Stability analysis of the generalized fractional differential equations with and without exogenous inputs
Volume 12, Issue 9, pp 562--572
http://dx.doi.org/10.22436/jnsa.012.09.01
Publication Date: April 12, 2019
Submission Date: September 22, 2018
Revision Date: February 14, 2019
Accteptance Date: February 28, 2019
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Authors
Ndolane Sene
- Laboratoire Lmdan, Departement de Mathematiques de la Decision, Universite Cheikh Anta Diop de Dakar, BP 5683 Dakar Fann, Senegal.
Abstract
The stability conditions of the fractional differential equations described by the Caputo generalized fractional derivative have been addressed. The generalized asymptotic stability of a class of the fractional differential equations has been investigated. The fractional input stability in the context of the fractional differential equations described by the Caputo generalized fractional derivative has been introduced. The Lyapunov characterizations of the generalized asymptotic stability and the generalized fractional input stability of the fractional differential equations with or without inputs have been provided. Several examples illustrating the main results of the paper have been proposed. The Caputo generalized fractional derivative and the generalized Gronwall lemma have been used.
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ISRP Style
Ndolane Sene, Stability analysis of the generalized fractional differential equations with and without exogenous inputs, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 9, 562--572
AMA Style
Sene Ndolane, Stability analysis of the generalized fractional differential equations with and without exogenous inputs. J. Nonlinear Sci. Appl. (2019); 12(9):562--572
Chicago/Turabian Style
Sene, Ndolane. "Stability analysis of the generalized fractional differential equations with and without exogenous inputs." Journal of Nonlinear Sciences and Applications, 12, no. 9 (2019): 562--572
Keywords
- Caputo generalized fractional derivative
- asymptotic stability
- fractional differential equations
MSC
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