Journal of Integral Equations and Applications

Generation of nonlocal fractional dynamical systems by fractional differential equations

N.D. Cong and H.T. Tuan

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Abstract

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.

Article information

Source
J. Integral Equations Applications, Volume 29, Number 4 (2017), 585-608.

Dates
First available in Project Euclid: 10 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1510282935

Digital Object Identifier
doi:10.1216/JIE-2017-29-4-585

Mathematical Reviews number (MathSciNet)
MR3722842

Zentralblatt MATH identifier
1385.34009

Subjects
Primary: 34A08: Fractional differential equations 34A10 34B10: Nonlocal and multipoint boundary value problems 34C11: Growth, boundedness 34C35

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

Citation

Cong, N.D.; Tuan, H.T. Generation of nonlocal fractional dynamical systems by fractional differential equations. J. Integral Equations Applications 29 (2017), no. 4, 585--608. doi:10.1216/JIE-2017-29-4-585. https://projecteuclid.org/euclid.jiea/1510282935


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