## Analysis and Applied Mathematics Seminar

Erkan Nane

Auburn University

Stochastic Models for Space-time fractional Dynamics

**Abstract:**Partial differential equations and random fields have been used as successful models in various areas of applied mathematics, statistical mechanics, theoretical physics, theoretical neuroscience, theory of complex chemical reactions, fluid dynamics, hydrology, cosmology, mathematical finance, and other scientific areas. In this talk I will consider non-linear space-time fractional (stochastic) heat type equations. These types of time fractional (stochastic) heat type equations are attractive models that can be used to model phenomenon with random effects with thermal memory. I will review my most recent work on (i) continuous time random walk limits; (ii) heat type Cauchy problems with fractional time derivatives; and (iii) stochastic fractional equations. In particular, I will talk about the asymptotic behavior of the solution with respect to time and a parameter $\lambda$; intermittency. These results are our recent joint work with Jebessa B Mijena, Mohammud Foondun, Sunday Asogwa and Guerngar Ngartelbaye.

Monday April 22, 2024 at 4:00 PM in 636 SEO