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Research Papers

Lyapunov–Schmidt Reduction for Fractional Differential Systems

[+] Author and Article Information
Changpin Li

Department of Mathematics,
Shanghai University,
Shanghai 200444, China
e-mail: lcp@shu.edu.cn

Li Ma

Department of Mathematics,
Shanghai University,
Shanghai 200444, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 20, 2015; final manuscript received May 6, 2016; published online May 24, 2016. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 11(5), 051022 (May 24, 2016) (5 pages) Paper No: CND-15-1385; doi: 10.1115/1.4033607 History: Received November 20, 2015; Revised May 06, 2016

Lyapunov–Schmidt reduction is one of the powerful and significant methods to simplify nonlinear ordinary differential systems (ODSs) with standard formulation. In this paper, we extend Lyapunov–Schmidt reduction to fractional ordinary differential systems (FODSs) with Caputo derivatives.

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References

Figures

Grahic Jump Location
Fig. 1

Phase diagram of system (36) when λ=−0.2, α=1.9, x(0)=0, and y(0)=−1

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