Counterexamples and corrections concerning a 2025 paper on Ulam stability of a fractional boundary-value problem

Abstract

This independent mathematical comment examines the published formulations in I. Nasrallah, R. Aouafi and S. Kouachi, Mathematics 13 (2025), 157, DOI: 10.3390/math13010157. An explicit example satisfies the printed hypotheses of the uniqueness theorem while admitting infinitely many solutions because the stated Green constant is a signed maximum. A separate zero-residual construction disproves the unrestricted stability definition when approximate solutions need not satisfy the boundary data. The note identifies failed assumptions and arithmetic in the illustrative example, explains an error in perturbing the implicit integral arguments, and proves a corrected conditional sup-norm stability estimate. A sufficient Caputo solution domain, precise quantifier arguments, and an explicit Volterra illustration are provided. The conclusions concern the printed statements and distinguish them from amended results that may be recovered. This is a preprint and independent comment, not an official erratum or an independently peer-reviewed article. The record includes the revised PDF and a ZIP containing LaTeX source, revision notes, and a Python numerical verification script. AI assistance: OpenAI ChatGPT assisted with mathematical analysis, construction and checking of counterexamples, drafting, LaTeX preparation, and numerical verification; the named author is responsible for the final content and its verification.