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September 12, 2025Open Access

Asymptotic Controllability of Coupled Fractional Stochastic Sobolev-Type Systems with a Nonlocal Condition

TBTayeb BlouhiUniversité des Sciences et de la Technologie d'Oran Mohamed Boudiaf HAHussien Albala FLFatima Zohra Ladrani

Key Points

Asymptotic controllability is achieved under specific conditions in fractional stochastic Sobolev-type systems.
The study presents new sufficient conditions based on semigroups and iterative methods, improving understanding of stochastic control.
Results assume controllability of the associated linear system, ensuring precise outcomes for the proposed methods.
An illustrative example demonstrates the theories applied, underlining the practical implications of the findings.

Abstract

This paper discusses the asymptotic controllability of fractional-order Sobolev-type perturbed stochastic control systems with Brownian motion and nonlocal fractional-order Sobolev stochastic conditions. A new set of sufficient conditions is established using the theory of semigroups together with iterative methods, with some advancements on the Brownian motion properties. Our main results are obtained assuming that the associated linear system is controllable. A most essential example is brought to illustrate the analysis obtained.

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