Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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