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pith:C23T3S4O

pith:2026:C23T3S4OD76DVBBA3DDBIN2F7N

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On the Convergence of a Spline Collocation Method for Nonlinear Fractional Boundary Value Problems with the Riesz-Caputo Operator

Chiara Sorgentone, Enza Pellegrino, Francesca Pitolli

An integral representation establishes existence for nonlinear fractional BVPs with the Riesz-Caputo operator, and a B-spline collocation method approximates their solutions with proven convergence.

arxiv:2605.16102 v1 · 2026-05-15 · math.NA · cs.NA

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Claims

C1strongest claim

We provide an integral representation of the solution to prove existence and uniqueness of the fractional differential problem. We introduce a B-spline collocation method to approximate the solution of the problem and provide a convergence analysis, with both theoretical insights and numerical experiments.

C2weakest assumption

The nonlinearity in the fractional BVP satisfies conditions (such as continuity or Lipschitz properties) that allow the integral representation to establish existence and uniqueness, as invoked to support the subsequent collocation analysis.

C3one line summary

A B-spline collocation method with convergence analysis is introduced for nonlinear fractional BVPs involving the Riesz-Caputo operator.

References

27 extracted · 27 resolved · 0 Pith anchors

[1] Fractional variational calculus in terms of Riesz fractional derivatives.Jour- nal of Physics A: Mathematical and Theoretical, 40, 6287, 2007 2007

[2] Baleanu, D.; Diethelm, K.; Scalas, E.; Trujillo, J.J.Fractional Calculus: Models and Numerical Methods.World Scientific, Singapore, 2016 2016

[3] Brunner, H; Pedas, A; Vainikko ,G.Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels.SIAM J. Numer. Anal. 39, pp. 957-982, 2001 2001

[4] de Boor, C.A practical guide to splines.Springer-Verlag, 1978 1978

[5] Diethelm, K.The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type.Springer Science & Business Media, 2010 2010

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:52.719252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16b73dcb8e1ffc3a8420d8c6143745fb741bb39a5828c409be74a180d4fee23b

Aliases

arxiv: 2605.16102 · arxiv_version: 2605.16102v1 · doi: 10.48550/arxiv.2605.16102 · pith_short_12: C23T3S4OD76D · pith_short_16: C23T3S4OD76DVBBA · pith_short_8: C23T3S4O

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/C23T3S4OD76DVBBA3DDBIN2F7N \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 16b73dcb8e1ffc3a8420d8c6143745fb741bb39a5828c409be74a180d4fee23b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2644d8facfa177cbc00050642227fdfe901c9e9bec45adf3bdbdbeffae929405",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-15T15:54:29Z",
    "title_canon_sha256": "f84220401c658163beec4dbbcea57c82efb22429db5fc3d46b50fc5f61cfb44b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16102",
    "kind": "arxiv",
    "version": 1
  }
}