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

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 $\alpha \in (\frac{1}{2},1)$, a cylindrical Wiener process, instantaneous impulses, and a singular kernel $(t-s{)}^{-\beta }$ with $\beta \in (0,1-\alpha )$. 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.