{
  "abstract": "The first criterion of convexity states that a differentiable function defined on an open interval is convex if and only if its first derivative is increasing. The second criterion of convexity states that a twice differential function is convex if and only if its second derivative is positive. In this work, by using a change of variable transforming the interval $[a,t]$ into $[0,1]$, we are able to get a new formulation of Caputo derivative. Then, we use this new version of Caputo derivative to investigate convexity and obtain generalizations to the first and second criteria of convexity depending on fractional orders $0<\\alpha<1$ and $1<\\alpha<2$, respectively. As a further application of the new representation of the Caputo derivative $(D_a^\\alpha f)(x)$ of a function $f$ defined on an interval $[a,b]$ and of order $n-1<\\alpha",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Mousaab Bouafia"
    },
    {
      "name": "Adnan Yassine"
    },
    {
      "name": "Thabet Abdeljawad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7t8eksafx3by5.bib",
  "cited_by": 0,
  "doi": "10.1051/ro/2026080",
  "fulltext_url": null,
  "id": "7t8eksafx3by5",
  "issns": [
    "0399-0559",
    "1290-3868"
  ],
  "landing_url": "https://hal.science/hal-05692615v1",
  "language": "en",
  "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": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7167979707",
  "pdf_url": "https://hal.science/hal-05692615/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": "EDP Sciences",
  "ris": "https://research.draconitic.com/paper/7t8eksafx3by5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:34Z",
      "native_id": "hal-05692615",
      "source": "hal",
      "url": "https://hal.science/hal-05692615v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Convexity in terms of Caputo fractional derivatives",
  "title_text": "Convexity in terms of Caputo fractional derivatives",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/7t8eksafx3by5",
  "venue": "RAIRO - Operations Research",
  "versions": []
}