Title: Evolution Equations with General Fractional Derivatives as Models of Anomalous Diffusion 

Abstract: In this talk, we discuss a class of anomalous diffusion models in form of evolution equations involving the general time-fractional derivatives with Sonin kernels. Under suitable conditions, these equations can be embedded within the framework of the classical continuous-time random walk model, with the waiting-time probability density function determined by the corresponding Sonin kernels.

Then we focus on an important particular case of this model in form of a fractional diffusion equation involving the general time-fractional derivatives with Sonin kernels. In particular, a concise formula for the mean squared displacement of the diffusing particles governed by this equation as well as an interpretation of its fundamental solution as a spatial probability density function evolving in time are discussed.  

Title: TBA

Abstract: TBA. 

Fractional Monge–Ampère equations

Abstract: A relatively long-standing open problem in the fractional and nonlocal PDE communities is to find the adequate, most appropriate version of a fractional, nonlocal Monge–Ampère equation. We will discuss several possible definitions and their properties, and present some recent progress.