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<p>This study investigates the regional controllability problem for fractional-order dynamical systems with time-varying delays in the state, employing Caputo’s standard derivative. Initially, we establish regional exact and weak controllability under two distinct scenarios: when the control operator <i>B</i> belongs to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {L}(\mathbb {R}^p,Y)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">L</mi> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>p</mi> </msup> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and when it does not. Moreover, we focus on identifying the control strategy that achieves regional controllability with minimal energy consumption. To validate our findings, we analyze two examples of fractional partial differential systems—the zonal actuator and the pointwise actuator—demonstrating the practical application of our approach.</p>

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REGIONAL CONTROLLABILITY OF FRACTIONAL-ORDER DYNAMICAL SYSTEM WITH TIME VARYING-DELAYS IN THE STATE

  • 期刊论文

  • 发表日期：

    2025年6月13日

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  • Wadii Ghandor,
  • Ahmed Aberqi,
  • Touria Karite

摘要

This study investigates the regional controllability problem for fractional-order dynamical systems with time-varying delays in the state, employing Caputo’s standard derivative. Initially, we establish regional exact and weak controllability under two distinct scenarios: when the control operator B belongs to \(\mathcal {L}(\mathbb {R}^p,Y)\) L ( R p , Y ) and when it does not. Moreover, we focus on identifying the control strategy that achieves regional controllability with minimal energy consumption. To validate our findings, we analyze two examples of fractional partial differential systems—the zonal actuator and the pointwise actuator—demonstrating the practical application of our approach.