Asymptotic behavior of solutions to fractional stochastic multi-term differential equation systems involving non-permutable matrices

The main theorem (asymptotic separation) in the paper matches the candidate’s claim: for any ε>0 and distinct initial data η≠γ, limsup_{t→∞} t^{α+ε} ||ϕ(t,η)−ϕ(t,γ)||_{ms} = ∞ (Theorem 5.1) . However, the paper’s proof uses (i) a mild formula (3.3) whose kernels require α>β but this condition is nowhere explicitly assumed (the paper says α∈(1/2,1), β∈(0,1) “independent”) , and (ii) a Beta-function calculation with a parameter 1−2λ<0 (since λ>α>1/2), which is not justified because the Beta integral diverges; the argument should instead split the integral at T and estimate directly, as the candidate solution effectively does . The candidate’s proof, based on subtracting the mild formulas, elementary convolution bounds, and Itô isometry, is logically sound under the natural and (in fact) needed condition α>β, and it avoids the paper’s gaps.