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<p>In this paper, we investigate the asymptotic stability of Hilfer fractional neutral stochastic differential equations driven by mixed fractional Brownian motion featuring time-varying delays and non-instantaneous impulses. Through combining resolvent operator theory, Banach fixed point theorem, and stochastic analysis techniques, we establish the existence and uniqueness of mild solution, the characterization of globally attracting sets and quasi-invariant sets properties, sufficient conditions for <i>p</i>-th moment exponential stability and almost sure exponential stability. Finally, an example is presented to illustrate our theory results.</p>

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Asymptotic stability of Hilfer fractional neutral stochastic differential equations with time-varying delays and non-instantaneous impulses

  • 期刊论文

  • 发表日期：

    2025年5月25日

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  • Xinhai Xiao,
  • Jingli Xie

摘要

In this paper, we investigate the asymptotic stability of Hilfer fractional neutral stochastic differential equations driven by mixed fractional Brownian motion featuring time-varying delays and non-instantaneous impulses. Through combining resolvent operator theory, Banach fixed point theorem, and stochastic analysis techniques, we establish the existence and uniqueness of mild solution, the characterization of globally attracting sets and quasi-invariant sets properties, sufficient conditions for p-th moment exponential stability and almost sure exponential stability. Finally, an example is presented to illustrate our theory results.