GENERATION OF NONLOCAL FRACTIONAL DYNAMICAL SYSTEMS BY FRACTIONAL DIFFERENTIAL EQUATIONS

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 ge...

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Bibliographic Details
Published in:The Journal of integral equations and applications 2017-12, Vol.29 (4), p.585-608
Main Authors: CONG, N.D., TUAN, H.T.
Format: Article
Language:English
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Summary: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.
ISSN:0897-3962
1938-2626
DOI:10.1216/JIE-2017-29-4-585