A new fractional derivative of variable order with non-singular kernel and fractional differential equations

E. Capelas de Oliveira; J. Vanterler da C. Sousa

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A new fractional derivative of variable order with non-singular kernel and fractional differential equations

J. Vanterler da C. Sousa, E. Capelas de Oliveira

Classical Analysis and ODEs · Submitted 18 Dec 2017

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

The authors' main claim In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations.

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arXiv ID1712.06506 (version 1)

Pith IDCDQVTBKP, Pith's permanent record of this paper and its review

CitationE. Capelas de Oliveira, J. Vanterler da C. Sousa. "A new fractional derivative of variable order with non-singular kernel and fractional differential equations." arXiv:1712.06506 (2017). https://pith.science/paper/CDQVTBKP

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,288 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of continuous functions, in particular the Comparison's principle, and others that allow, the study of the limitation of fractional nonlinear differential equations.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations.	contribution 1.00	0.96	0.39	asserted 1.00
s1	We present some important results of uniformly convergent sequences of continuous functions, in particular the Comparison's principle, and others that allow, the study of the limitation of fractional nonlinear differential equations.	contribution 0.74	0.83	0.19	asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.80 · evidence from proof or derivation 1.00.

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arXiv listing abstract v1

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full text
figures and tables
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S sections
T body sentences
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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, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of continuous functions, in particular the Comparison's principle, and others that allow, the study of the limitation of fractional nonlinear differential equations.

Human review

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

It is shown for some selected classes of functions that a necessary condition for a function to be the kernel of a fractional derivative is an integrable singularity at 0.

A comment on a controversial issue: a Generalized Fractional Derivative cannot have a regular kernel · 0.92

Papers citing it · 1 sentence without a confident label

Cites it as background 1 paper

The investigation of the Ulam-Hyers stability theme in the FC has been growing and other works related to stability with the $ψ$-Hilfer fractional derivative and other derivatives [ref] will be presented in the near future.

Ulam-Hyers-Rassias stability for a class of fractional integro-differential equations · Concluding remarks · 0.93

What it cites · 2 sentences without a confident label

Cites as background 2 papers

On the other hand, recently, two new classes of fractional derivatives have appeared by means of limit, first of all, that said local, we mention some formulations: conformable fractional derivative, $𝒱-$fractional derivative, $M-$derivative, among others [ref] .

A New Fractional Derivative with Classical Properties · Introduction · 0.98
Other fractional derivative formulations with non-singular kernel and applications can be found in references [ref] .

Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems · Introduction · 0.91

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