{
  "abstract": "We propose a hybrid numerical framework combining a redefined quintic B-spline collocation method with a Physics-Informed Neural Network (PINN) correction layer for solving nonlinear space-time fractional advection-diffusion-reaction equations. The spatial fractional derivative is discretised via a shifted Grünwald–Letnikov approximation embedded in the B-spline basis, achieving high-order spatial accuracy. The temporal Caputo derivative is handled by an L2-1σ Crank–Nicolson scheme surpassing standard methods. A PINN residual corrector suppresses oscillations in high-Péclet-number regimes without mesh refinement. Adaptive time-stepping reduces computational cost by over 60%. Rigorous stability and convergence analysis are provided. Seven benchmark problems confirm the framework outperforms existing quintic B-spline, spectral, and PINN-only methods by one to two orders of magnitude.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Centurion University of Technology and Management, Odisha, India"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Balaji Padhy"
    },
    {
      "affs": [
        0
      ],
      "name": "Prabhu Sankardarshi Mahapatra"
    },
    {
      "affs": [
        0
      ],
      "name": "Tumbanath Samantara",
      "orcid": "0000-0002-0839-8565"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0zab75j4przj2.bib",
  "cited_by": 9,
  "doi": "10.56947/amcs.v35.864",
  "fulltext_url": null,
  "id": "0zab75j4przj2",
  "issns": [
    "2789-7206"
  ],
  "landing_url": "https://doi.org/10.56947/amcs.v35.864",
  "language": "en",
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7169859655",
  "pdf_url": "https://annalsmcs.org/index.php/amcs/article/download/864/260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0zab75j4przj2.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:20:59Z",
      "native_id": "W7169859655",
      "source": "openalex",
      "url": "https://doi.org/10.56947/amcs.v35.864"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2611|Fractional Differential Equations Solutions",
      "subfield": "general"
    }
  ],
  "title": "Adaptive Hybrid B-Spline PINN for Fractional Equations",
  "title_text": "Adaptive Hybrid B-Spline PINN for Fractional Equations",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T13:20:21Z",
  "url": "https://research.draconitic.com/paper/0zab75j4przj2",
  "venue": "Annals of Mathematics and Computer Science",
  "versions": []
}