{
  "abstract": "Accurate evaluation of the Caputo fractional derivative (CFD) of arbitrary non-integer order is essential for modeling memory-dependent phenomena. However, the classical Shifted Gegenbauer Pseudospectral (SGPS) method attains exponential convergence only on a zero-measure set of the fractional order parameter; for all other orders, the transformed integrand exhibits reduced endpoint regularity, limiting quadrature convergence to algebraic rates. We introduce a ϕ-generalized algebraic transformation that enforces Cr endpoint regularity for any prescribed integer r>0, and establish a convergence hierarchy for the interpolation-induced truncation error (ITE) across analytic, Gevrey, C∞, and finitely smooth data. For data analytic in a disc around the evaluation point, the transformed integrand has a convergent fractional power series with geometrically decaying coefficients, which explains the fast pre-asymptotic quadrature convergence observed numerically. Precomputable weighted Fractional Shifted Gegenbauer Integration Matrices (FSGIMs), assembled by a batched formulation, reduce each online evaluation to one O(Mn) matrix–vector product whose cost does not depend on the history length, apart from the retained sample buffer. Double-precision MATLAB benchmarks give excellent accuracies for problems with known solutions and improve on several finite-difference, diffusive-representation, and adaptive-quadrature baselines by orders of magnitude. Microsecond-scale latency on a Cortex-M4-class microcontroller is projected from operation counts and desktop timings; it has not been measured on hardware. A two-cycle NASA battery case study illustrates the feasibility of CFD-based State-of-Health features.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates",
    "Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Kareem T. Elgindy",
      "orcid": "0000-0001-7369-4988"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/evj1rccvka2ww.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10110752",
  "fulltext_url": null,
  "id": "evj1rccvka2ww",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/11/752",
  "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": "W7224125182",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/evj1rccvka2ww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:32Z",
      "native_id": "10.3390/fractalfract10110752",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/11/752"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2504-3110",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Offline–Online Decoupled Architecture for Projected Microsecond-Latency and near Machine-Precision Caputo Fractional Derivative Evaluation, with an Edge-Computing Feasibility Study",
  "title_text": "Offline–Online Decoupled Architecture for Projected Microsecond-Latency and near Machine-Precision Caputo Fractional Derivative Evaluation, with an Edge-Computing Feasibility Study",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:32Z",
  "url": "https://research.draconitic.com/paper/evj1rccvka2ww",
  "venue": "Fractal and Fractional",
  "versions": []
}