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Impulsive stochastic fractional integro-differential equations with delay and weakly singular kernels in Banach spaces
Electronic Research Archive 2026, 34(3): 1900-1916
Published: 03 March 2026
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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.

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