Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

. In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differen...

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Bibliographic Details
Published in:European physical journal plus 2017-01, Vol.132 (1), p.36, Article 36
Main Authors: He, Shaobo, Sun, Kehui, Mei, Xiaoyong, Yan, Bo, Xu, Siwei
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Calculus
Chaos theory
Complex Systems
Condensed Matter Physics
Decomposition
Differential equations
Fractional calculus
Lorenz system
Mathematical and Computational Physics
Molecular
Nonlinear equations
Numerical analysis
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Theoretical
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Summary:. In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differential equations. Taking the conformable fractional-order simplified Lorenz system as an example, the numerical solution and chaotic behaviors of the conformable fractional-order simplified Lorenz system are investigated. It is found that rich dynamics exist in the conformable fractional-order simplified Lorenz system, and the minimum order for chaos is even less than 2. The results are validated by means of bifurcation diagram, Lyapunov characteristic exponents and phase portraits.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/i2017-11306-3