aspg-33-4473-1792223309 20261017074829 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2026 13 2 Takaaki Fujita Independent Researcher, Tokyo, Japan Ajoy Kanti Das Department of Mathematics, Tripura University, Agartala-799022, Tripura, India Suman Das Department of Education, National Institute of Technology Calicut, Kozhikode-673601, Kerala, India Sankar Prasad Mondal Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata-741249, West Bengal, India A neutrosophic set assigns to each element three (generally independent) degrees: truth, indeterminacy, and falsity. A q-fractional fuzzy set assigns membership and nonmembership degrees in [0,1] to each element, constrained by (μ +ν)/q ≤ 1 for q ≥ 2. A q-fractional fuzzy graph is a graph whose vertices and edges carry q-fractional fuzzy degrees, with edge membership bounded by endpoints and edge nonmembership dominating them. In this paper, we introduce q-fractional neutrosophic sets and graphs as an extension of q-fractional fuzzy sets and q-fractional fuzzy graphs, and we investigate their fundamental properties. 2026 17 24 4473 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.130204 https://americaspg.com/journal/33/article/4473 https://americaspg.com/storage/articles/manuscripts/01KYND01F2XE4WWTQM69Q50K0W.pdf