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

Authors

  • Eliana Contharteze Grigoletto Universidade Estadual Paulista "Júlio de Mesquita Filho" (Unesp), Campus Botucatu. https://orcid.org/0000-0003-4336-5387
  • Edmundo Capelas Oliveira Universidade Estadual de Campinas (Unicamp).
  • Rubens Figueiredo Camargo Universidade Estadual Paulista "Júlio de Mesquita Filho" (Unesp), Campus Bauru.

DOI:

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

Keywords:

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

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.

Author Biographies

Eliana Contharteze Grigoletto, Universidade Estadual Paulista "Júlio de Mesquita Filho" (Unesp), Campus Botucatu.

Departamento de Bioprocessos e Biotecnologia.

Edmundo Capelas Oliveira, Universidade Estadual de Campinas (Unicamp).

IMECC - Instituto de Matemática, Estatística e Computação Científica.

Rubens Figueiredo Camargo, Universidade Estadual Paulista "Júlio de Mesquita Filho" (Unesp), Campus Bauru.

Departamento de Matemática.

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Published

2019-07-29

How to Cite

Grigoletto, E. C., Oliveira, E. C., & Camargo, R. F. (2019). Integral representations of Mittag-Leffler function on the positive real axis. Trends in Computational and Applied Mathematics, 20(2), 217. https://doi.org/10.5540/tema.2019.020.02.217

Issue

Vol. 20 No. 2 (2019)

Section

Original Article

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