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<p>We establish an averaging principle for Hilfer fractional neutral impulsive stochastic delay differential equations with Lévy noise (small jumps), proving <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1753_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathtt {L^p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="monospace">L</mi> <mi mathvariant="monospace">p</mi> </msup> </math></EquationSource> </InlineEquation> convergence between original and averaged solutions. The analysis combines Lipschitz and growth conditions with key inequalities like Jensen, Burkholder–Davis–Gundy, Hölder, Doob’s martingale, Gronwall–Bellman to handle both deterministic and stochastic jumps. An illustration with numerical simulations validates the theory through probability density comparisons, demonstrating convergence.</p>

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Averaging Principle for Hilfer Fractional Neutral Impulsive Stochastic Delay Differential Equation with \(\mathtt {L^p}\) Convergence Driven by Lévy Noise

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • A. Jalisraj,
  • R. Udhayakumar

摘要

We establish an averaging principle for Hilfer fractional neutral impulsive stochastic delay differential equations with Lévy noise (small jumps), proving \(\mathtt {L^p}\) L p convergence between original and averaged solutions. The analysis combines Lipschitz and growth conditions with key inequalities like Jensen, Burkholder–Davis–Gundy, Hölder, Doob’s martingale, Gronwall–Bellman to handle both deterministic and stochastic jumps. An illustration with numerical simulations validates the theory through probability density comparisons, demonstrating convergence.