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<p>This paper explores the optimal control results for generalized Riemann-Liouville (Hilfer) fractional Volterra-Fredholm integrodifferential systems of order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1733_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta \in (1,2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> under nonlocal conditions. First, the existence and uniqueness of mild solutions for the system are shown using the cosine family of operators and the Banach fixed point theorem. Then, the existence of an optimal control for the system is demonstrated. Finally, an example is provided to illustrate the obtained results.</p>

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Investigation of optimal control results for generalized Riemann-Liouville fractional integrodifferential systems of Volterra-Fredholm type with nonlocal initial conditions

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • M. Johnson,
  • V. Vijayakumar,
  • Kiwoon Kwon

摘要

This paper explores the optimal control results for generalized Riemann-Liouville (Hilfer) fractional Volterra-Fredholm integrodifferential systems of order \(\eta \in (1,2)\) η ∈ ( 1 , 2 ) under nonlocal conditions. First, the existence and uniqueness of mild solutions for the system are shown using the cosine family of operators and the Banach fixed point theorem. Then, the existence of an optimal control for the system is demonstrated. Finally, an example is provided to illustrate the obtained results.