Displaying similar documents to “Stabilization of fractional exponential systems including delays”

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.

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...

Existence results for fractional integro-differential inclusions with state-dependent delay

Giovana Siracusa, Hernán R. Henríquez, Claudio Cuevas (2017)

Nonautonomous Dynamical Systems

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In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

Synchronization of fractional-order chaotic systems with multiple delays by a new approach

Jianbing Hu, Hua Wei, Lingdong Zhao (2015)

Kybernetika

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In this paper, we propose a new approach of designing a controller and an update rule of unknown parameters for synchronizing fractional-order system with multiple delays and prove the correctness of the approach according to the fractional Lyapunov stable theorem. Based on the proposed approach, synchronizing fractional delayed chaotic system with and without unknown parameters is realized. Numerical simulations are carried out to confirm the effectiveness of the approach.

Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space

Mouffak Benchohra, Soufyane Bouriah, Jamal E. Lazreg, Juan J. Nieto (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.