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Faouzi Haddouchi

Publications and source records attributed to Faouzi Haddouchi.

At least 19 recordsLinked to original sources
arXiv2023

Solvability of a sixth-order boundary value problem with multi-point and multi-term integral boundary conditions

This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii-Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two examples are included to show the applicability of our main results.

math.CA↗
arXiv2023

Existence and stability results for a sequential $ψ$-Hilfer fractional integro-differential equations with nonlocal boundary conditions

This paper deals with the existence and uniqueness of solutions for a nonlinear boundary value problem involving a sequential $ψ$-Hilfer fractional integro-differential equations with nonlocal boundary conditions. The existence and uniqueness of solutions are established for the considered problem by using the Banach contraction principle, Sadovski's fixed point theorem, and Krasnoselskii-Schaefer fixed point theorem due to Burton and Kirk. In addition, the Ulam-Hyers stability of solutions is discussed. Finally, the obtained results are illustrated by examples.

math.AP↗
arXiv2021

Existence results for a generalized fractional boundary value problem in $b$-metric space

This paper is concerned with a class of nonlinear boundary value problem involving fractional derivative in the $φ$-Riemann-Liouville sense. Some Properties of the Green's function for this problem are mentioned. By means of the Banach contraction principle in $b$-metric space and the technique of the $γ$-$ψ$- Geraghty contractive maps, existence and uniqueness results are obtained. Two examples are given to support the theoretical results.

math.CA↗
arXiv2020

Positive solutions of nonlocal fractional boundary value problem involving Riemann-Stieltjes integral condition

In this paper, we investigate the existence of positive solutions for a nonlocal fractional boundary value problem involving Caputo fractional derivative and nonlocal Riemann-Stieltjes integral boundary condition. By using the spectral analysis of the relevant linear operator and Gelfand's formula, we obtain an useful upper and lower bounds for the spectral radius. Our discussion is based on the properties of the Green's function and the fixed point index theory in cones.

math.CA↗
arXiv2019

Positive solutions of $p$-Laplacian fractional differential equations with fractional derivative boundary condition

In this paper, we show some results about the existence and the uniqueness of the positive solution for a $p$-Laplacian fractional differential equations with fractional derivative boundary condition. Our results are based on Krasnosel'skii's fixed point theorem, the nonlinear alternative of Leray-Schauder type and contraction mapping principle. Three examples are given to illustrate the applicability of our main results.

math.CA↗
arXiv2019

Existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions and a parameter

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of the Green's function and the fixed point theorem in a cone, we obtain some existence results of positive solution. we also provide some examples to illustrate our results.

math.CA↗
arXiv2018

On the existence and uniqueness of solution for fractional differential equations with nonlocal multi-point boundary conditions

This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our analysis relies on the Banach contraction principle, Boyd and Wong fixed point theorem, Leray-Schauder nonlinear alternative. Finally, examples are provided to illustrate our main results.

math.CA↗
arXiv2018

Existence results for a class of Caputo type fractional differential equations with Riemann-Liouville fractional integrals and Caputo fractional derivatives in boundary conditions

In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our results are based on some known tools of fixed point theory. Finally, some illustrative examples are included to verify the validity of our results.

math.CA↗
arXiv2017

A note on existence results for a nonlinear fourth-order integral boundary value problem

In this short note, we present some new existence results for a nonlinear fourth-order two-point boundary value problem with integral condition. The existence results are obtained by using the Leray-Schauder fixed point theorem. Our work improves the main results of Benaicha and Haddouchi \cite% {Benai}. In addition, examples are included to show the validity of our results.

math.CA↗
arXiv2016

Remarks on the Periodic Boundary Value Problems for Nonlinear Second Order Ordinary Differential Equations

This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $α$ and $β$ violate the boundary conditions $ α(0)=α(2π)$ and $β(0)=β(2π)$. We present several comparison results. We show that the method of lower and upper solutions coupled with the monotone iterative technique is valid to obtain constuctive proof of existence of solutions.

math.CA↗
arXiv2016

Positive solutions of a nonlinear three-point eigenvalue problem with integral boundary conditions

In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+λa(t)f(u(t))=0,\ \ 0 0$ is a parameter, $0<η<1$, $0<α< \frac{1}{η}$. By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

math.CA↗
arXiv2015

Positive solutions of a nonlinear three-point boundary value problem with integral boundary conditions

In this paper, by using Krasnoselskii's fixed point theorem in a cone, we study the existence of single and multiple positive solutions to the three-point integral boundary value problem (BVP) \begin{equation*} \label{eq-1} \begin{gathered} {u^{\prime \prime}}(t)+a(t)f(u(t))=0, 0<t<T, u^{\prime}(0)=0, \ u(T)=α\int_{0}^ηu(s)ds, \end{gathered} \end{equation*} where $0<η<T$, $0<α< \frac{1}{η}$, are given constants.

math.CA↗
arXiv2014

Existence of positive solutions for a three-point integral boundary-value problem

In this paper, by using the Krasnosel'skii's fixed-point theorem, we study the existence of at least one or two positive solutions to the three-point integral boundary value problem {equation*} \label{eq-1} {gathered} {u^{\prime \prime}}(t)+a(t)f(u(t))=0,\ 0<t<T, u(0)=βu(η),\ u(T)=α\int_{0}^ηu(s)ds, {gathered} {equation*} where $0<η<T$, $0<α< \frac{2T}{η^{2}}$, $0\leqβ<\frac{2T-αη^{2}}{αη^{2}-2η+2T}$ are given constants.

math.CA↗
arXiv2014

On the output stabilizability of the diffusion equation

This note is devoted to study the output stabilizability of a simplified and a one-dimensional diffusion equation. Necessary and sufficient conditions for the system to be output stabilizable will be given. These conditions are given in terms of the eigenvalues of the infinitesimal generator and the Fourier coefficients of input and output operators.

math.OC↗
arXiv2014

A generalized result of output stabilizability

Output stabilizability of a class of infinite dimensional linear systems is studied in this paper. A criterion for the system to be output stabilizable by a linear bounded feedback $u=Fx$, $F\in L(Z,\mathbb{R}^{^{p}})$ will be given.

math.OC↗