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This equation can be written in the abstract It\\^o form as $$ \\dd X(t) + \\left (\\int_0^t b(t-s) A X(s) \\, \\dd s \\right) \\, \\dd t = \\dd W^{_Q}(t), t\\in (0,T]; ~ X(0) =X_0\\in H, $$ \\noindent where $W^Q$ is a $Q$-Wiener process on the Hilbert space $H$ and where the time kernel $b$ is the locally integrable potential $t^{\\rho-2}$, $\\rho \\in (1,2)$, or slightly more general. 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