On Hyers-Ulam Mittag-Leffler Stability of Discrete Fractional Duffing Equation With Application on Inverted Pendulum
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Date
2020
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Publisher
Springer
Open Access Color
GOLD
Green Open Access
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Top 10%
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Abstract
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.
Description
D, Vignesh/0000-0002-9942-4035; Abbas, Syed/0000-0001-5694-2011; Alzabut, Prof. Dr. Jehad/0000-0002-5262-1138
Keywords
Fractional Duffing Equation, Mittag-Leffler Function, Hyers-Ulam Stability, Inverted Pendulum, 26A33, 39A30, Geometry, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Duffing equation, Pendulum, Differential equation, Machine learning, QA1-939, FOS: Mathematics, Inverted pendulum, Stability (learning theory), Anomalous Diffusion Modeling and Analysis, Hyers–Ulam stability, Mittag-Leffler function, Forcing (mathematics), Applied Mathematics, Physics, Stability of Functional Equations in Mathematical Analysis, Hyers-Ulam Stability, Applied mathematics, Computer science, Modeling and Simulation, Physical Sciences, Nonlinear system, Fractional Duffing equation, Mathematics, Ordinary differential equation, Consistency (knowledge bases), fractional Duffing equation, Fractional ordinary differential equations, Fractional derivatives and integrals, Hyers-Ulam stability, Stability for nonlinear problems in mechanics, inverted pendulum
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Selvam, A.G.M...et al. (2020). "On Hyers–Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum", Advances in Difference Equations, Vol. 2020, No. 1.
WoS Q
Q1
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OpenCitations Citation Count
39
Source
Advances in Difference Equations
Volume
2020
Issue
1
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CrossRef : 6
Scopus : 49
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