The failure of certain fractional calculus operators in two physical models

Manuel D. Ortigueira; Valeriy Martynyuk; Mykola Fedula; J. Tenreiro Machado

doi:10.1515/fca-2019-0017

The failure of certain fractional calculus operators in two physical models

Manuel D. Ortigueira, Valeriy Martynyuk, Mykola Fedula, J. Tenreiro Machado

Research output: Contribution to journal › Review article › peer-review

28 Citations (Scopus)

Abstract

The ability of the so-called Caputo-Fabrizio (CF) and Atangana-Baleanu (AB) operators to create suitable models for real data is tested with real world data. Two alternative models based on the CF and AB operators are assessed and compared with known models for data sets obtained from electrochemical capacitors and the human body electrical impedance. The results show that the CF and AB descriptions perform poorly when compared with the classical fractional derivatives.

Original language	English
Pages (from-to)	255-270
Number of pages	16
Journal	Fractional Calculus and Applied Analysis
Volume	22
Issue number	2
DOIs	https://doi.org/10.1515/fca-2019-0017
Publication status	Published - 24 Apr 2019

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34K07
Primary 26A33
Secondary 34K05

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AB - The ability of the so-called Caputo-Fabrizio (CF) and Atangana-Baleanu (AB) operators to create suitable models for real data is tested with real world data. Two alternative models based on the CF and AB operators are assessed and compared with known models for data sets obtained from electrochemical capacitors and the human body electrical impedance. The results show that the CF and AB descriptions perform poorly when compared with the classical fractional derivatives.

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The failure of certain fractional calculus operators in two physical models

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