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<p>This study examined the controllability of mild solutions to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((k,\Phi)\)</EquationSource> </InlineEquation> Hilfer fractional differential equations (HFDE) with initial condition, delay and impulsive condition of non-integer order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(0 &lt; \zeta &lt; 1\)</EquationSource> </InlineEquation>. The noncompactness measures and the Mönch fixed point theorem are used to determine the controllability. To demonstrate the theoretical results, we give an example.</p>

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Controllability results of \((k,\Phi)\) Hilfer fractional differential equations with delay and impulsive conditions

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Balachander Sandhiya,
  • Kulandhaivel Karthikeyan,
  • Meltem Erden Ege,
  • Ozgur Ege,
  • Sina Etemad

摘要

This study examined the controllability of mild solutions to \((k,\Phi)\) Hilfer fractional differential equations (HFDE) with initial condition, delay and impulsive condition of non-integer order \(0 < \zeta < 1\) . The noncompactness measures and the Mönch fixed point theorem are used to determine the controllability. To demonstrate the theoretical results, we give an example.