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<p>This paper is concerned with the relatively exact controllability of a class of fractional stochastic dynamical systems(FSDSs) with distributed delays in control. Firstly, with the aid of unsymmetric Fubini theorem, the solution of this FSDSs are derived. Subsequently, we show that relatively exact controllability of linear systems are equivalent to positive definiteness of Grammian matrix. In addition, Schauder’s fixed point theorem and It<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2473_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hat{o}\)</EquationSource> </InlineEquation> isometry are used to prove the relatively exact controllability results for nonlinear case. Finally, an example is offered to illustrated the theory.</p>

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Controllability of fractional stochastic differential system with distributed delays in control

  • 期刊论文

  • 发表日期：

    2025年4月18日

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  • Yihong Yuan,
  • Danfeng Luo

摘要

This paper is concerned with the relatively exact controllability of a class of fractional stochastic dynamical systems(FSDSs) with distributed delays in control. Firstly, with the aid of unsymmetric Fubini theorem, the solution of this FSDSs are derived. Subsequently, we show that relatively exact controllability of linear systems are equivalent to positive definiteness of Grammian matrix. In addition, Schauder’s fixed point theorem and It \(\hat{o}\) isometry are used to prove the relatively exact controllability results for nonlinear case. Finally, an example is offered to illustrated the theory.