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Sinc based inverse laplace transforms, mittag-leffler functions and their approximation for fractional calculus

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peer-reviewed

Erstveröffentlichung
2021-05-10
Authors
Baumann, Gerd
Wissenschaftlicher Artikel


Published in
Fractal and Fractional ; 5 (2021), 2. - Art.-Nr. 43. - eISSN 2504-3110
Link to original publication
https://dx.doi.org/10.3390/fractalfract5020043
Faculties
Fakultät für Mathematik und Wirtschaftswissenschaften
Institutions
Institut für Numerische Mathematik
Document version
published version (publisher's PDF)
Abstract
We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, 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 headings
[GND]: Gebrochene Analysis | Mittag-Leffler-Funktion
[LCSH]: Galerkin methods | Fractional calculus
[Free subject headings]: Sinc methods | inverse Laplace transform | indefinite integrals | Mittag-Leffler function | Prabhakar function | variable fractional order differentiation | variable fractional order integration
[DDC subject group]: DDC 510 / Mathematics
License
CC BY 4.0 International
https://creativecommons.org/licenses/by/4.0/

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DOI & citation

Please use this identifier to cite or link to this item: http://dx.doi.org/10.18725/OPARU-45466

Baumann, Gerd (2022): Sinc based inverse laplace transforms, mittag-leffler functions and their approximation for fractional calculus. Open Access Repositorium der Universität Ulm und Technischen Hochschule Ulm. http://dx.doi.org/10.18725/OPARU-45466
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