Open Access
2017 Generation of nonlocal fractional dynamical systems by fractional differential equations
N.D. Cong, H.T. Tuan
J. Integral Equations Applications 29(4): 585-608 (2017). DOI: 10.1216/JIE-2017-29-4-585


We show that any two trajectories of solutions of a one-dimensional fractional differential equation (FDE) either coincide or do not intersect each other. However, in the higher-dimensional case, two different trajectories can meet. Furthermore, one-dimensional FDEs and triangular systems of FDEs generate nonlocal fractional dynamical systems, whereas a higher-dimensional FDE does not, in general, generate a nonlocal dynamical system.


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N.D. Cong. H.T. Tuan. "Generation of nonlocal fractional dynamical systems by fractional differential equations." J. Integral Equations Applications 29 (4) 585 - 608, 2017.


Published: 2017
First available in Project Euclid: 10 November 2017

zbMATH: 1385.34009
MathSciNet: MR3722842
Digital Object Identifier: 10.1216/JIE-2017-29-4-585

Primary: 34A08 , 34A10 , 34B10 , 34C11 , 34C35

Keywords: dynamical system , Fractional differential equations , growth and boundedness , Initial value problem , nonlocal boundary problem , two parameter flow

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

Vol.29 • No. 4 • 2017
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