Article
Version 1
Preserved in Portico This version is not peer-reviewed
Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus
Version 1
: Received: 14 April 2021 / Approved: 20 April 2021 / Online: 20 April 2021 (12:45:42 CEST)
A peer-reviewed article of this Preprint also exists.
Baumann, G. Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus. Fractal Fract. 2021, 5, 43. Baumann, G. Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus. Fractal Fract. 2021, 5, 43.
Abstract
We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi-
mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods
are exact methods of inverse Laplace transforms which allow us a numerical approximation
using Sinc methods. The inverse Laplace transform converges exponentially and does not use
Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions
incorporating one, two, and three parameters. The three parameter Mittag-Leffler function
represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential
equations of constant and variable differentiation order.
Keywords
Sinc methods; inverse Laplace transform; indefinite integrals; fractional calculus; Mittag−Leffler function; Prabhakar function; variable fractional order differentiation; variable fractional order integration
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment