Application of the efros theorem to the function represented by the inverse laplace transform of s−µ exp(−sν)

Alexander Apelblat, Francesco Mainardi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−µ exp(−sν) with µ ≥ 0 and 0 < ν < 1 are presented.

Original languageEnglish
Article number354
Pages (from-to)1-15
Number of pages15
JournalSymmetry
Volume13
Issue number2
DOIs
StatePublished - 1 Feb 2021

Keywords

  • Efros theorem
  • Finite
  • Infinite and convolution integrals
  • Inverse laplace transforms
  • Mittag–Leffler functions
  • Modified bessel functions
  • Volterra functions
  • Wright functions

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)

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