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...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
MDPI AG
2023-03-01
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Series: | Fractal and Fractional |
Subjects: | |
Online Access: | https://www.mdpi.com/2504-3110/7/4/296 |
Summary: | 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. |
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ISSN: | 2504-3110 |