A singular-forcing obstruction to a claimed Caputo existence theorem: Comments on "Analysis of Coupled G-Caputo Variable-Order Fractional Differential Equations Subject to Nonlocal Integral Boundary Conditions"

This independent mathematical comment examines the weighted-singularity framework in Moumen et al., International Journal of Analysis and Applications 24 (2026), article 286, DOI 10.28924/2291-8639-24-2026-286. Explicit constant-order data satisfy hypotheses (H1)-(H4), yet the associated boundary-corrected integral equation has the zero solution while the ordinary Caputo differential equation has no solution with absolutely continuous first derivative. The exact obstruction is I^(3/2)(t^(-1/2)) = sqrt(pi)*t. A genuinely coupled version with nonzero boundary kernels is included. The note distinguishes the stated continuous-forcing inverse convention from a weighted extension, demonstrates non-single-valuedness of an unrestricted extension, provides a constant-order range characterization, and corrects the interior-interface slope claim. Version 1.2 contains 13 references, including 12 supporting sources cited in the text, with a dedicated verification section and a comparison with the singularity restriction in Webb (2019). The counterexamples are derived explicitly in this note; the references support definitions, identities and the domain analysis. The integral contraction estimates are distinguished from differential existence. The source ZIP includes reproducible numerical checks. This is an independent preprint, not a journal-issued corrigendum.