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<p>The work aims to establish the existence, Hyers-Ulam stability, and trajectory controllability of Hilfer fractional stochastic pantograph equations with random impulses in the <i>p</i>th mean. The existence results of the proposed system are studied using fractional calculus, semigroup theory, M<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1801_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ddot{o}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>o</mi> <mo>¨</mo> </mover> </math></EquationSource> </InlineEquation>nch fixed point theorem, and stochastic analysis. Furthermore, the Hyers-Ulam stability of the aforementioned system is established. Moreover, the trajectory (T-) controllability of the system is investigated. The article is concluded with the numerical simulation using the Euler Maruyama method with suitable quadrature techniques.</p>

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Trajectory Controllability of Hilfer Fractional Stochastic Pantograph Equations with Random Impulses

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Ravikumar Kasinathan,
  • Ramkumar Kasinathan,
  • Dimplekumar Chalishajar,
  • Dhanalakshmi Kasinathan,
  • Mitali Rautaray

摘要

The work aims to establish the existence, Hyers-Ulam stability, and trajectory controllability of Hilfer fractional stochastic pantograph equations with random impulses in the pth mean. The existence results of the proposed system are studied using fractional calculus, semigroup theory, M \(\ddot{o}\) o ¨ nch fixed point theorem, and stochastic analysis. Furthermore, the Hyers-Ulam stability of the aforementioned system is established. Moreover, the trajectory (T-) controllability of the system is investigated. The article is concluded with the numerical simulation using the Euler Maruyama method with suitable quadrature techniques.