Fractional Scale Calculus: Hadamard vs. Liouville

Fractional Scale Calculus: Hadamard vs. Liouville

A general fractional scale derivative is introduced and studied. Its relation with the Hadamard derivatives is established and reformulated. A new derivative similar to the Grünwald–Letnikov’s is deduced. Tempered versions are also introduced. Scale-invariant systems are described and exemplified. F...

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Veröffentlicht in:Fractal and fractional 2023-04, Vol.7 (4), p.296
Hauptverfasser: Ortigueira, Manuel D., Bohannan, Gary W.
Format: Artikel
Sprache:eng
Schlagworte:
Calculus
Derivatives
Differential equations
Eigenvalues
Hadamard derivative
Liouville derivative
logarithmic series
scale derivative
Signal processing
tempered derivative
Wavelet transforms
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Zusammenfassung:A general fractional scale derivative is introduced and studied. Its relation with the Hadamard derivatives is established and reformulated. A new derivative similar to the Grünwald–Letnikov’s is deduced. Tempered versions are also introduced. Scale-invariant systems are described and exemplified. For solving the corresponding differential equations, a new logarithmic Mittag-Leffler series is proposed.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7040296