Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations

Dumitru Baleanu, Wu, Guo–Cheng and Zeng, Sheng–Da

Chaos, Solitons & Fractals, 2017, vol. 102, issue C, 99-105

Abstract: This paper investigates chaotic behavior and stability of fractional differential equations within a new generalized Caputo derivative. A semi–analytical method is proposed based on Adomian polynomials and a fractional Taylor series. Furthermore, chaotic behavior of a fractional Lorenz equation are numerically discussed. Since the fractional derivative includes two fractional parameters, chaos becomes more complicated than the one in Caputo fractional differential equations. Finally, Lyapunov stability is defined for the generalized fractional system. A sufficient condition of asymptotic stability is given and numerical results support the theoretical analysis.

Keywords: Generalized Caputo derivative; Lyapunov direct method; Asymptotic stability; Chaos; Adomian decomposition method; Numerical solutions (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (24)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:102:y:2017:i:c:p:99-105

DOI: 10.1016/j.chaos.2017.02.007

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