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1
Content available Nonlinear fractional differential equations with non-instantaneous impulses in Banach spaces
Benchohra M., Slimane M.
Journal of Mathematics and Applications
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2018
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Vol. 41
39--51
EN
This paper is devoted to study the existence of solutions for a class of initial value problems for non-instantaneous impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Monch's fixed point theorem and the technique of measures of noncompactness.
2
Content available remote Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces
Abbas S., Agarwal R. P., Benchohra M., Berhoun F.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
131--140
EN
In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Hadamard fractional order. We use an extension of the Burton-Kirk fixed point theorem in Fréchet spaces.
3
Content available remote Second order evolution equations with nonlocal conditions
Benchohra M., Nieto J. J., Rezoug N.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
309--319
EN
In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.
4
Content available Some new existence results and stability concepts for fractional partial random differential equations
Abbas S., Benchohra M., Darwish M. A.
Journal of Mathematics and Applications
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2016
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Vol. 39
5--22
EN
In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.
5
Content available Measure of noncompactness and neutral functional differential equations with state-dependent delay
Benchohra M., Henderson J., Medjadj I.
Journal of Mathematics and Applications
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2016
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Vol. 39
23--45
EN
Our aim in this work is to study the existence of solutions of first and second order for neutral functional differential equations with state-dependent delay. We use the Mönch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness.
6
Global existence and stability results for partial fractional random differential equations
Abbas S., Albarakati W., Benchohra M., Hilal E.
Journal of Applied Analysis
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2015
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Vol. 21, nr 2
79--87
EN
We investigate some existence and stability results for the Darboux problem of partial fractional random differential equations in Banach spaces. Our existence results are based upon some fixed point theorems.
7
Content available remote Ulam stabilities for the Darboux problem for partial fractional differential inclusions
Abbas S., Benchohra M.
Demonstratio Mathematica
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2014
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Vol. 47, nr 4
826--838
EN
In this article, we investigate some Ulam’s type stability concepts for the Darboux problem of partial fractional differential inclusions with a nonconvex valued right hand side. Our results are based upon Covitz-Nadler fixed point theorem and fractional version of Gronwall’s inequality.
8
Content available remote Impulsive Hyperbolic System of Partial Differential Equations of Fractional Order with Delay
Benchohra M., Boutefal Z.
Commentationes Mathematicae
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2014
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Vol 54, No. 2
179--189
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.
9
Content available Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay
Abbas S., Benchohra M.
Opuscula Mathematica
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2013
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Vol. 33, no. 2
209--222
EN
In the present paper we investigate the existence of solutions for a system of integral inclusions of fractional order with multiple delay. Our results are obtained upon suitable fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler for the nonconvex case.
10
Content available remote Uniqueness results for fredholm type Fractional order Riemann-Liouville integral equations
Abbas S., Benchohra M.
Fasciculi Mathematici
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2013
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Nr 51
5--19
EN
In this paper we study the existence and uniqueness of solutions of a certain Fredholm type Riemann-Liouville integral equation of two variables by using Banach contraction principle.
11
Content available remote On the set of solutions of fractional order Riemann-Liouville integral inclusions
Abbas S., Benchohra M.
Demonstratio Mathematica
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2013
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Vol. 46, nr 2
271--281
EN
In this paper, we prove the arcwise connectedness of the solution set of a nonclosed, nonconvex Fredholm type, Riemann–Liouville integral inclusion of fractional order.
12
Content available remote Semilinear functional differential equations of fractional order with state-dependent delay
Benchohra M., Bennihi O., Ezzinbi K.
Commentationes Mathematicae
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2013
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Vol 53, No. 1
47--59
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 Fr´echet spaces combined with -resolvent family is the main tool in our analysis.
13
Content available Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces
Benchohra M., Mostefai F.
Opuscula Mathematica
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2012
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Vol. 32, no. 1
31-40
EN
The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
14
Content available remote On the Existence and Local Asymptotic Stability of Solutions of Fractional Order Integral Equations
Abbas S., Benchohra M.
Commentationes Mathematicae
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2012
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Vol. 52, [Z] 1
91-100
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.
15
Content available remote Impulsive partial hyperbolic differential inclusions of fractional order
Abbas S., Benchohra M.
Demonstratio Mathematica
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2010
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Vol. 43, nr 4
775-797
EN
In this paper we investigate the existence of solutions of a class of partial impulsive hyperbolic differential inclusions involving the Caputo fractional derivative. Our main tools are appropriate fixed point theorems from multivalued analysis.
16
Content available remote Boundary Value Problems for Differential Equations with Fractional Order and Nonlinear Integral Conditions
Benchohra M., Hamani S.
Commentationes Mathematicae
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2009
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Vol. 49, [Z] 2
147-159
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.
17
Existence and controllability results for nonlinear differential inclusions with nonlocal conditions in Banach spaces
Benchohra M., Ntouyas S. K.
Journal of Applied Analysis
|
2002
|
Vol. 8, nr 1
33-48
EN
In this paper we investigate the existence and controllability of mild solutions to the first order semilinear evolution inclusions in Banach spaces with nonlocal conditions. We shall rely of a fixed point theorem for condensing maps due to Martelli.
18
Content available remote On an hyperbolic functional differential inclusion in Banach spaces
Benchohra M., Ntouyas S. K.
Fasciculi Mathematici
|
2002
|
Nr 33
27-35
EN
In this paper we investigate the existence of solutions to an hyperbolic functional differential inclusion in Banach spaces. We shall rely on a fixed point theorem for condensing maps due to of Martelli.
19
Content available remote An existence result for hyperbolic functional differential inclusions
Benchohra M., Ntouyas S. K.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2002
|
[Z] 42(1)
1-16
EN
In this paper we investigate the existence of solutions on an unbounded domain to an hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension to multivalued on locally convex topological spaces, of Schaefer's theorem.
20
Content available remote Controllability of nonlinear integrodifferential inclusions in Banach spaces with nonlocal conditions
Benchohra M., Ntouyas S. K.
Fasciculi Mathematici
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2001
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Nr 31
5-22
EN
In this paper, we shall establish sufficient conditions for the controllability of semilinear integrodifferential inclusions in Banach spaces, with nonlocal conditions. We shall rely of a fixed point theorem for condensing maps due to Martelli.
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