattices, plasma turbulence, dynamics of polymeric materials, diffusion behaviour in complex systems such as the motion of tracer particles in living biological cells, etc.

The aim of this special session is to bring together experts in the field and to strengthen the interaction between various branches involved in fractional differential equation (FDE) research, in particular, those ranging from classical analysis and probability to the modelling of processes arising in the many applications in the natural sciences and engineering. Thus we want to promote the interaction of those experts that have a special focus on the applications and modelling issues involving FDEs, as well as those interested in the mathematical aspects as rigorous derivation or the mathematical analysis of solutions.

We want to clarify several mathematical issues, such as the behaviour of solutions, generalisations of the methods borrowed from dynamical systems and partial differential equations, etc., ideas and techniques that may shed light on the mathematical treatment and the behaviour of FDEs. In particular, there are still important gaps in our understanding of how several methods from the theories of dynamical systems can or cannot be transferred to the analysis of their FDE counterparts.

• Carlota Cuesta (University of the Basque Country, Spain)
• Gianni Pagnini (Basque Center for Applied Mathematics, Spain) - gpagnini@bcamath.org

Below you can download the schedule and the abstracts of all talks of this special session.

• Franz Achleitner (Vienna University of Technology, Austria)

           Travelling waves for a non-local Korteweg-de Vries-Burgers equation

• Maxim Dolgushev (University of Freiburg, Germany)

           Anomalous dynamics of semiflexible polymers

• Roberto Garra (University of Rome La Sapienza, Italy)

          Fractional Klein--Gordon equation and related processes

• Agnieszka Jurlewicz (Wrocław University of Technology, Poland)

           Anomalous diffusion subordination scenarios related with continuous-time random walks

• Christian Kuehn (Austrian Academy of Sciences/Vienna University of Technology, Austria)

          Operator Perturbations of Dynamical Systems

• József Lörinczi (Loughborough University, United Kingdom)

          Some results on fractional eigenvalue problems

• Enrico Scalas (University of Sussex, United Kingdom)

          On the compound fractional Poisson process

• Noèlia Viles (University of Barcelona, Spain)

          Functional limit theorems for the quadratic variation of a continuous time random walk and for certain stochastic integrals