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<p>This manuscript explores the stability of impulses driven by Poisson jumps within fractional stochastic integro-differential delay systems <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {FSIDDS}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">FSIDDS</mi> </math></EquationSource> </InlineEquation>s. Employing tools from fractional calculus, stochastic analysis, semigroup theory, and the Mönch fixed point theorem in infinite-dimensional spaces, we establish sufficient conditions for the existence of a mild solution to a class of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {FSIDDS}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">FSIDDS</mi> </math></EquationSource> </InlineEquation>s subject to impulsive effects. The Mönch fixed point theorem is particularly instrumental due to its association with the Hausdorff measure of noncompactness <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {HMNC}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">HMNC</mi> </math></EquationSource> </InlineEquation>, which facilitates the verification of relative compactness. To demonstrate the applicability of the theoretical findings, a representative example is presented.</p>

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New Results on Dynamical Systems with Impulsive Fractional Stochastic Integro-Differential Delay Conditions

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • R. Pradeepa,
  • M. Sathish Kumar,
  • R. Jayaraman

摘要

This manuscript explores the stability of impulses driven by Poisson jumps within fractional stochastic integro-differential delay systems \(\mathcal {FSIDDS}\) FSIDDS s. Employing tools from fractional calculus, stochastic analysis, semigroup theory, and the Mönch fixed point theorem in infinite-dimensional spaces, we establish sufficient conditions for the existence of a mild solution to a class of \(\mathcal {FSIDDS}\) FSIDDS s subject to impulsive effects. The Mönch fixed point theorem is particularly instrumental due to its association with the Hausdorff measure of noncompactness \(\mathcal {HMNC}\) HMNC , which facilitates the verification of relative compactness. To demonstrate the applicability of the theoretical findings, a representative example is presented.