Trajectory controllability of Clarke subdifferential type Hilfer fractional stochastic differential inclusion with non-instantaneous impulsive effects and deviated argument

Abstract

This manuscript is devoted to analyse the solvability and trajectory controllability of Hilfer fractional non-instantaneous impulsive stochastic differential inclusion with Clarke subdifferential and deviated argument. The proposed Hilfer fractional impulsive inclusion system’s solvability in Hilbert space is established by employing fractional calculus, multivalued analysis, stochastic analysis, semigroup theory and a multivalued fixed point theorem. Furthermore, under some suitable assumptions, the considered system’s trajectory controllability is established using a generalized Gronwall’s inequality. At last, an example is provided to verify the developed theoretical results.