Approximation of the Mittag-Leffler Functions by Elementary Functions with Physics Applications

Authors

  • Alvaro H. Salas S. Universidad Nacional de Colombia, Fizmako Research Group, Bogotá, Colombia.

DOI:

https://doi.org/10.9734/bpi/cppsr/v7/2864G

Keywords:

Fractional oscillator, Caputo derivative, nonlinear fractional oscillator, Duffing equation, fractional pendulum, fractional Van der Pol equation, Duffing-Mathieu fractional oscillator

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 illustrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

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Published

2024-02-15

How to Cite

Alvaro H. Salas S. (2024). Approximation of the Mittag-Leffler Functions by Elementary Functions with Physics Applications. Current Perspective to Physical Science Research Vol. 7, 138–163. https://doi.org/10.9734/bpi/cppsr/v7/2864G

Issue

Current Perspective to Physical Science Research Vol. 7

Section

Chapters