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Approximation of the Mittag-Leffler functions by Elementary Functions with Physics Applications
Version 1
: Received: 11 January 2023 / Approved: 23 January 2023 / Online: 23 January 2023 (01:31:54 CET)
How to cite: Salas, A. Approximation of the Mittag-Leffler functions by Elementary Functions with Physics Applications. Preprints 2023, 2023010382. https://doi.org/10.20944/preprints202301.0382.v1 Salas, A. Approximation of the Mittag-Leffler functions by Elementary Functions with Physics Applications. Preprints 2023, 2023010382. https://doi.org/10.20944/preprints202301.0382.v1
Abstract
In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.
Keywords
fractional oscillator; caputo derivative; nonlinear fractional oscillator; duffing equatio; fractional pendulum; fractional Van der Pol equation; duffing; mathieu fractional oscillator
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.
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