期刊
ADVANCES IN DIFFERENCE EQUATIONS
卷 2020, 期 1, 页码 -出版社
SPRINGER
DOI: 10.1186/s13662-020-02920-6
关键词
Fractional Duffing equation; Mittag-Leffler function; Hyers-Ulam stability; Inverted pendulum; 26A33; 39A30
资金
- Prince Sultan University [RG-DES-2017-01-17]
A human being standing upright with his feet as the pivot is the most popular example of the stabilized inverted pendulum. Achieving stability of the inverted pendulum has become common challenge for engineers. In this paper, we consider an initial value discrete fractional Duffing equation with forcing term. We establish the existence, Hyers-Ulam stability, and Hyers-Ulam Mittag-Leffler stability of solutions for the equation. We consider the inverted pendulum modeled by Duffing equation as an example. The values are tabulated and simulated to show the consistency with theoretical findings.
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