Wellposedness and controllability results of stochastic integrodifferential equations with noninstantaneous impulses and Rosenblatt process

Abstract

Abstract The purpose of this work is to investigate a novel class of noninstantaneous impulsive stochastic integrodifferential equations (SIDEs) driven by Brownian motion and Rosenblatt process. We construct a new set of adequate assumptions for the existence and uniqueness of mild solutions using stochastic analysis, analytic semigroup theory, integral equation theory, and a fixed point methodology. Additionally, we study the asymptotic behavior of mild solutions and provide stochastic system controllability results. Finally, we include an example to illustrate the application of our main findings.

Keywords

• Integrodifferential evolution equations
• Resolvent operator
• Controllability
• Stability
• Rosenblatt process