an:05055715
Zbl 1101.33015
Berberan-Santos, M??rio N.
Properties of the Mittag-Leffler relaxation function
EN
J. Math. Chem. 38, No. 4, 629-635 (2005).
00121386
2005
j
33E12 44A10
Mittag-Leffler function; Laplace transform; relaxation kinetics
Summary: The Mittag-Leffler relaxation function, \(E_\alpha(-x)\), with \(0\leq\alpha\leq 1\), which arises in the description of complex relaxation processes, is studied. A relation that gives the relaxation function in terms of two Mittag-Leffler functions with positive arguments is obtained, and from it a new form of the inverse Laplace transform of \(E_\alpha(-x)\) is derived and used to obtain a new integral representation of this function, its asymptotic behaviour and a new recurrence relation. It is also shown that the fastest initial decay of \(E_\alpha(-x)\) occurs for \(\alpha=1/2\), a result that displays the peculiar nature of the interpolation made by the Mittag-Leffler relaxation function between a pure exponential and a hyperbolic function.