{
  "abstract": "General fractional derivatives (GFDs) generalize classical fractional operators by considering the specific kernel functions; however, extending this generalization to a multi-layered structure remains unexplored. Here, we propose a systematic analysis of the nth-level GFDs, which extend the framework developed in earlier studies. We begin by revisiting the first- and second-level GFDs, proceeding to explore the properties of general fractional integrals (GFIs) to provide a higher-level mathematical foundation. Subsequently, we examine illustrative examples and establish the first and second fundamental theorems of fractional calculus (FC) within the nth-level setting. The proof of the first fundamental theorem follows the pattern of the lower-level cases, while the second fundamental theorem is verified by deriving an inductive representation for the null-space of associated kernels. Finally, the paper concludes with an analysis of fractional differential equations (FDEs) employing GFDs.",
  "abstract_shown": true,
  "affiliations": [
    "Faculty of Mathematics, K. N. Toosi University of Technology, Tehran 16315-1618, Iran",
    "Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, 48940 Leioa, Bizkaia, Spain"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mina Ghasemi"
    },
    {
      "affs": [
        0
      ],
      "name": "Hashem P. Masiha"
    },
    {
      "affs": [
        1
      ],
      "name": "Manuel De La De La Sen",
      "orcid": "0000-0001-9320-9433"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bp8fg15ygv8w4.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213894",
  "fulltext_url": null,
  "id": "bp8fg15ygv8w4",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3894",
  "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",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7223690521",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/bp8fg15ygv8w4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14213894",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3894"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2611|Fractional Differential Equations Solutions",
      "subfield": "general"
    }
  ],
  "title": "Multi-Level General Fractional Derivatives: Fundamental Theorems and Applications",
  "title_text": "Multi-Level General Fractional Derivatives: Fundamental Theorems and Applications",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/bp8fg15ygv8w4",
  "venue": "Mathematics",
  "versions": []
}