On Hyers–Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum

Advances in Difference Equations

article

Selvam, A. G. M.¹  Baleanu, D.²  Alzabut, J.⁴  Vignesh, D.¹  Abbas, S.⁵ 

[1] Department of Mathematics, Sacred Heart College;Department of Mathematics and Computer Sciences, Çankaya University;Institute of Space Sciences;Department of Mathematics and General Sciences, Prince Sultan University;School of Basic Sciences, Indian Institute of Technology Mandi

关键词: Fractional Duffing equation;    Mittag-Leffler function;    Hyers–Ulam stability;    Inverted pendulum;   

DOI  :  10.1186/s13662-020-02920-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY