{
  "abstract": "We develop a fractional pseudo-spectral collocation method for steady and time-dependent fractional differential equations on the half-line, which are based on previously introduced generalized rational Jacobi functions (GJRFs). Rational cardinal functions are constructed at mapped Jacobi–Gauss points, yielding explicit nodal differentiation matrices for left-sided Riemann–Liouville and right-sided Weyl operators, including higher-order derivatives. A boundary-adapted second-kind construction enforces the homogeneous condition at the finite endpoint. For the representative left-sided order-μ matrix with 0<μ<1, we make explicit its diagonal equivalence to a Jacobi-weighted fractional Lagrange matrix on [−1,1]; in GJRF modal coordinates, this gives a finite-N factorization, determinant identity, inverse bound, and a conditional consistency-to-solution nodal error estimate. These transferred finite-dimensional structural results do not constitute a uniform-in-N convergence theorem. The method is applied to fractional advection and diffusion equations, multi-term problems, Burgers-type equations, and Schrödinger-type equations with unilateral fractional spatial operators. A Jacobi-parameter sensitivity study shows that matching the basis parameter to the endpoint behavior of the solution is essential for rapid convergence; with this choice, the linear and nonlinear tests exhibit rapid error reduction across the tested fractional orders. Temporal refinement recovers the expected L1 convergence rates, and matched-degree-of-freedom comparisons with GJRF Petrov–Galerkin discretizations are also reported. The results demonstrate the effectiveness of the GJRF collocation framework for the half-line problems considered.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Emtnan E. Al-humaidan"
    },
    {
      "affs": [
        0
      ],
      "name": "Saleh F. Aljurbua"
    },
    {
      "affs": [
        0
      ],
      "name": "Tarek Aboelenen",
      "orcid": "0000-0003-3332-7950"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7t54yck5gjsq.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10110754",
  "fulltext_url": null,
  "id": "b7t54yck5gjsq",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/11/754",
  "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": "W7224131514",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/b7t54yck5gjsq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:32Z",
      "native_id": "10.3390/fractalfract10110754",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/11/754"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2504-3110",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fractional Spectral Collocation with Generalized Rational Jacobi Functions on the Half-Line",
  "title_text": "Fractional Spectral Collocation with Generalized Rational Jacobi Functions on the Half-Line",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:32Z",
  "url": "https://research.draconitic.com/paper/b7t54yck5gjsq",
  "venue": "Fractal and Fractional",
  "versions": []
}