Integral representations of Mittag-Leffler function on the positive real axis

Eliana Contharteze Grigoletto, Edmundo Capelas Oliveira, Rubens Figueiredo Camargo

Abstract


The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N. Berberan-Santos, to show that the three-parameter Mittag-Leffler function has similar integral representations on the positive real axis. Some of the integrals are also presented.

Keywords


Inverse Laplace transform, Mittag-Leffler functions, Integral representation, Fractional calculus.

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DOI: https://doi.org/10.5540/tema.2019.020.02.217

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Trends in Computational and Applied Mathematics

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