{
  "abstract": "We consider a coupled system of Caputo–Katugampola integro–fractional stochastic differential equations with Volterra memory, nonlocal integral boundary conditions, Wiener perturbations, and compensated Poisson jumps. The main purpose is to give a mathematically explicit fixed-point treatment in which the two components are solved simultaneously on a product space. A Green representation is derived directly from the two boundary conditions; this derivation fixes the boundary denominator and the complete Green kernel used in all subsequent estimates. Integral contractors are formulated with a correction operator and a residual modulus. In particular, a cubic nonlinearity is used to show that a coefficient need not be globally Lipschitz on the whole state space in order to satisfy the contractor hypothesis on an invariant ball. The moment order p≥2 is fixed throughout each theorem, so all contractor and contraction constants are explicitly allowed to depend on p. The coupled fixed-point problem is represented by a nonnegative 2×2 matrix Qp and the condition ρ(Qp)<1 is used as the actual contraction condition. Ulam–Hyers stability is obtained from the same matrix by an explicit Neumann-series estimate. For trajectory control we distinguish ordinary predictable finite-energy controls from generalized semimartingale controls; this distinction is necessary because a two-point stochastic boundary-value problem is generally noncausal and an ordinary drift control cannot cancel independent martingale terms pathwise. A numerical experiment based on the same Green representation verifies the contraction criterion, the non-Lipschitz contractor construction, the Ulam–Hyers estimate, and the generalized trajectory-control mechanism. The presentation also records the precise scope of the adaptedness assumption for the stochastic integrals.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye",
    "Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan",
    "Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Muhammad Imran Liaqat",
      "orcid": "0000-0002-5732-9689"
    },
    {
      "affs": [
        2
      ],
      "name": "Abdulaziz Khalid Alsharidi",
      "orcid": "0009-0007-2527-7398"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9s8z937se17t.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100737",
  "fulltext_url": null,
  "id": "e9s8z937se17t",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/737",
  "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",
      "2604|Nonlinear Differential Equations Analysis"
    ]
  ],
  "openalex": "W7215838220",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/e9s8z937se17t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100737",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/737"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Nonlinear Differential Equations Analysis",
      "subfield": "general"
    }
  ],
  "title": "Integral Contraction Approach to Coupled Integro-Fractional Stochastic Differential Systems",
  "title_text": "Integral Contraction Approach to Coupled Integro-Fractional Stochastic Differential Systems",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/e9s8z937se17t",
  "venue": "Axioms",
  "versions": []
}