Journal
NONLINEAR DYNAMICS
Volume 71, Issue 4, Pages 621-633Publisher
SPRINGER
DOI: 10.1007/s11071-012-0601-1
Keywords
Fractional dynamical system; Fractional flow; Caputo derivative; Linearization theorem
Categories
Funding
- Key Program of Shanghai Municipal Education Commission [12ZZ084]
- Shanghai Leading Academic Discipline Project [S30104]
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Nowadays, it is known that the solution to a fractional differential equation can't generally define a dynamical system in the sense of semigroup property due to the history memory induced by the weakly singular kernel. But we can still establish the similar relationship between a fractional differential equation and the corresponding fractional flow under a reasonable condition. In this paper, we firstly present some results on fractional dynamical system defined by the fractional differential equation with Caputo derivative. Furthermore, the linearization and stability theorems of the nonlinear fractional system are also shown. As a byproduct, we prove Audounet-Matignon-Montseny conjecture. Several illustrative examples are given as well to support the theoretical analysis.
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