Search results for: Assia Guezane-Lakoud

Items from 1 to 8 out of 8 results

article

Lyapunov-type inequality for a fractional boundary value problem with natural conditions

Assia Guezane-Lakoud, Rabah Khaldi, Delfim F. M. Torres

SeMA Journal > 2018 > 75 > 1 > 157-162

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.

article

Positive Solutions for Higher-Order Nonlinear Fractional Differential Equations

Abdourazek Souahi, Assia Guezane-Lakoud, Amara Hitta

Vietnam Journal of Mathematics > 2017 > 45 > 3 > 441-450

This paper investigates the existence of positive solutions for a class of higher-order nonlinear fractional differential equations with initial conditions given for ordinary as well as fractional derivatives of the unknown function. We assume that the nonlinear term f involves also derivatives of fractional order. The results are established by converting the problem into an equivalent integral equation...

article

Positive solutions for an oscillator fractional initial value problem

Amar Chidouh, Assia Guezane-Lakoud, Rachid Bebbouchi

Journal of Applied Mathematics and Computing > 2017 > 54 > 1-2 > 57-68

In this paper, we will study a fractional initial value problem. By using Laplace transform, we obtain an equivalent fixed point problem, that is a Volterra integral equation involving the generalized Mittag-Leffler function in the kernel. The existence results are obtained by some fixed point theorems.

article

Positive Solutions for a System of Fractional Differential Equations with Nonlocal Integral Boundary Conditions

Assia Guezane-Lakoud, Allaberen Ashyralyev

Differential Equations and Dynamical Systems > 2017 > 25 > 4 > 519-526

In this paper, we discuss by means of a fixed point theorem, the existence of positive solutions of a system of nonlinear Caputo fractional differential equations with integral boundary conditions. An example is given to illustrate the main results.

article

Existence and localization of positive solutions for a fractional boundary value problem at resonance

Samia Kouachi, Assia Guezane-Lakoud, Fateh Ellagoune

Advances in Difference Equations > 2015 > 2015 > 1 > 1-9

We investigate the existence of positive solutions for a fractional boundary value problem at resonance. By means of a fixed point theorem of increasing operators, the minimal and maximal nonnegative solutions for the problem are obtained.

article

Full discretization of wave equation

Abderrazak Chaoui, Fateh Ellaggoune, Assia Guezane-Lakoud

Boundary Value Problems > 2015 > 2015 > 1 > 1-11

Rothe’s method for time discretization and Crouseix-Raviart nonconforming finite element method to the spatial variable. After introducing error estimators, we prove the equivalence between the error and its indicators.

article

Unbounded solution for a fractional boundary value problem

Assia Guezane-Lakoud, Adem Kılıçman

Advances in Difference Equations > 2014 > 2014 > 1 > 1-15

This paper concerns the existence of unbounded positive solutions of a fractional boundary value problem on the half line. By means of the properties of the Green function and the compression and expansion fixed point theorem (Kwong in Fixed Point Theory Appl. 2008:164537, 2008), sufficient conditions are obtained to guarantee the existence of a solution to the posed problem. MSC: 26A33, 34B15, 34B27.

article

Rothe-Galerkin's method for a nonlinear integrodifferential equation

Abderrazek Chaoui, Assia Guezane-Lakoud

Boundary Value Problems > 2012 > 2012 > 1 > 1-15

In this article we propose approximation schemes for solving nonlinear initial boundary value problem with Volterra operator. Existence, uniqueness of solution as well as some regularity results are obtained via Rothe-Galerkin method. Mathematics Subject Classification 2000: 35k55; 35A35; 65M20.

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Keywords

FIXED POINT THEOREM (3)
INTEGRAL CONDITION (2)
POSITIVE SOLUTION (2)
A POSTERIORI ESTIMATE (1)
A PRIORI ESTIMATE (1)
BOUNDARY VALUE PROBLEM (1)
CAPUTO DERIVATIVE (1)
CROUSEIX-RAVIART NONCONFORMING FINITE ELEMENT METHOD (1)
EIGENVALUE PROBLEM (1)
EXISTENCE OF SOLUTION (1)
FIXED POINT THEOREM GUO–KRASNOSELSKII (1)
FRACTIONAL BOUNDARY VALUE PROBLEM (1)
FRACTIONAL CALCULUS (1)
FRACTIONAL CAPUTO DERIVATIVE (1)
FRACTIONAL DERIVATIVE (1)
FRACTIONAL DIFFERENTIAL EQUATION (1)
FRACTIONAL DIFFERENTIAL EQUATIONS (1)
GALERKIN METHOD (1)
GUO-KRASNOSEL’SKII FIXED POINT THEOREM (1)
INITIAL VALUE PROBLEM (1)
INTEGRODIFFERENTIAL EQUATION (1)
LAPLACE TRANSFORM (1)
LERAY-SCHAUDER NONLINEAR ALTERNATIVE (1)
LYAPUNOV INEQUALITY (1)
MITTAG-LEFFLER FUNCTION (1)
POSITIVE SOLUTIONS (1)
RESONANCE (1)
ROTHE'S METHOD (1)
ROTHE’S METHOD (1)
UNBOUNDED SOLUTION (1)
VOLTERRA INTEGRAL EQUATION (1)
WAVE EQUATION (1)
WEAK SOLUTION (1)
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Journal

Advances in Difference Equations (2)
Boundary Value Problems (2)
Differential Equations and Dynamical Systems (1)
Journal of Applied Mathematics and Computing (1)
SeMA Journal (1)
Vietnam Journal of Mathematics (1)

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