An analysis of approximate controllability in fuzzy neutral impulsive stochastic differential system in Caputo order propelled by Rosenblatt process and Brownian motion

Abstract

Emphasizing recent improvements of dynamical systems in the approximation controllability is the key intent of the paper. In Caputo order $0< \varsigma< 1$ and fuzzy settings, the study examines a stochastic fractional differential equation with infinite delay governed by the Rosenblatt process and Brownian motion for approximate controllability. This research is accomplished through the Krasnoselskii-Schaefer theorem and the existence of the system is investigated. An example is illustrated in the end.