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1

Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces

100%
Benchohra M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1999
|
tom 19
|
nr 1-2
111-121
EN
In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.
2
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On the Existence and Local Asymptotic Stability of Solutions of Fractional Order Integral Equations

64%
Abbas S. d., Benchohra M.
Commentationes Mathematicae
|
2012
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tom 52
|
nr 1
EN
In this paper, we present some results concerning the existence and the local asymptotic stability of solutions for a functional integral equation of fractional order, by using some fixed point theorems.
3
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Existence and attractivity for fractional order integral equations in Fréchet spaces

64%
Abbas S., Benchohra M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2013
|
tom 33
|
nr 1
47-63
EN
In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Riemann-Liouville fractional order, by using an extension of the Burton-Kirk fixed point theorem in the case of a Fréchet space.
4
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Boundary value problems for differential inclusions with fractional order

64%
Benchohra M., Hamani S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2008
|
tom 28
|
nr 1
147-164
EN
In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
5
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The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses

64%
Abbas S., Benchohra M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2010
|
tom 30
|
nr 1
141-161
EN
In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.
6
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An existence theorem for an hyperbolic differential inclusion in Banach spaces

64%
Benchohra M., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
|
nr 1
5-16
EN
In this paper, we investigate the existence of solutions on unbounded domain to a hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma which is an extension to multivalued between locally convex topological spaces of Schaefer's theorem.
7
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Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay

64%
Baliki A., Benchohra M.
Nonautonomous Dynamical Systems
|
2014
|
tom 1
|
nr 1
EN
In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
8
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Global uniqueness results for fractional partial hyperbolic differential equations with state-dependent delay

64%
Benchohra M., Hellal M.
Annales Polonici Mathematici
|
2014
|
tom 110
|
nr 3
259-281
EN
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.
9
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Impulsive Hyperbolic System of Partial Differential Equations of Fractional Order with Delay

64%
Benchohra M., Boutefal Z.
Commentationes Mathematicae
|
2014
|
tom 54
|
nr 2
EN
This paper deals with the existence of solutions to impulsive partial hyperbolic differential equations with finite delay, involving the Caputo fractional derivative. Our results will be obtained using Krasnoselskii fixed point theorem.
10
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Boundary Value Problems for Differential Equations with Fractional Order and Nonlinear Integral Conditions

64%
Benchohra M., Hamani S.
Commentationes Mathematicae
|
2009
|
tom 49
|
nr 2
EN
In this paper, we shall establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative and nonlinear integral conditions.
11
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Semilinear Functional Differential Equations of Fractional order with State-Dependent Delay

52%
Benchohra M., Bennihi O., Ezzinbi K.
Commentationes Mathematicae
|
2013
|
tom 53
|
nr 1
EN
In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon-Granas type for contractions maps in Frechet spaces combined with \(\alpha\)-resolvent family is the main tool in our analysis.
12
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On initial value problems for a class of first order impulsive differential inclusions

52%
Benchohra M., Boucherif A., Nieto J.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
|
tom 21
|
nr 2
159-171
EN
We investigate the existence of solutions to first order initial value problems for differential inclusions subject to impulsive effects. We shall rely on a fixed point theorem for condensing maps to prove our results.
13
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Fractional order impulsive partial hyperbolic differential inclusions with variable times

52%
Abbas S., Benchohra M., Górniewicz L.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2011
|
tom 31
|
nr 1
91-114
EN
This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.
14
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Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

52%
Benchohra M., Górniewicz L., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
|
tom 21
|
nr 2
261-282
EN
In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.
15
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Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

52%
Abbas S., Benchohra M., Abdalla Darwish M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2016
|
tom 36
|
nr 2
155-179
EN
In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions
16
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Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

52%
Abbas S., Alaidarous E., Albarakati W., Benchohra M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2015
|
tom 35
|
nr 2
105-122
EN
In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions.
17
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Fractional integro-differential inclusions with state-dependent delay

52%
Aissani K., Benchohra M., Ezzinbi K.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2014
|
tom 34
|
nr 2
153-167
EN
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.
18
Content available remote

New existence and stability results for partial fractional differential inclusions with multiple delay

46%
Abbas S., Albarakati W., Benchohra M., Darwish M., Hilal E.
Annales Polonici Mathematici
|
2015
|
tom 114
|
nr 1
81-100
EN
We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.
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