Résumé: This paper deals with a fractional boundary value problem involving variable delays. Sufficient conditions for the existence of a unique solution are investigated. Moreover the stability of the unique solution is discussed. A numerical example that emphasizes the importance of the results obtained in this article is also included.

Résumé: In this paper, we apply the reproducing kernel Hilbert space method (RKHSM) for solving third order differential equations with multiple characteristics in a rectangular domain. The exact solution is expressed in a series form. The numerical examples are given to demonstrate the good performance of the presented method. The results obtained indicate that the method is simple and effective.

Résumé: In this paper, we study the existence of positive solutions in a Sobolev space for a Reimann Liouville fractional boundary value problem. The main tools are the lower and upper solutions method and Schauder fixed point theorem. A numerical example is given to illustrate the obtained results.

Résumé: In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, we apply the Schaefer’s fixed point theorem. Furthermore, we present the Lyapunov inequality for the corresponding problem.

Résumé: In this paper we shall use the upper and lower solutions method to prove the existence of at least one solution for the second order equation defined on unbounded intervals with integral conditions on the boundary: \begin{equation*} u^{\prime \prime }\left( t\right) -m^{2}u\left( t\right) +f( t,e^{-mt}u\left( t\right) ,e^{-mt}\,u^{\prime }\left( t\right)) =0,\quad \mbox{for all}\;t\in % \left[ 0,+\infty \right) , \end{equation*} \begin{equation*} u\left( 0\right) -\frac{1}{m}u^{\prime }\left( 0\right) =\int\limits_{0}^{+\infty }e^{-2ms}u\left( s\right) ds,\underset{% t\rightarrow +\infty }{\lim }{\left\{e^{-mt}u\left( t\right) \right\}} =B, \end{equation*}% where $m>0,m\neq \frac{1}{6},B\in \mathbb{R}$ and $f:\left[ 0,+\infty \right) \times \mathbb{R}^{2}\rightarrow \mathbb{R} $ is a continuous function satisfying a suitable locally $L^1$ bounded condition and a kind of Nagumo's condition with respect to the first derivative.

Résumé: The main objective of this paper is to prove the existence of solutions for a fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo fractional derivatives. The proofs are based on the upper and lower solutions method and Schauder’s fixed point theorem. The paper is ended by a numerical example.

Résumé: This paper is devoted to the study of a nonlinear Euler-Bernoulli Beam type equation involving both left and right Caputo fractional derivatives. Differently from the approaches of the other papers where they established the existence of solution for the linear Euler-Bernoulli Beam type equation numerically, we use the lower and upper solutions method with some new results on the monotonicity of the right Caputo derivative. Furthermore, we give the explicit expression of the upper and lower solutions. A numerical example is given to illustrate the obtained results.

Résumé: The aim of this paper is the study of a multipoint boundary value problem for second order differential equations in both regular and singular cases. The main tools are upper and lower solutions method and Schauder’s fixed point theorem.

Résumé: In this paper, we establish a new Lyapunov-type inequality for a differential equation involving left Riemann-Liouville and right Caputo fractional derivatives subject to Dirichlet-type boundary conditions.

Résumé: The aim of this paper is the study of a nonlinear fractional Euler–Lagrange type equation with a nonlocal condition by means of lower and upper solutions method. For this purpose, we begin by solving an auxiliary problem by using Laplace transform, then we convert the posed problem to an equivalent right Caputo fractional differential equation with a vanishing terminal boundary condition. After constructing the lower and upper solutions, we define a sequence of modified problems that we solve by Schauder fixed point theorem. Finally, two numerical examples are given to illustrate the obtained results.

Résumé: We derive a new Lyapunov type inequality for a boundary value problem involving both left Riemann–Liouville and right Caputo fractional derivatives in presence of natural conditions. Application to the corresponding eigenvalue problem is also discussed.

Résumé: The aim of this paper is to discuss the existence and localization of solutions for a generalized Emden-Fowler equation involving a conformable derivative and with a Dirichlet boundary condition. Our approach is based on the lower and upper solutions method and Schauder fixed-point theorem under a Nagumo condition.

Résumé: This paper is devoted to the study of a Riemann-Liouville fractional boundary value problem on an unbounded inteval. The problem is assumed to be at resonance and the boundary conditions are of nonlocal type. We obtain some existence results for the maximal and minimal solutions by means of a fixed point theorem for an increasing operator and lower and upper solutions.

Résumé: This paper is devoted to the study of a Riemann-Liouville fractional boundary value problem on an unbounded inteval. The problem is assumed to be at resonance and the boundary conditions are of nonlocal type. We obtain some existence results for the maximal and minimal solutions by means of a fixed point theorem for an increasing operator and lower and upper solutions.

Résumé: In this paper, we establish sufficient conditions for the existence of positive solutions for a class of higher order Riemann–Liouville fractional initial value problems. First, we construct an appropriate Banach space and prove the equivalence between the posed problem and the associated Volterra integral equation, then by means of Guo–Krasnoselskii fixed point theorem, we investigate the existence of at least one positive solution under sublinearity conditions.

Résumé: In this paper, we study a boundary value problem at resonance with a multi-integral boundary conditions. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin. An example is given to show the effectiveness of our results.

Résumé: In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann-Liouville and right Caputo-type fractional derivatives. For this, we convert the posed problem to a sum of two integral operators, then we apply Krasnoselskii’s fixed point theorem to conclude the existence of nontrivial solutions.

Résumé: In this paper, we use fixed point theorems to prove the existence and uniqueness of solution for a nonlinear fractional system with boundary conditions. At the end we present two examples illustrating the obtained results.

Résumé: Some results regarding the existence of solutions for a nonlinear higher order fractional differential equation involving both the left Riemann-Liouville and the right Caputo fractional derivatives with a natural boundary condition are obtained. The results presented in this paper are based on the method of upper and lower solutions and the monotonicity of the right Caputo derivative. Moreover, we give the explicit expression of the lower and upper solutions. Two illustrative numerical examples are also provided.

Résumé: We consider a boundary value problem involving conformable derivative of order a, 1 < a < 2 and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's fixed-point theorem. Futhermore, we give the Lyapunov inequality for the corresponding problem.

Résumé: We derive a new Lyapunov type inequality for a boundary value problem involving both left Riemann–Liouville and right Caputo fractional derivatives in presence of natural conditions. Application to the corresponding eigenvalue problem is also discussed.

Résumé: This paper concerns the existence of solution to an oscillation equation involving Riemann-Liouville fractional derivative with initial conditions. The main tools for this study are the upper and lower solutions method and Schauder’s fixed point theorem. For this, we reduce the posed problem to a first order ordinary initial value problem, then we give an explicit expression for the upper and lower solutions. The obtained results are illustrated by an example.

Résumé: This paper is devoted to the study of existence of solutions for two point boundary value problems (P1) for fractional differential equations of arbitrary order q ≥ 2, by applying upper and lower solutions method together with Schauder’s fixed point Theorem. First, we transform the posed problem to an ordinary first order initial value problem, that we modify to prove the existence of solutions for the problem (P1), moreover we give the explicit expression of the upper and lower solutions of problem (P1). The obtained results are illustrated by some examples.

Résumé: In this paper, we study a nonlinear higher order fractional differential equation with initial and integral conditions. By constructing the lower and upper solutions and applying the Schauder fixed point theorem, we prove the existence of positive solutions.

Résumé: In this paper, we focus on the solvability of a fractional boundary value problem at resonance on an unbounded interval. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin. The obtained results are illustrated by an example.

Résumé: We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the problem into an equivalent lower order fractional boundary value problem followed by the use of an upper and lower solutions method. To succeed with such approach, we first prove a result on the monotonicity of the right Caputo derivative.

Résumé: In this paper, we study the existence of positive solutions for a class of multi-order systems of fractional differential equations with nonlocal conditions. The main tool used is Schauder fixed point theorem and upper and lower solutions method. The results obtained are illustrated by a numerical example.

Résumé: This paper concerns the existence of solution to an initial fractional problem of arbitrary order. The main tools for this study are the lower ad upper solutions method and Schauder’s fixed point Theorem.

Résumé: This paper is devoted to the study of existence of solutions for two point boundary value problems (P1) for fractional differential equations of arbitrary order q ≥ 2, by applying upper and lower solutions method together with Schauder’s fixed point Theorem. First, we transform the posed problem to an ordinary first order initial value problem, that we modify to prove the existence of solutions for the problem (P1), moreover we give the explicit expression of the upper and lower solutions of problem (P1). The obtained results are illustrated by some examples

Résumé: This paper investigates the existence and uniqueness of solution for a class of nonlinear fractional differential equations of fractional order in arbitrary time scales. The results are established using extensions of Krasnoselskii-Krein, Rogers, and Kooi conditions.

Résumé: This paper concerns the solvability of a nonlinear fractional boundary value problem at resonance. By using fixed point theorems we prove that the perturbed problem has a solution, then by some ideas from analysis we show that the original problem is solvable. An example is given to illustrate the obatined results.

Résumé: In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for a class of higher order Caputo fractional initial value problem. We transform the posed problem to a Volterra integral equation. Under Krasnoselskii-Krein type conditions and by using successive approximations, we discuss the existence and uniqueness questions.

Résumé: We apply the reproducing kernel Hilbert space (RKHS) method for getting analytical and approximate solutions for second-order hyperbolic integrodifferential equations with a weighted integral condition. The analytical solution is represented in the form of series; thus, the n-terms approximate solutions are obtained. The results of the numerical examples are compared with the exact solutions to illustrate the accuracy and the effectivity of this method.

Résumé: We apply the reproducing kernel Hilbert space (RKHS) method for getting analytical and approximate solutions for second-order hyperbolic integrodifferential equations with a weighted integral condition. The analytical solution is represented in the form of series; thus, the n-terms approximate solutions are obtained. The results of the numerical examples are compared with the exact solutions to illustrate the accuracy and the effectivity of this method.

Résumé: We apply the reproducing kernel Hilbert space (RKHS) method for getting analytical and approximate solutions for second-order hyperbolic integrodifferential equations with a weighted integral condition. The analytical solution is represented in the form of series; thus, the n-terms approximate solutions are obtained. The results of the numerical examples are compared with the exact solutions to illustrate the accuracy and the effectivity of this method.

Résumé: Our aim in this work is to study the existence of solutions for a fractional Lidstone boundary value problems. We use some fixed point theorems to show the existence and uniqueness of solution under suitable conditions. Two examples are given to ilustrate the obtained results.

Résumé: Our aim in this work is to study the existence of solutions for a fractional Lidstone boundary value problems. We use some fixed point theorems to show the existence and uniqueness of solution under suitable conditions. Two examples are given to ilustrate the obtained results.

Résumé: This paper deals with a second order boundary value problem withonly integrals conditions. Our aim is to give new conditions on the nonlinearterm; then, using Banach contraction principle and Leray Schauder nonlinearalternative, we establish the existence of nontrivial solution of the consideredproblem. As an application, some examples to illustrate our results are given

Résumé: In this work, we study a telegraph integro-differential equation with a weighted integral condition. By means of the Galerkin method, we establish the existence and uniqueness of a generalized solution.

Résumé: This work is devoted to the study of uniqueness and existence of positive solutions for a second-order boundary value problem with integral condition. The arguments are based on Banach contraction principle, Leray Schauder nonlinear alternative, and Guo-Krasnosel’skii fixed point theorem in cone. Two examples are also given to illustrate the main results.

Résumé: This work is devoted to the study of uniqueness and existence of positive solutions for a second-order boundary value problem with integral condition. The arguments are based on Banach contraction principle, Leray Schauder nonlinear alternative, and Guo-Krasnosel’skii fixed point theorem in cone. Two examples are also given to illustrate the main results.

Résumé: This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.

Résumé: We consider a third-order three-point boundary value problem. We introduce a generalized polynomial growth condition to obtain the existence of a nontrivial solution by using Leray-Schauder nonlinear alternative, then we give an example to illustrate our results.

Résumé: In this paper we study the fractional boundary value problem cDq0+u(t)=f(t,u(t)),0

Résumé: Using Banach contraction principle and Leray–Schauder nonlinear alternative we establish sufficient conditions for the existence and uniqueness of solutions for boundary value problems for fractional differential equations with fractional integral condition, involving the Caputo fractional derivative. Some examples are given to illustrate our results.

Résumé: The aim of this paper is the study of the existence and uniqueness of solutions for a two-point fractional boundary value problem, by means of Banach contraction principle and Leray Schauder nonlinear alternative. Some examples are given.

Résumé: We investigate the asymptotic behaviour of Lp extremal polynomials for p > 0 on the unit circle plus a denumerable set of mass points, with only Szegő’s condition imposed on the absolute part of the measure.

Résumé: This paper deals with a third‐order three‐point boundary value problem. By using Leray Schauder nonlinear alternative, we establish the existence of a nontrivial solution, then we give some examples to illustrate our results.

Résumé: This paper deals with a third‐order three‐point boundary value problem. By using Leray Schauder nonlinear alternative, we establish the existence of a nontrivial solution, then we give some examples to illustrate our results.

Résumé: We study the asymptotic behavior of Lp(σ) extremal polynomials with respect to a measure of the form σ=α+γ, where α is a measure concentrated on a rectifiable Jordan curve in the complex plane and γ is a discrete measure concentrated on an infinite number of mass points.

Résumé: We study the strong asymptotics of orthogonal polynomials with respect to a measure of the type dμ/2π+∑j=1∞Ajδ(z−zk), where μ is a positive measure on the unit circle Γ satisfying the Szegö condition and {zj}j=1∞ are fixed points outside Γ. The masses {Aj}j=1∞ are positive numbers such that ∑j=1∞Aj<+∞. Our main result is the explicit strong asymptotic formulas for the corresponding orthogonal polynomials.

Résumé: We study the asymptotic behavior of orthogonal polynomials. The measure is concentrated on a complex rectifiable arc and has an infinity of masses in the region exterior to the arc.