Controllability for impulsive neutral stochastic delay partial differential equations driven by fBm and Lévy noise

This paper aims to investigate the controllability for impulsive neutral stochastic delay partial differential equations (PDEs) driven by fractional Brownian motion (fBm) with Hurst index [Formula: see text] and Lévy noise in Hilbert spaces. By using a fixed point approach without imposing a severe compactness condition on the semigroup, a new set of sufficient conditions is derived. The results in this paper are generalization and continuation of the recent results on this issue. At the end, an application to the stochastic nonlinear heat equation with delays driven by a fBm and Lévy noise is given.