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

Mouffak Benchohra — 1999

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses

Saïd AbbasMouffak Benchohra — 2010

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Upper and Lower Solutions Method for Darboux Problem for Fractional Order Implicit Impulsive Partial Hyperbolic Differential Equations

Saïd AbbasMouffak Benchohra — 2012

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we investigate the existence of solutions for the initial value problems (IVP for short), for a class of implicit impulsive hyperbolic differential equations by using the lower and upper solutions method combined with Schauder’s fixed point theorem.

Fractional order impulsive partial hyperbolic differential inclusions with variable times

Saïd AbbasMouffak BenchohraLech Górniewicz — 2011

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Fractional integro-differential inclusions with state-dependent delay

Khalida AissaniMouffak BenchohraKhalil Ezzinbi — 2014

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Semilinear Functional Differential Equations of Fractional order with State-Dependent Delay

Mouffak BenchohraOmar BennihiKhalil Ezzinbi — 2013

Commentationes Mathematicae

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 α -resolvent family is the main tool in our analysis.

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