Stability Analysis of Short Memory Fractional Differential Equations

The paper’s Theorem 4 proves Lyapunov asymptotic stability for short‑memory fractional systems via a rigorous comparison with a Caputo fractional delay equation and requires λ > 1/(ω^α Γ(1−α)) (proof uses a> b stability for the delay system) . The candidate solution pivots on an unsubstantiated key inequality claiming a lower bound on the short‑memory Caputo integral that would yield a window‑to‑window contraction V(t) ≤ q V(t−ω). That bound is not given in the paper and is generally false without extra monotonicity/variation assumptions on V′. Consequently, the contraction step and the stronger claim that any λ>0 suffices are not justified. The paper’s sufficient condition and proof are sound (via Theorem 3’s comparison result) .