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<p>In this study, we examine the existence and approximate controllability results for stochastic evolution inclusions with the Hilfer fractional substantial derivative of order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1689_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu \in (1,2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Initially, we derive the mild solution for our considered system by using fractional calculus, cosine families, and stochastic analysis. After that, we prove the existence of mild solutions for stochastic evolution inclusions with the Hilfer fractional substantial derivative by using Bohnenblust–Karlin’s fixed point theorem. Subsequently, we determine that the considered system is approximately controllable. Our theoretical findings are finally shown with an example.</p>

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Approximate Controllability Results for Stochastic Evolution Inclusions with Hilfer Fractional Substantial Derivative

  • 期刊论文

  • 发表日期：

    2025年4月18日

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  • K. Nandhaprasadh,
  • R. Udhayakumar

摘要

In this study, we examine the existence and approximate controllability results for stochastic evolution inclusions with the Hilfer fractional substantial derivative of order \(\mu \in (1,2)\) μ ∈ ( 1 , 2 ) . Initially, we derive the mild solution for our considered system by using fractional calculus, cosine families, and stochastic analysis. After that, we prove the existence of mild solutions for stochastic evolution inclusions with the Hilfer fractional substantial derivative by using Bohnenblust–Karlin’s fixed point theorem. Subsequently, we determine that the considered system is approximately controllable. Our theoretical findings are finally shown with an example.