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2019 Smooth solutions to mixed-order fractional differential systems with applications to stability analysis
Javier A. Gallegos, Norelys Aguila-Camacho, Manuel A. Duarte-Mermoud
J. Integral Equations Applications 31(1): 59-84 (2019). DOI: 10.1216/JIE-2019-31-1-59

Abstract

Conditions for existence, uniqueness and smoothness of solutions for systems of fractional differential equations of Caputo and/or Riemann-Liouville type having all of them in general and not of the same derivation order are established in this paper. It includes mixed-order, multi-order or non-commensurate fractional systems. The smooth property is shown to be relevant for drawing consequences on the global behavior of solutions for such systems. In particular, we obtain sufficient conditions for global boundedness of solutions to mixed-order nonlinear systems and asymptotic stability of nonlinear fractional systems using backstepping control.

Citation

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Javier A. Gallegos. Norelys Aguila-Camacho. Manuel A. Duarte-Mermoud. "Smooth solutions to mixed-order fractional differential systems with applications to stability analysis." J. Integral Equations Applications 31 (1) 59 - 84, 2019. https://doi.org/10.1216/JIE-2019-31-1-59

Information

Published: 2019
First available in Project Euclid: 27 June 2019

zbMATH: 07080015
MathSciNet: MR3974983
Digital Object Identifier: 10.1216/JIE-2019-31-1-59

Subjects:
Primary: 26A33, 34A30, 34D20

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.31 • No. 1 • 2019
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