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<p>The purpose of this article is to explore the existence results for Hilfer fractional stochastic differential systems of order <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2024_2330_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt;\mu &lt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>μ</mi> <mo>&lt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> with optimal controls in Hilbert spaces. It employs fractional calculus, cosine families, stochastic analysis, and fixed-point methods to demonstrate the main results. The initial focus is on proving the existence of a mild solution using the Banach fixed-point approach. Subsequently, the article outlines the necessary conditions for validating the optimal control in Hilfer fractional stochastic systems. Finally, it includes an example to illustrate the theoretical findings.</p>

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A note concerning the optimal control results for Hilfer fractional stochastic differential equations of order \(1<{\mu }<2\)

  • 期刊论文

  • 发表日期：

    2025年1月4日

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  • J. Pradeesh,
  • Sumati Kumari Panda,
  • V. Vijayakumar,
  • Yong-Ki Ma

摘要

The purpose of this article is to explore the existence results for Hilfer fractional stochastic differential systems of order \(1<\mu <2\) 1 < μ < 2 with optimal controls in Hilbert spaces. It employs fractional calculus, cosine families, stochastic analysis, and fixed-point methods to demonstrate the main results. The initial focus is on proving the existence of a mild solution using the Banach fixed-point approach. Subsequently, the article outlines the necessary conditions for validating the optimal control in Hilfer fractional stochastic systems. Finally, it includes an example to illustrate the theoretical findings.