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<p>This work investigates the existence of mild solutions for a fractional stochastic system governed by hemivariational inequalities (HIs) with a history-dependent operator(HDO). By integrating fractional derivatives, the system provides a more detailed and accurate reflection of real-world processes. HIs introduce a non-linear relationship between the state and a multivalued operator. Further, the HDO allows the past states to influence the systems dynamics. Furthermore, controllability properties are explored, determining under what conditions the system can be steered from one state to another within a specified time frame. Ultimately, an illustrative example is given to support our theoretical findings.</p>

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A Note on Approximate Controllability Results for History-Dependent Fractional Stochastic Hemivariational Inequalities

  • 期刊论文

  • 发表日期：

    2025年6月26日

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  • S. Vivek,
  • V. Vijayakumar

摘要

This work investigates the existence of mild solutions for a fractional stochastic system governed by hemivariational inequalities (HIs) with a history-dependent operator(HDO). By integrating fractional derivatives, the system provides a more detailed and accurate reflection of real-world processes. HIs introduce a non-linear relationship between the state and a multivalued operator. Further, the HDO allows the past states to influence the systems dynamics. Furthermore, controllability properties are explored, determining under what conditions the system can be steered from one state to another within a specified time frame. Ultimately, an illustrative example is given to support our theoretical findings.