New discussion on trajectory controllability of time-variant impulsive neutral stochastic functional integrodifferential equations via noncompact semigroup

The purpose of this paper is to determine a new discussion on trajectory-(T) controllability of time variant impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion (fBm) via noncompact semigroup in a Hilbert space. Initially, with the help of the Hausdorff measure of noncompactness (HMN), the Mönch fixed point theorem and some inequality techniques, some new standards to guarantee the mild solution for INSFIDEs are obtained. The system’s T-controllability is then examined using Gronwall’s inequality. An example is given to validate the results at the end. This work is applicable to the heart disease biological system using parametric smoothing technique with modifying time variable. Our work extends the work of Boufoussi and Hajji (2012), Chen (2010), Caraballoa et al., (2011), Boudaoui et al., (2015).