On stable manifolds for planar fractional differential equations

DOI10.1016/J.AMC.2013.10.010zbMath1354.34015OpenAlexW2033649367MaRDI QIDQ505731

Stefan Siegmund, Nguyen Dinh Cong, Thai Son Doan, Hoang The Tuan

Publication date: 26 January 2017

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.10.010

zbMATH Keywords

fractional differential equationsCaputo derivativestable manifold theorem

Mathematics Subject Classification ID

Stability of manifolds of solutions to ordinary differential equations (34D35) Fractional ordinary differential equations (34A08)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mittag-Leffler functions and their applications
• Laplace transform and fractional differential equations
• Global existence theory and chaos control of fractional differential equations
• On systems of linear fractional differential equations with constant coefficients
• Analytic study on linear systems of fractional differential equations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Completely monotone generalized Mittag-Leffler functions
• Smoothness and stability of the solutions for nonlinear fractional differential equations
• Exponential asymptotics of the Mittag–Leffler function
• On the bound of the Lyapunov exponents for the fractional differential systems
• The completely monotonic character of the Mittag-Leffler function 𝐸ₐ(-𝑥)

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