{
  "abstract": "Caputo fractional derivatives describe causal power-law memory, whereas the fractional Fourier transform represents continuous rotations in the time–frequency plane. This study derives an Abel–Gaussian-regularized coupling for endpoint-compatible causal signals. Unlike a direct composition of the two operators, the coupling is induced by embedding the causal Caputo convolution into a chirp-conjugated fractional convolution compatible with the adopted transform phase convention. Evaluation of the two transform branches shows that their quadratic phases cancel the additional convolution phase. On a compactly supported smooth core, removal of the regularization yields a rotation–memory–rotation factorization in which the fractional-memory multiplier acts at the ordinary Fourier node and the outer rotation maps the weighted spectrum to the prescribed fractional domain. At the discrete level, modulo-four reduction of the transform order is kept separate from decomposition of the derivative order, while a one-sided Grünwald–Letnikov approximation preserves causal history accumulation. Numerical experiments confirm fixed-spectral rotation identities and forward–inverse reconstruction at double-precision roundoff, approximately first-order convergence to an analytic Caputo reference, and decreasing low-frequency discrepancies under grid refinement. Further tests distinguish the effects of the sampling interval, observation length, fractional order, and nonzero endpoint traces. Exact boundary-term retention preserves the finite record, whereas compatible tapering produces a modified surrogate. For the tested dense implementations, the spectral implementation is faster than the direct full-history Grünwald–Letnikov implementation, while the shared dense operators dominate the storage requirements.",
  "abstract_shown": true,
  "affiliations": [
    "Yantai Research Institute, Harbin Engineering University, Yantai 264000, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Xiao Sun",
      "orcid": "0009-0008-1576-507X"
    },
    {
      "affs": [
        0
      ],
      "name": "Yi Fan"
    },
    {
      "affs": [
        0
      ],
      "name": "Yanyan Wang"
    },
    {
      "affs": [
        0
      ],
      "name": "Haitao Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4atxqn29yhz92.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10100684",
  "fulltext_url": "https://www.mdpi.com/2504-3110/10/10/684",
  "id": "4atxqn29yhz92",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/10/684",
  "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": [
    [
      "lcc",
      "QA1-939"
    ],
    [
      "lcc",
      "QA299.6-433"
    ],
    [
      "lcc",
      "QC310.15-319"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7214931910",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/4atxqn29yhz92.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:32Z",
      "native_id": "10.3390/fractalfract10100684",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/10/684"
    },
    {
      "first_seen": "2026-10-31T14:21:29Z",
      "native_id": "07da8e004a4d4f218cca48cba47e5ae5",
      "source": "doaj",
      "url": "https://doi.org/10.3390/fractalfract10100684"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2504-3110",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "lcc:QC310.15-319",
      "subfield": "general"
    }
  ],
  "title": "Caputo–FRFT Coupling Induced by Compatible Fractional Convolution: Representation and Discrete Realization",
  "title_text": "Caputo–FRFT Coupling Induced by Compatible Fractional Convolution: Representation and Discrete Realization",
  "type": "peer-reviewed",
  "updated_at": "2026-10-31T14:21:29Z",
  "url": "https://research.draconitic.com/paper/4atxqn29yhz92",
  "venue": "Fractal and Fractional",
  "versions": []
}