{
  "abstract": "In this paper, we study the problem D0+αu+f(t,u)=0 on (0,1), u(0)=0, D0+α−1u(1)=∫01u dA, where 1<α≤2 and the measure dA may change sign. For a measure made of two point masses of opposite sign, we show that the function KA(s)=∫01G(τ,s) dA(τ), through which dA enters the Green function, is nonnegative exactly when the positive weight is at least θ∗ times the size of the negative one, where θ∗ is given in closed form. Together with a simple condition Δ>0, this makes the Green function nonnegative. The threshold θ∗ decreases in α and tends to infinity as α→1+. For α<2 the Green function has no uniform Harnack estimate, so we work in a cone weighted by Ψ(t)=∫01G(t,s) ds, where Schauder’s theorem gives a positive solution with explicit bounds whenever f lies between two positive constants. For the omitted ray fixed point theorem of Avery, Henderson and Liu, we describe exactly when its key inequality holds for the two-point functional used here, and we show that the hypotheses under which we can verify it already imply the classical inward condition. Examples with α=3/2 and α=1.08 illustrate the results.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Vignan’s Institute of Information Technology (Autonomous), Visakhapatnam 530049, Andhra Pradesh, India",
    "School of Sciences, Woxsen University, Hyderabad 500033, Telangana, India",
    "Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Mahammad Khuddush",
      "orcid": "0000-0002-1236-8334"
    },
    {
      "affs": [
        2
      ],
      "name": "Saleh S. Almuthaybiri",
      "orcid": "0000-0002-9399-3253"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czw724xzq18m0.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10100716",
  "fulltext_url": null,
  "id": "czw724xzq18m0",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/10/716",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Nonlinear Differential Equations Analysis"
    ]
  ],
  "openalex": "W7221708495",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/czw724xzq18m0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:32Z",
      "native_id": "10.3390/fractalfract10100716",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/10/716"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2504-3110",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Positive Solutions of a Fractional BVP and the Reach of the Omitted Ray Fixed Point Theorem",
  "title_text": "Positive Solutions of a Fractional BVP and the Reach of the Omitted Ray Fixed Point Theorem",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:32Z",
  "url": "https://research.draconitic.com/paper/czw724xzq18m0",
  "venue": "Fractal and Fractional",
  "versions": []
}