Introduction to the fractional derivative : Mittag-Leffler exponential

Mittag-Leffler exponential
Introduction to the fractional derivative

Authors : François DUBOIS, Ana Cristina GALUCIO, Nelly POINT

Publication date: April 10, 2010 | Lire en français

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4. Mittag-Leffler exponential

For $θ \in ℂ$ and 0 < α < 1, the following function is called a Mittag-Leffler exponential and is denoted E_α(•) :

E_{α} (θ) = \sum_{k = 0}^{\infty} \frac{θ^{k}}{Γ (1 + αk)}

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Mittag-Leffler exponential

(1) - BAGLEY (R.L.), TORVIK (P.J.) - Fractional calculus – a different approach to the analysis of viscoelastically damped structures - AIAA Journal, 21 : 741-748 (1983).
(2) - BAGLEY (R.L.), TORVIK (P.J.) - On the fractional calculus model of viscoelastic behavior - Journal of Rheology, 30 : 133-155...

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