Showing papers by "Mouffak Benchohra published in 2018"

Caputo-Hadamard fractional differential equations in banach spaces

Abstract: Abstract This article deals with some existence results for a class of Caputo–Hadamard fractional differential equations. The results are based on the Mönch’s fixed point theorem associated with the technique of measure of noncompactness. Two illustrative examples are presented.

Existence of periodic solutions for nonlinear implicit Hadamard’s fractional differential equations

Abstract: In this paper, by applying the coincidence degree theory which was first introduced by Mawhin, we obtain an existence result for a class of problem for nonlinear implicit fractional differential equations (IFDE for short) with Hadamard fractional derivative. We present two examples to show the applicability of our results.

Coupled systems of Hilfer fractional differential inclusions in banach spaces

Abstract: This paper deals with some existence results in Banach spaces for Hilfer and Hilfer-Hadamard fractional differential inclusions. The main tools used in the proofs are Monch's fixed point theorem and the concept of a measure of noncompactness.

Implicit coupled Hilfer–Hadamard fractional differential systems under weak topologies

Abstract: In this article, we present some existence of weak solutions for a coupled system of implicit fractional differential equations of Hilfer–Hadamard type. Our approach is based on Monch’s fixed point theorem associated with the technique of measure of weak noncompactness.

Existence and Attractivity Results for Coupled Systems of Nonlinear Volterra–Stieltjes Multidelay Fractional Partial Integral Equations

Abstract: We are concerned with some existence and attractivity results of a coupled fractional Riemann–Liouville–Volterra–Stieltjes multidelay partial integral system. We prove the existence of solutions using Schauder’s fixed point theorem; then we show that the solutions are uniformly globally attractive.

Coupled Hilfer fractional differential systems with random effects

Abstract: This paper deals with some existence results for two classes of coupled systems of Hilfer and Hilfer–Hadamard random fractional differential equations. The main tool used to carry out our results is Itoh’s random fixed point theorem.

Periodic solutions for nonlinear fractional differential systems

Abstract: In this paper, we establish some existence and uniqueness results for periodic solutions for a class of fractional differential equations with the Caputo fractional derivative. The arguments are based upon the Banach contraction principle, and Schaefer’s fixed point theorem.

Existence and stability results for nonlocal initial value problems for differential equations with Hilfer fractional derivative

Abstract: In this paper, we establish sufficient conditions for the existence and stability of solutions for a class of nonlocal initial value problems for differential equations with Hilfer's fractional derivative, The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results.

Semilinear fractional order integro-differential inclusions with infinite delay

Abstract: Abstract In this paper, we study the existence of mild solutions for a class of semilinear fractional order integro-differential inclusions with infinite delay in Banach spaces. Sufficient conditions for the existence of solutions are derived by using a nonlinear alternative of Leray–Schauder type for multivalued maps due to Martelli. An example is given to illustrate the theory.

Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces

Abstract: Abstract 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.

Coupled Pettis-Hadamard Fractional Differential Systems with Retarded and Advanced Arguments

Abstract: In this study, we present some results concerning the existence of weak solutions for some coupled systems of Hadamard fractional differential equations involving the both retarded and advanced arguments. Our results are obtained by using fixed point theory and the technique of measure of weak noncompactness.

Some existence results and stability concepts for partial fractional random integral equations with multiple delay

Abstract: Abstract In this paper, we present some results concerning the existence and the stability of solutions for some functional integral equations of Riemann–Liouville fractional order with random effects and multiple delay, by applying a random fixed point theorem with stochastic domain and the measure of noncompactness.

Measure of Noncompactness and Partial Functional Differential Equations with State-Dependent Delay

Abstract: Our aim in this work is to study the existence of solutions of first and second order functional differential equations with state-dependent delay. We use the Monch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness.

On a System of Volterra Type Hadamard Fractional Integral Equations in Fréchet Spaces

Abstract: In this article we present some results concerning the existence of solutions for a system of Hadamard integral equations. Our investigation is conducted with an application of an extension of the fixed point theorem of Burton-Kirk in Frechet spaces.