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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.

Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

Saïd AbbasEman AlaidarousWafaa AlbarakatiMouffak Benchohra — 2015

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

Saïd AbbasMouffak BenchohraMohamed Abdalla Darwish — 2016

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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

Fractional q -difference equations on the half line

Saïd AbbasMouffak BenchohraNadjet LaledjYong Zhou — 2020

Archivum Mathematicum

This article deals with some results about the existence of solutions and bounded solutions and the attractivity for a class of fractional q -difference equations. Some applications are made of Schauder fixed point theorem in Banach spaces and Darbo fixed point theorem in Fréchet spaces. We use some technics associated with the concept of measure of noncompactness and the diagonalization process. Some illustrative examples are given in the last section.

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

Saïd AbbasWafaa A. AlbarakatiMouffak BenchohraMohamed Abdalla DarwishEman M. Hilal — 2015

Annales Polonici Mathematici

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.

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

Abbas, SaïdBenchohra, Mouffak — 2010

Fractional Calculus and Applied Analysis

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.

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