On algebraic consistency, stability estimates, and Lyapunov diagnostics in a fractional convection–diffusion discretization

This independent technical comment examines the internal consistency of the numerical and dynamical analysis of the time–space fractional convection–diffusion equation studied by Lizama, Yousif, Qadir, Baleanu, and Mohammed (2026), DOI: 10.36922/IJOCTA026350230. It identifies an algebraic mismatch between Eqs. (9) and (10), an incorrect L1 history-weight identity, a false integration-by-parts equality, a reversed inequality in the convergence proof, and a missing derivation of the announced planar system. It gives a harmonic-oscillator counterexample to a Jacobian-only QR procedure and recalculates selected convergence orders. Further checks concern spatial nonlocality, norm compatibility, and manufactured boundary data. The findings concern published derivations; they neither refute all possible corrected schemes nor independently reproduce the original computational experiments. Independent technical-comment preprint, revised working manuscript dated 7 November 2026; not a journal-issued corrigendum. Files: seven-page PDF and Overleaf ZIP containing matching PDF, LaTeX source, independent Python verification script, and README. Author: Rafik Zeraoulia. Affiliations: Department of Mathematics, Faculty of Matter Sciences and Computer Science, University of Djilali Bounaama Khemis Miliana, Khemis Miliana, Algeria; Laboratory of Pure and Applied Mathematics, Amar Teledji University, Laghouat, Algeria. Funding: No external funding. Competing interests: None declared. AI-assisted work disclosure: An OpenAI language model was used for English improvement and numerical checks, and assisted with drafting and mathematical analysis, including development of counterexamples and draft arguments. The author bears full responsibility for the construction and verification of counterexamples, lemmas and propositions, all proofs and conclusions, and the final wording and mathematical correctness of the manuscript.