Impulsive stochastic fractional integro-differential equations with delay and weakly singular kernels in Banach spaces

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Abstract

This paper studies the existence of mild solutions for impulsive stochastic fractional integro-differential equations with finite delay and weakly singular kernels in separable Banach spaces. The model involves a Caputo derivative of order α ∈ (¹₂, 1), a cylindrical Wiener process, instantaneous impulses, and a singular kernel (t − s)^−β with β ∈ (0, 1 − α). To the best of our knowledge, the combined presence of impulsive effects, stochastic noise, finite delay, and weakly singular kernels has not yet been analyzed in the literature within a Caputo fractional framework in Banach spaces of type 2. Using resolvent families, Itô calculus in Banach spaces, and Krasnoselskii’s fixed point theorem, we establish the existence of mean-square mild solutions under natural growth and continuity assumptions. An example illustrates the applicability of the results.

Keywords

stochastic fractional differential equations / impulsive effects / weakly singular kernels / delay / mild solutions / Caputo derivative / cylindrical Wiener process / Krasnoselskii fixed point theorem

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