@article{Mesri2026, 
author = {Fatima Mesri and Abdelkrim Salim and Mouffak Benchohra},
title = {Impulsive stochastic fractional integro-differential equations with delay and weakly singular kernels in Banach spaces},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {3},
pages = {1900-1916},
keywords = {stochastic fractional differential equations, impulsive effects, weakly singular kernels, delay, mild solutions, Caputo derivative, cylindrical Wiener process, Krasnoselskii fixed point theorem},
url = {https://www.sciopen.com/article/10.3934/era.2026085},
doi = {10.3934/era.2026085},
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  ∈  (            1      2        ,  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.}
}