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 (\tfrac{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.
Citation: Fatima Mesri, Abdelkrim Salim, Mouffak Benchohra. Impulsive stochastic fractional integro-differential equations with delay and weakly singular kernels in Banach spaces[J]. Electronic Research Archive, 2026, 34(3): 1900-1916. doi: 10.3934/era.2026085
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 (\tfrac{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.
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Fatima Mesri, Abdelkrim Salim, Mouffak Benchohra. Impulsive stochastic fractional integro-differential equations with delay and weakly singular kernels in Banach spaces[J]. Electronic Research Archive, 2026, 34(3): 1900-1916. doi: 10.3934/era.2026085
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