A Green-function mismatch in a Caputo boundary value application: comments on "Fixed Point Results for Large Contraction Mappings in b-Metric Spaces with Applications to Fractional Differential Equations"
Abstract
This technical note examines the fractional boundary value application in Mesmouli, Abulhamil, Iambor and Hassan, Mathematics 14 (2026), 1991, DOI: 10.3390/math14111991. The displayed Green function has the Riemann–Liouville form rather than the form required by the stated Caputo problem. Constant forcing at order 3/2 satisfies all listed assumptions but yields distinct functions in the differential and integral formulations. The note derives the correct, generally sign-changing Caputo kernel and gives an absolute-kernel contraction repair, distinguishing integral solutions from classical solutions. It also corrects an elementary contraction example and explains a reduction of the stronger fixed-point hypothesis. The bounded-orbit proof of the main theorem is not challenged. Files include the revised PDF and self-contained LaTeX source ZIP.
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BibTeX
@misc{zeraoulia2026greenfunction,
title = {{A Green-function mismatch in a Caputo boundary value application: comments on "Fixed Point Results for Large Contraction Mappings in b-Metric Spaces with Applications to Fractional Differential Equations"}},
author = {Rafik Zeraoulia},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23473939},
url = {https://zenodo.org/records/23473939},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Green-function mismatch in a Caputo boundary value application: comments on "Fixed Point Results for Large Contraction Mappings in b-Metric Spaces with Applications to Fractional Differential Equations"
AU - Rafik Zeraoulia
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23473939
UR - https://zenodo.org/records/23473939
AB - This technical note examines the fractional boundary value application in Mesmouli, Abulhamil, Iambor and Hassan, Mathematics 14 (2026), 1991, DOI: 10.3390/math14111991. The displayed Green function has the Riemann–Liouville form rather than the form required by the stated Caputo problem. Constant forcing at order 3/2 satisfies all listed assumptions but yields distinct functions in the differential and integral formulations. The note derives the correct, generally sign-changing Caputo kernel and gives an absolute-kernel contraction repair, distinguishing integral solutions from classical solutions. It also corrects an elementary contraction example and explains a reduction of the stronger fixed-point hypothesis. The bounded-orbit proof of the main theorem is not challenged. Files include the revised PDF and self-contained LaTeX source ZIP.
ER -