Displaying similar documents to “Existence results for fractional integro-differential inclusions with state-dependent delay”

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.

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...

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 impulsive semilinear fractional differential inclusions with delay in Banach spaces

Hammouche Hadda, Guerbati Kaddour, Benchohra Mouffak, Abada Nadjat (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.

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.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

Abbas, Saïd, Benchohra, Mouffak (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11 This paper deals with the existence and uniqueness of solutions of two classes of partial impulsive hyperbolic differential equations with fixed time impulses and state-dependent delay involving the Caputo fractional derivative. Our results are obtained upon suitable fixed point theorems.