Memory-consistent sensitivity and diagnostic corrections for a fractional cardiac APD map: Comments on Bououden et al., JNMA 8 (2026), 368–382

This independent technical comment examines the published diagnostic formulas in Bououden, Houmor, Jarad and Abdelouahab, “Nonlinear Dynamics and Chaos in Fractional-Order Cardiac Action Potential Duration Mapping Model,” Journal of Nonlinear Modeling and Analysis 8(2) (2026), 368–382, DOI 10.12150/jnma.2026.368. It derives the memory-consistent initial-state sensitivity recurrence and demonstrates an explicit two-step discrepancy with the ordinary scalar derivative product. An exact constant-signal example shows divergence of the unnormalised mean-square displacement printed for the 0–1 test. The note also identifies incomplete block selection, corrects a falling-factorial identity typo, and qualifies the periodicity and period-doubling interpretations. Independent computations under an explicitly assumed current-state closure support some reported regimes, including the stability boundary near 308 ms and high correlation-test statistics at two reported chaotic parameter values. These findings concern the published formulas and do not establish that all reported dynamics are false or determine the original authors’ undocumented implementation. The deposit contains the revised manuscript PDF and a ZIP with LaTeX source, Python verification code, runtime metadata, numerical output, and instructions. Checks include finite differences at three step sizes, the integer-order limit, longer runs, and extended precision where supported. This is an independent preprint, not an official journal corrigendum or an independently peer-reviewed publication. AI assistance and author responsibility. AI-assisted tools supported preparation and verification of this note, including English editing and numerical checks. The author is responsible for all mathematical claims, counterexamples, proofs, interpretations, references, and the final text.