Variable-Order Fractional Scale Calculus

Duarte Valério; Manuel D. Ortigueira

doi:10.3390/math11214549

Variable-Order Fractional Scale Calculus

Duarte Valério, Manuel D. Ortigueira

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Abstract

General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses.

Original language	English
Article number	4549
Number of pages	13
Journal	Mathematics
Volume	11
Issue number	21
DOIs	https://doi.org/10.3390/math11214549
Publication status	Published - 4 Nov 2023

Keywords

Hadamard derivative
logarithmic series
scale derivative
variable-order derivative

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10.3390/math11214549Licence: CC BY

Variable-Order Fractional Scale CalculusFinal published version, 328 KBLicence: CC BY

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abstract = "General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses.",

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AU - Valério, Duarte

AU - Ortigueira, Manuel D.

PY - 2023/11/4

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N2 - General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses.

AB - General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses.

KW - Hadamard derivative

KW - logarithmic series

KW - scale derivative

KW - variable-order derivative

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U2 - 10.3390/math11214549

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JO - Mathematics

JF - Mathematics

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Variable-Order Fractional Scale Calculus

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Keywords

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