Mittag-Leffler stability theorem for fractional nonlinear systems with delay.
Sadati, S.J., Baleanu, D., Ranjbar, A., Ghaderi, R., Abdeljawad, T. (Maraaba) (2010)
Abstract and Applied Analysis
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Displaying similar documents to “Razumikhin stability theorem for fractional systems with delay.”
Mittag-Leffler stability theorem for fractional nonlinear systems with delay.
Weighted fractional differential equations with infinite delay in Banach spaces
Qixiang Dong, Can Liu, Zhenbin Fan (2016)
Open Mathematics
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This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality...
Fractional integro-differential inclusions with state-dependent delay
Khalida Aissani, Mouffak Benchohra, Khalil Ezzinbi (2014)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.
Integrable solutions for implicit fractional order functional differential equations with infinite delay
Mouffak Benchohra, Mohammed Said Souid (2015)
Archivum Mathematicum
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In this paper we study the existence of integrable solutions for initial value problem for implicit fractional order functional differential equations with infinite delay. Our results are based on Schauder type fixed point theorem and the Banach contraction principle fixed point theorem.
Global output feedback stabilization for nonlinear fractional order time delay systems
Hanen Benali (2021)
Kybernetika
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This paper investigates the problem of global stabilization by state and output-feedback for a family of for nonlinear Riemann-Liouville and Caputo fractional order time delay systems written in triangular form satisfying linear growth conditions. By constructing a appropriate Lyapunov-Krasovskii functional, global asymptotic stability of the closed-loop systems is achieved. Moreover, sufficient conditions for the stability, for the particular class of fractional order time-delay system...
Stabilization of fractional exponential systems including delays
Catherine Bonnet, Jonathan R. Partington (2001)
Kybernetika
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This paper analyzes the BIBO stability of fractional exponential delay systems which are of retarded or neutral type. Conditions ensuring stability are given first. As is the case for the classical class of delay systems these conditions can be expressed in terms of the location of the poles of the system. Then, in view of constructing robust BIBO stabilizing controllers, explicit expressions of coprime and Bézout factors of these systems are determined. Moreover, nuclearity is analyzed...
Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
Yakar, Coşkun (2010)
Abstract and Applied Analysis
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Stability of Caputo fractional differential equations by Lyapunov functions
Ravi P. Agarwal, Donal O'Regan, Snezhana Hristova (2015)
Applications of Mathematics
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The stability of the zero solution of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov-like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov-like function along the given fractional equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based...