# Fractional impulsive stochastic differential equations with unbounded delay

Tomas Caraballo is a Professor of University of Sevilla, Spain. Hisresearch field is stochastic partial differential equations and partialfunctional differential equations.

This talk is first devoted to the local and global existence of mildsolutions for a class of fractional impulsive stochastic differential equationswith infinite delay driven by both $\mathbb{K}$-valued Q-cylindrical Brownianmotion and fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. Ageneral framework which provides an effective way to prove the continuousdependence of mild solutions on initial value is established under someappropriate assumptions. Furthermore, it is also proved the exponential decayto zero of solutions to fractional stochastic impulsive differential equationswith infinite delay. Finally, some comments and remarks will be mentionedconcerning the existence of attractings sets.