Hilfer Fractional Neutral Stochastic Differential Inclusions with Clarke’s Subdifferential Type and fBm: Approximate Boundary Controllability

In this paper, the approximate boundary controllability of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion (fBm) and Clarke’s subdifferential in Hilbert space is discussed. The existence of a mild solution of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion and Clarke’s subdifferential is proved by using fractional calculus, compact semigroups, the fixed point theorem, stochastic analysis, and multivalued maps. The required conditions for the approximate boundary controllability of this system are defined according to a corresponding linear system that is approximately controllable. To demonstrate how our primary findings may be used, a final example is provided.