Physics

Aerospace engineering

Nonlinear system

Mathematics

Biology

Sobolev space

Engineering

Fractional calculus

Mathematical analysis

Ecology

Type (biology)

Fixed point

Quantum mechanics

Applied mathematics

Fixed-point theorem

Controllability

Hilbert space

Differential inclusion

Differential (mechanical device)

Asian Journal of Control

In this paper, the approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions in Hilbert spaces is considered. By using the stochastic analysis theory, fractional calculus, multivalued maps, and Karlin's fixed point technique, a new set of necessary and sufficient conditions, are formulated which guarantees the approximate controllability of the nonlinear Hilfer fractional stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, two examples are presented to illustrate the theory of the obtained results.

A discussion on approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions