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Fourier Series in Fractional Dimensional Space

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Ali Dorostkar, Ahmad Sabihi

General Mathematics · Submitted 1 Dec 2022

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

The authors' main claim It is also shown that the fractional derivative of a periodic function can be realized through (fractional) Fourier series with modified coefficients.

how it is stated · asserted 1.00 read the record →

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arXiv ID2212.00049 (version 1)
Pith IDWOCFECY3, Pith's permanent record of this paper and its review
CitationAhmad Sabihi, Ali Dorostkar. "Fourier Series in Fractional Dimensional Space." arXiv:2212.00049 (2022). https://pith.science/paper/WOCFECY3
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,519 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. We call it fractional Fourier series of the order $\alpha$. Extending the basis functions of the linear space into fractional one, by rotation transformation, we define a real and complex Fourier series and obtain their coefficients. It is also shown that the fractional derivative of a periodic function can be realized through (fractional) Fourier series with modified coefficients.

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 In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. contribution 1.00 0.92 0.17 asserted 1.00
s1 We call it fractional Fourier series of the order $\alpha$. contribution 0.93 0.85 0.07 asserted 0.97
s2 Extending the basis functions of the linear space into fractional one, by rotation transformation, we define a real and complex Fourier series and obtain their coefficients. method 0.96 0.92 0.13 asserted 1.00
s3 It is also shown that the fractional derivative of a periodic function can be realized through (fractional) Fourier series with modified coefficients. result 0.92 0.88 0.32 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.78 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. We call it fractional Fourier series of the order $\alpha$. Extending the basis functions of the linear space into fractional one, by rotation transformation, we define a real and complex Fourier series and obtain their coefficients. It is also shown that the fractional derivative of a periodic function can be realized through (fractional) Fourier series with modified coefficients.

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