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arXiv · 1810.12520

On asymptotic properties of solutions to fractional differential equations

N. D. Cong·H. T. Tuan·Hieu Trinh
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Abstract

We present some distinct asymptotic properties of solutions to Caputo fractional differential equations (FDEs). First, we show that the non-trivial solutions to a FDE can not converge to the fixed points faster than $t^{-\alpha}$, where $\alpha$ is the order of the FDE. Then, we introduce the notion of Mittag-Leffler stability which is suitable for systems of fractional-order. Next, we use this notion to describe the asymptotical behavior of solutions to FDEs by two approaches: Lyapunov's first method and Lyapunov's second method. Finally, we give a discussion on the relation between Lipschitz condition, stability and speed of decay, separation of trajectories to scalar FDEs.

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BibTeXRIS

N. D. Cong, H. T. Tuan, Hieu Trinh. 2018-10-30. On asymptotic properties of solutions to fractional differential equations. https://doi.org/10.1016/j.jmaa.2019.123759

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