Speaker: Dr. Erkan Nane

 

Title: Probabilistic approach to fractional calculus

Abstract: The link between concepts from probability and partial differential equations (PDEs) helped solve problems in analysis or find easier and shorter proofs for well-known results. Researchers have been fascinated by these kinds of links. The classical well-known connection of a PDE and a stochastic process is the Brownian motion and heat equation connection.

In this talk,  first I will give a short introduction to fractional calculus and then I will consider the Cauchy problems that can be solved by running time-changed Markov processes. These are obtained by taking Markov processes and replacing the time parameter with other processes such as Brownian motion, symmetric \(\alpha\)-stable process of index \(\alpha \in (0,2]\),  with an inverse of a stable subordinator.