We examine the stochastic parabolic integral equation of convolution type (Equation) where U(t) takes values in Lq(O; ℝ) with O a σ-finite measure space, and q ∈ [2,∞). The linear operator A maps D(A) ⊂ Lq(O; ℝ) into Lq(O;ℝ), is nonnegative and admits a bounded H∞-calculus on Lq(O; ℝ). The kernels are powers of t, with k1(t) = 1/Γ(α)t α-1, k2(t) = 1/Γ(β)tβ-1, and α ∈ (0, 2), β ∈(1/2,2). We show ... [Show full abstract] that, in the maximal regularity case, where - β- αθ -η = 1/2, one has the estimate (Equation) where c is independent of G. Here θ ∈ (0,1) and Dηt denotes fractional integration if η∈ (-1,0), and fractional differentiation if η∈ (0,1), both with respect to the t-variable. The proof relies on recent work on stochastic differential equations by van Neerven, Veraar and Weis, and extends their maximal regularity result to the integral equation case.