an:01256365
Zbl 0916.34011
Gorenflo, R.; Mainardi, F.
Fractional oscillations and Mittag-Leffler functions
EN
Hamoui, Adnan (ed.) et al., International workshop on the recent advances in applied mathematics, RAAM '96, State of Kuwait, Kuwait, May 4--7, 1996. Kuwait: Kuwait Univ., Department of Mathematics and Computer Science, 193-208 (1996).
1996
a
34A25 26A33 33E20 33E30 45E10 45J05 70J35
linear oscillations; Mittag-Leffler functions
Summary: The fractional oscillation equation is obtained from the classical equation for linear oscillations by replacing the second-order time derivative by a fractional derivative of order \(\alpha\) with \(1<\alpha<2\). Using the Laplace transform, it is shown that the fundamental solutions can be expressed in terms of Mittag-Leffler functions, and exhibit a finite number of damped oscillations with an algebraic decay. For completeness the authors discuss both the cases \(0<\alpha<1\) (fractional relaxation) and \(2<\alpha\leq 3\) (growing oscillations), showing the key role of the Mittag-Leffler functions.
For the entire collection see [Zbl 0879.00037].