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Relation between the inverse Laplace transforms of I(tβ) and I(t): Application to the Mittag-Leffler and asymptotic inverse power law relaxation functions

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Abstract

The relation between H(k), inverse Laplace transform of a relaxation function I(t), and Hβ(k), inverse Laplace transform of I(tβ), is obtained. It is shown that for β < 1 the function Hβ(k) can be expressed in terms of H(k) and of the Lévy one-sided distribution Lβ(k). The obtained results are applied to the Mittag-Leffler and asymptotic inverse power law relaxation functions. A simple integral representation for the Lévy one-sided density function L1/4(k) is also obtained.

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Authors and Affiliations

  1. Centro de Química-Física Molecular, Instituto Superior Técnico, 1049-001, Lisboa, Portugal

    Mário N. Berberan-Santos

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  1. Mário N. Berberan-Santos
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Correspondence to Mário N. Berberan-Santos.

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AMS (MOS) classification: 33E12 Mittag-Leffler functions and generalizations, 44A10 Laplace transform, 60E07 Infinitely divisible distributions; stable distributions

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Berberan-Santos, M.N. Relation between the inverse Laplace transforms of I(tβ) and I(t): Application to the Mittag-Leffler and asymptotic inverse power law relaxation functions. J Math Chem 38, 265–270 (2005). https://doi.org/10.1007/s10910-005-5412-x

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  • DOI: https://doi.org/10.1007/s10910-005-5412-x

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