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<p>This paper investigates a class of periodic problems for fractional evolution equations with piecewise Caputo derivatives and periodic impulses in an ordered Banach space. By constructing the solution operator for the linear periodic problem and employing a monotone iterative technique based on upper and lower solutions, we establish the existence of extremal periodic mild solutions. Our results extend existing conclusions in this field. Finally, two illustrative examples are provided to demonstrate the applicability of the abstract theory.</p>

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Extremal solutions for periodic problems of fractional impulsive evolution equation with piecewise Caputo derivative

  • 期刊论文

  • 发表日期：

    2025年7月5日

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  • Qiang Li,
  • Weili Zhou

摘要

This paper investigates a class of periodic problems for fractional evolution equations with piecewise Caputo derivatives and periodic impulses in an ordered Banach space. By constructing the solution operator for the linear periodic problem and employing a monotone iterative technique based on upper and lower solutions, we establish the existence of extremal periodic mild solutions. Our results extend existing conclusions in this field. Finally, two illustrative examples are provided to demonstrate the applicability of the abstract theory.