{
  "abstract": "Convex analysis and mathematical inequalities play a fundamental role in both pure and applied sciences. In this work, we first explore the notion of n-fractional polynomial s-like m-convexity involving Raina’s mapping and also its algebraic properties. We then introduce a novel Hermite–Hadamard (H-H), midpoint H-H, trapezoid H-H type inequalities based on this generalized concept and the k-fractional operator. Several related corollaries and examples are examined, particularly in connection with the Mittag–Leffler function. The practical utility of the proposed inequalities is demonstrated through applications to viscoelastic materials with fractional damping, supported by computational algorithms, and a numerical example involving fractional diffusion in fractured media. The results provide meaningful refinements and novel insights that extend and enrich existing research in the field.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics , Capt Waqar Kakar Shaheed Balochistan Residential College , Loralai , 84800 , Balochistan , Pakistan",
    "Mathematics Research Center , Near East University , Near East Boulevard , PC: 99138 , Nicosia / Mersin 10 , Turkey",
    "Department of Basic Sciences and Related Studies , Mehran UET , Jamshoro , Sindh , Pakistan",
    "Abdus Salam School of Mathematical Sciences , GC University , Lahore 54600 , Pakistan",
    "Center for Theoretical Physics , Khazar University , 41 Mehseti Str. , Baku , AZ1096 , Azerbaijan",
    "National Institute for Theoretical and Computational Sciences (NITheCS) , South Africa",
    "Sefako Makgatho Health Sciences University , Garankuwa , Medusa , 0204 , South Africa",
    "Baku Engineering University , Scientific Research Centre , H.Aliyev , 120 , Baku , AZ0101 , Azerbaijan"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "name": "Hijaz Ahmad",
      "orcid": "0000-0002-5438-5407"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Muhammad Usman Tariq"
    },
    {
      "affs": [
        2
      ],
      "name": "Ali Asghar"
    },
    {
      "affs": [
        3,
        4
      ],
      "name": "Waqar Afzal",
      "orcid": "0000-0001-7879-1920"
    },
    {
      "affs": [
        5,
        6
      ],
      "name": "Maggie Aphane",
      "orcid": "0000-0002-9640-7846"
    },
    {
      "affs": [
        7
      ],
      "name": "Rakib Efendiev",
      "orcid": "0000-0001-9864-5410"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8714a5n7zz5w.bib",
  "cited_by": 12,
  "doi": "10.28924/2291-8639-24-2026-175",
  "fulltext_url": null,
  "id": "e8714a5n7zz5w",
  "issns": [
    "2291-8639"
  ],
  "landing_url": "https://doi.org/10.28924/2291-8639-24-2026-175",
  "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": [
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7162801834",
  "pdf_url": "https://etamaths.com/index.php/ijaa/article/download/5118/1753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-29",
  "publisher": "Etamaths Publishing",
  "ris": "https://research.draconitic.com/paper/e8714a5n7zz5w.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:20:59Z",
      "native_id": "W7162801834",
      "source": "openalex",
      "url": "https://doi.org/10.28924/2291-8639-24-2026-175"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Mathematical Inequalities and Applications",
      "subfield": "general"
    }
  ],
  "title": "Some New Notions of Mathematical Integral Inequalities: Theory and Applications",
  "title_text": "Some New Notions of Mathematical Integral Inequalities: Theory and Applications",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/e8714a5n7zz5w",
  "venue": "International Journal of Analysis and Applications",
  "versions": []
}