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<p>The main goal of this work is to analyze the optimal feedback control for a class of Sobolev-type fractional integrodifferential systems of Volterra-type of order <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2558_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(1 &lt; \mu &lt; 2\)</EquationSource> </InlineEquation> in Caputo sense. The analysis begins by establishing the existence results under sufficient conditions such as cosine operator families and a fixed-point theorem. Then, we utilize the Cesari property and Filippov theorem to formulate a set of conditions ensuring the existence of feasible pairs for the system. Moreover, the study extends on establishing optimal feedback control pairs which offers a comprehensive perspective on control strategies. Finally, a theoretical example is established to validate the main results.</p>

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New results concerning to optimal feedback control for Sobolev-type fractional integrodifferential systems of order \(1 < \mu < 2\)

  • 期刊论文

  • 发表日期：

    2025年6月22日

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  • A. Dhanush,
  • V. Vijayakumar

摘要

The main goal of this work is to analyze the optimal feedback control for a class of Sobolev-type fractional integrodifferential systems of Volterra-type of order \(1 < \mu < 2\) in Caputo sense. The analysis begins by establishing the existence results under sufficient conditions such as cosine operator families and a fixed-point theorem. Then, we utilize the Cesari property and Filippov theorem to formulate a set of conditions ensuring the existence of feasible pairs for the system. Moreover, the study extends on establishing optimal feedback control pairs which offers a comprehensive perspective on control strategies. Finally, a theoretical example is established to validate the main results.