Journal of Integral Equations and Applications

Smooth solutions to mixed-order fractional differential systems with applications to stability analysis

Javier A. Gallegos, Norelys Aguila-Camacho, and Manuel A. Duarte-Mermoud

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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.

Article information

Source
J. Integral Equations Applications, Volume 31, Number 1 (2019), 59-84.

Dates
First available in Project Euclid: 27 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1561601026

Digital Object Identifier
doi:10.1216/JIE-2019-31-1-59

Mathematical Reviews number (MathSciNet)
MR3974983

Zentralblatt MATH identifier
07080015

Subjects
Primary: 26A33: Fractional derivatives and integrals 34A30: Linear equations and systems, general 34D20: Stability

Keywords
Fractional differential equations smoothness stability boundedness backstepping

Citation

Gallegos, Javier A.; Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A. Smooth solutions to mixed-order fractional differential systems with applications to stability analysis. J. Integral Equations Applications 31 (2019), no. 1, 59--84. doi:10.1216/JIE-2019-31-1-59. https://projecteuclid.org/euclid.jiea/1561601026


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