| Title: |
On asymptotic properties of solutions to fractional differential equations |
| Authors: |
ND Cong; HT Tuan; Hieu Trinh |
| Publication Year: |
2020 |
| Subject Terms: |
Electrical engineering not elsewhere classified; Applied mathematics not elsewhere classified; Pure mathematics not elsewhere classified; Science & Technology; Physical Sciences; Mathematics; Applied; Fractional differential equation; Lyapunov's first method; Lyapunov's second method; Asymptotic behavior; Asymptotic stability; Mittag-Leffler stability; ORDER NONLINEAR-SYSTEMS; LYAPUNOV FUNCTIONS; STABILITY ANALYSIS; School of Engineering; 090602 Control Systems; Robotics and Automation; 010203 Calculus of Variations; Systems Theory and Control Theory; 010204 Dynamical Systems in Applications; 970109 Expanding Knowledge in Engineering; 970101 Expanding Knowledge in the Mathematical Sciences; 4901 Applied mathematics |
| Description: |
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 cannot converge to the fixed points faster than t−α, where α 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 asymptotic 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. |
| Document Type: |
article in journal/newspaper |
| Language: |
unknown |
| Relation: |
http://hdl.handle.net/10536/DRO/DU:30134162; https://figshare.com/articles/journal_contribution/On_asymptotic_properties_of_solutions_to_fractional_differential_equations/20723170 |
| Availability: |
http://hdl.handle.net/10536/DRO/DU:30134162; https://figshare.com/articles/journal_contribution/On_asymptotic_properties_of_solutions_to_fractional_differential_equations/20723170 |
| Rights: |
All Rights Reserved |
| Accession Number: |
edsbas.B40104B7 |
| Database: |
BASE |