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<p>This paper investigates exponential stability and averaging principle the higher-order <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((1&lt; \alpha &lt; 2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>&lt;</mo> <mi>α</mi> <mo>&lt;</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> fractional evolution systems with sectorial operators, time delays, and impulsive effects. First, the existence and uniqueness of mild solutions are established via Schaefer’s fixed point theorem and Grönwall inequality. Schaefer’s fixed point theorem. Next, exponentially stability criteria are derived through suitable assumptions on the associated fractional resolvent families together with an impulsive smallness condition. The averaging principle is then obtained, showing convergence of the original system to its averaged counterpart over finite time intervals as the perturbation parameter tends to zero. Finally, the theoretical results are illustrated through a nontrivial example and numerical simulations based on spectral truncation.</p>

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Stability and averaging principle for impulsive fractional delay evolution systems of order \(1<\alpha <2\)

  • 期刊论文

  • 发表日期：

    2026年7月4日

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  • A. Jalisraj,
  • R. Udhayakumar

摘要

This paper investigates exponential stability and averaging principle the higher-order \((1< \alpha < 2)\) ( 1 < α < 2 ) fractional evolution systems with sectorial operators, time delays, and impulsive effects. First, the existence and uniqueness of mild solutions are established via Schaefer’s fixed point theorem and Grönwall inequality. Schaefer’s fixed point theorem. Next, exponentially stability criteria are derived through suitable assumptions on the associated fractional resolvent families together with an impulsive smallness condition. The averaging principle is then obtained, showing convergence of the original system to its averaged counterpart over finite time intervals as the perturbation parameter tends to zero. Finally, the theoretical results are illustrated through a nontrivial example and numerical simulations based on spectral truncation.