Properties of the Mittag-Leffler relaxation function. (English) Zbl 1101.33015

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.


33E12 Mittag-Leffler functions and generalizations
44A10 Laplace transform
Full Text: DOI Link


This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.