2406.15114
Approximate Controllability of Linear Fractional Impulsive Evolution Equations in Hilbert Spaces
Javad A. Asadzade, Nazim I. Mahmudov
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper states the right equivalences but leaves key implications as assertions (e.g., (i)⇔(iii), (iv)⇔(v)) and mis-defines approximate controllability as Im M = H before using density, while the candidate solution supplies the missing Hilbert-space arguments (MM* identity, duality Ran(M)⊥ = Ker(M*), and the spectral-theorem limit ε(εI+T)^{-1} → P_{Ker T}) and clarifies the definition.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The main claims are aligned with standard Hilbert-space controllability theory adapted to fractional impulsive systems, but the proof of the central equivalences is incomplete and relies on unproved 'standard' facts. There is also a definitional inconsistency (Im M = H vs density). With corrected definition and inclusion of the missing duality and spectral-theorem arguments, the paper would be a sound, self-contained contribution for specialists.