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A Generalized Neumann Solution for the Two-Phase Fractional Lam\'{e}-Clapeyron-Stefan Problem

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Sabrina D. Roscani, Domingo A. Tarzia

Analysis of PDEs · Submitted 22 May 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We obtain a generalized Neumann solution for the two-phase fractional Lam\'{e}-Clapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions.

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arXiv ID1405.5928 (version 1)
Pith IDPINSAQHA, Pith's permanent record of this paper and its review
CitationDomingo A. Tarzia, Sabrina D. Roscani. "A Generalized Neumann Solution for the Two-Phase Fractional Lam\'{e}-Clapeyron-Stefan Problem." arXiv:1405.5928 (2014). https://pith.science/paper/PINSAQHA
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,019 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.24 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.85 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We obtain a generalized Neumann solution for the two-phase fractional Lam\'{e}-Clapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions. In this problem, the two governing equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order $0<\al\leq 1$. When $ \al \nearrow $ 1 we recover the classical Neumann solution for the two-phase Lam\'{e}-Clapeyron-Stefan problem given through the error function.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We obtain a generalized Neumann solution for the two-phase fractional Lam\'{e}-Clapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions. contribution 0.85 0.96 0.85 asserted 1.00
s1 In this problem, the two governing equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order $0<\al\leq 1$. background 0.86 0.45 0.07 asserted 1.00
s2 When $ \al \nearrow $ 1 we recover the classical Neumann solution for the two-phase Lam\'{e}-Clapeyron-Stefan problem given through the error function. result 0.58 0.74 0.25 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We obtain a generalized Neumann solution for the two-phase fractional Lam\'{e}-Clapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions. In this problem, the two governing equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order $0<\al\leq 1$. When $ \al \nearrow $ 1 we recover the classical Neumann solution for the two-phase Lam\'{e}-Clapeyron-Stefan problem given through the error function.

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