What question did this study set out to answer?

The aim is to explore sufficient conditions for mild solutions and approximate controllability in nonlinear fractional stochastic inclusions.

New Exploration on Approximate Controllability of Nonlinear Ψ‐Hilfer Fractional Neutral‐Type Delayed Integro‐Differential Stochastic Inclusions

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Randomized trial investigates mild solutions and controllability in nonlinear stochastic inclusions, suggesting new conditions.

The aim is to explore sufficient conditions for mild solutions and approximate controllability in nonlinear fractional stochastic inclusions.
Investigated nonlinear fractional neutral-type integro-differential stochastic inclusions in a separable Hilbert space.
Applied the Bohnenblust–Karlin fixed point theorem to establish the existence of mild solutions.
Utilized multivalued maps, fractional calculus, and stochastic analysis techniques to derive results.
Confirmed existence of mild solutions for the stochastic control problem under given conditions.
Established approximate controllability for the control system based on the controllability of the corresponding linear system.
Provided an illustrative example to support the theoretical findings.

Sharma et al. (2026) studied this question.

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