A note on a semilinear fractional differential equation of neutral type with infinite delay.
Mophou, Gisle M., N'Guérékata, Gaston M. (2010)
Advances in Difference Equations [electronic only]
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Displaying similar documents to “Editorial: Abstract differential and difference equations.”
A note on a semilinear fractional differential equation of neutral type with infinite delay.
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.
Existence of mild solutions to fractional integrodifferential equations of neutral type with infinite delay.
Li, Fang, Zhang, Jun (2011)
Advances in Difference Equations [electronic only]
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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.
Nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces
JinRong Wang, Wei Wei (2012)
Annales Polonici Mathematici
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This paper is mainly concerned with existence of mild solutions and optimal controls for nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces. We do not assume that the relevant strongly continuous semigroup is compact.
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...
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...
Existence results for nonlinear fractional difference equation.
Chen, Fulai, Luo, Xiannan, Zhou, Yong (2011)
Advances in Difference Equations [electronic only]
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Razumikhin stability theorem for fractional systems with delay.
Baleanu, D., Sadati, S.J., Ghaderi, R., Ranjbar, A., Abdeljawad, T., Jarad, F. (2010)
Abstract and Applied Analysis
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Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces
Zuomao Yan, Hongwu Zhang (2014)
Annales Polonici Mathematici
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We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the α-resolvent operator. An example is given to illustrate...
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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Global uniqueness results for fractional partial hyperbolic differential equations with state-dependent delay
Mouffak Benchohra, Mohamed Hellal (2014)
Annales Polonici Mathematici
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We investigate the existence and uniqueness of solutions of hyperbolic fractional order differential equations with state-dependent delay by using a nonlinear alternative of Leray-Schauder type due to Frigon and Granas for contraction maps on Fréchet spaces.