On exponential stability of nonlinear fractional multidelay integro-differential equations defined by pairwise permutable matrices

In this paper, systems of nonlinear differential equations with Caputo fractional derivative and multiple delays are considered. Using representation of a solution of differential equation with multiple delays in the form of matrix polynomial and stability results such as Gronwall’s and Pinto’s ineq...

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Bibliographic Details
Published in:Applied mathematics and computation 2014-01, Vol.227, p.456-468
Main Authors: Medved’, M., Pospíšil, M., Škripková, L.
Format: Article
Language:English
Subjects:
Delay
Derivatives
Differential equations
Exponential stability
Integro-differential equation
Mathematical analysis
Mathematical models
Multiple delays
Nonlinearity
Polynomials
Stability
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Summary:In this paper, systems of nonlinear differential equations with Caputo fractional derivative and multiple delays are considered. Using representation of a solution of differential equation with multiple delays in the form of matrix polynomial and stability results such as Gronwall’s and Pinto’s inequality, sufficient conditions for the exponential stability of a trivial solution of nonlinear multidelay fractional differential equations are proved.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.11.012