On asymptotic properties of solutions to fractional differential equations
Classical Analysis and ODEs
2020-02-17 v2
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 , where 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.
Keywords
Cite
@article{arxiv.1810.12520,
title = {On asymptotic properties of solutions to fractional differential equations},
author = {N. D. Cong and H. T. Tuan and Hieu Trinh},
journal= {arXiv preprint arXiv:1810.12520},
year = {2020}
}