Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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.

Journal reference: Fractal Fract. 2021, 5, 43
DOI: 10.3390/fractalfract5020043

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.

Subject Areas

Sinc methods; inverse Laplace transform; indefinite integrals; fractional calculus; Mittag−Leffler function; Prabhakar function; variable fractional order differentiation; variable fractional order integration

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