Journal
FRACTAL AND FRACTIONAL
Volume 7, Issue 4, Pages -Publisher
MDPI
DOI: 10.3390/fractalfract7040296
Keywords
scale derivative; Liouville derivative; Hadamard derivative; tempered derivative; logarithmic series
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A general fractional scale derivative is introduced and its relation with Hadamard derivatives is established. A new derivative similar to the Grunwald-Letnikov's is deduced. Tempered versions are also introduced. Scale-invariant systems are described and a new logarithmic Mittag-Leffler series is proposed for solving the corresponding differential equations.
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 Grunwald-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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