{
  "abstract": "In this work, we investigate the Ulam–Hyers stability and generalized Ulam–Hyers stability for a class of hybrid differential equations involving both proportional fractional derivatives and classical derivatives, coupled with the μ-Laplacian operator and subject to fractional integral boundary conditions. Building upon recent existence results for this class of equations, we establish sufficient conditions under which solutions exhibit Ulam–Hyers stability. The analysis relies on nonlinear analysis techniques and properties of the μ-Laplacian operator. Two illustrative examples are provided: one for classical Ulam–Hyers stability and another for uniform stability under a variable perturbation described by a power-type control function.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Mathematics and Computer Science, Ibn Khaldoun University of Tiaret, Tiaret, 14000, Algeria",
    "Department of Mathematics, College of Science, University of Hail, Ha’il55473, Saudi Arabia",
    "Department of Mathematics, Faculty of Sciences, King Khalid University, PO Box 9004, Abha, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Maazouz Kadda"
    },
    {
      "affs": [
        0
      ],
      "name": "Ouardani Abderrahmane"
    },
    {
      "affs": [
        0
      ],
      "name": "Bechayeb Rabah"
    },
    {
      "affs": [
        1
      ],
      "name": "Moumen Abdelkader"
    },
    {
      "affs": [
        2
      ],
      "name": "Bouye Mohamed"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78ac7zhfq29he.bib",
  "cited_by": 0,
  "doi": "10.1515/math-2025-0296",
  "fulltext_url": "https://doi.org/10.1515/math-2025-0296",
  "id": "78ac7zhfq29he",
  "issns": [
    "2391-5455"
  ],
  "landing_url": "https://doi.org/10.1515/math-2025-0296",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ],
    [
      "openalex",
      "2604|Nonlinear Differential Equations Analysis"
    ]
  ],
  "openalex": "W7223208303",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": "De Gruyter",
  "ris": "https://research.draconitic.com/paper/78ac7zhfq29he.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:47:23Z",
      "native_id": "b526b4b96b4648d1a25473a4ef822344",
      "source": "doaj",
      "url": "https://doi.org/10.1515/math-2025-0296"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Nonlinear Differential Equations Analysis",
      "subfield": "general"
    }
  ],
  "title": "Ulam–Hyers stability for hybrid differential equations with mixed fractional derivatives and the μ-Laplacian operator",
  "title_text": "Ulam–Hyers stability for hybrid differential equations with mixed fractional derivatives and the μ-Laplacian operator",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:47:23Z",
  "url": "https://research.draconitic.com/paper/78ac7zhfq29he",
  "venue": "Open Mathematics",
  "versions": []
}