TY  - JOUR
AU  - Mesri, Fatima
AU  - Salim, Abdelkrim
AU  - Benchohra, Mouffak
PY  - 2026
TI  - Impulsive stochastic fractional integro-differential equations with delay and weakly singular kernels in Banach spaces
JO  - Electronic Research Archive
SP  - 1900
EP  - 1916
VL  - 34
IS  - 3
AB  - 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.
UR  - https://doi.org/10.3934/era.2026085
DO  - 10.3934/era.2026085