Journal Articles

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Open Access
ADAPTED SOLUTION WITH NEWTON-KANTOROVICH METHOD FOR NONLINEAR VOLTERRA INTEGRAL EQUATIONS
(Université de M'sila, 2018) AMINA, KHIRANI
Find an approximate solution is one of the most important problems in our days, in this paper we look for an approximate solution for Volterra nonlinear integral equation using a combination between Newton-Kantorovich method and adapted trapezoidal method. Then we do a comparaison between the numerical results obtained by this method against ones obtained by another authors.
Open Access
ANALYSIS OF A DYNAMIC ELASTO-VISCOPLASTIC FRICTIONLESS ANTIPLAN CONTACT PROBLEM WITH NORMAL COMPLIANCE
(Université de M'sila, 2021) OURAHMOUN ABBES
We consider a mathematical model which describes the dynamic evolution of a thermo elasto viscoplastic contact problem between a body and a rigid foundation. The mechanical and thermal properties of the obstacle coating material near its surface. A variational formulation of this dynamic contact phenomenon is derived in the context of general models of thermo elasto viscoplastic materials. The displacements and temperatures of the bodies in contact are governed by the coupled system consisting of a variational inequality and a parabolic differential equation. The proof is based on a classical existence and uniqueness result on parabolic inequalities,differential equations and fixed point arguments
Open Access
Anisotropic non-local problems: asymptotic behaviour and existence results
(Université de M'sila, 2021) Ahlem Yahiaoui; Senoussi Guesmia; Abdelmouhcene Sengouga
We deal with anisotropic singular perturbation problems in some weighted spaces of Sobolev type. The perturbed problems are elliptic, semi-linear and non-local. Using a variational approach, we establish the existence of their solutions as critical points of some C1- functionals. Besides, we study the asymptotic behaviour of these solutions with respect to the parameter of perturbation ε and, as ε → 0, we obtain existence results for some non-standard integrodifferential problems. A non-local eigenvalue problem related to the considered problems is also investigated and used to carry out this study.
Open Access
ANISOTROPIC SINGULAR PERTURBATIONS OF VARIATIONAL INEQUALITIES
(Université de M'sila, 2018-02) Sengouga, Abdelmouhcene; Guesmia, Senoussi; Michel, Chipot
We consider variational inequalities involving the p{ Laplace operator with anisotropic singular perturbations where the convex set, on which the problem is de ned, is also subject to perturbations. This leads to introduce a new convergence of sets, in some suitable sense, conceived from the Mosco convergence and matching well to the anisotropic singular perturbations. Convergence results and their rates are established. In order to illustrate the introduced convergence sets, obstacle and elasto-plastic perturbed problems are dealt with. This allows to go deeper in the analysis of the suggested convergence on concrete sets in Sobolev spaces.
Open Access
Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica XX (2021)
(2021) Farid Nouioua; Bilal Basti
This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation
Open Access
Boundary Control and Stabilization of an Axially Moving Viscoelastic String under a Boundary Disturbance
(Université de M'sila, 2017) Abdelkarim Kelleche
In this paper, we consider a system modelling an axially moving vis- coelastic string subject to an unknown boundary disturbance. It is controlled by a hydraulic touch-roll actuator at the right boundary which is capable of suppressing the transverse vibrations that occur during the movement of the string. The mul- tiplier method is employed to design a robust boundary control law to ensure the reduction of the transvesre vibrations of the string.
Open Access
BOUNDARY VALUE PROBLEM FOR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS
(Université de M'sila, 2017) Arioua, Yacine; Benhamidouche, Nouredine
The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain. We used the standard and Krasnoselskii’s fixed point theorems. Some new results of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained.
Open Access
CLASSIFICATION OF ELEMENTS IN ELLIPTIC CURVE OVER THE RING F
(Université de M'sila, 2022) Bilel Selikh; Douadi Mihoubi
Let Fq["] := Fq[X]/(X4 − X3) be a finite quotient ring where "4 = "3, with Fq is a finite field of order q such that q is a power of a prime number p greater than or equal to 5. In this work, we will study the elliptic curve over Fq["], "4 = "3 of characteristic p 6= 2, 3 given by homogeneous Weierstrass equation of the form Y 2Z = X3 + aXZ2 + bZ3 where a and b are parameters taken in Fq["]. Firstly, we study the arithmetic operation of this ring. In addition, we define the elliptic curve Ea,b(Fq["]) and we will show that E 0(a), 0(b)(Fq) and E 1(a), 1(b)(Fq) are two elliptic curves over the finite field Fq, such that 0 is a canonical projection and 1 is a sum projection of coordinate of element in Fq["]. Precisely, we give a classification of elements in elliptic curve over the finite ring Fq["].
Open Access
Commutator estimates for vector fields on variable Triebel–Lizorkin spaces
(Université de M'sila, 2022) Ben Mahmoud Salah
In this paper we present a bilinear estimate for commutators on Triebel–Lizorkin spaces with variable smoothness and integrability, and under no vanishing assumptions on the divergence of vector fields.
Open Access
COMPARISON BETWEEN TAYLOR AND PERTURBED METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE FIRST KIND
(Université de M'sila, 2020) Noui Djaidja; Mostefa Nadir
As it is known the equation A' = f with injective compact oper- ator has a unique solution for all f in the range R(A):Unfortunately, the right- hand side f is never known exactly, so we can take an approximate data f and used the perturbed problem ' + A' = f where the solution ' depends continuously on the data f ; and the bounded inverse operator ( I + A)􀀀1 approximates the unbounded operator A􀀀1 but not stable. In this work we obtain the convergence of the approximate solution of ' of the perturbed equation to the exact solution ' of initial equation provided tends to zero with p :
Open Access
COMPOSITIONS OF TERNARY RELATIONS
(Université de M'sila, 2021) Norelhouda Bakri; Lemnaouar Zedam; Bernard De Baets
In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension
Open Access
CONTINUITY OF THE FREE BOUNDARY IN ELLIPTIC PROBLEMS WITH NEUMAN BOUNDARY CONDITION
(Université de M'sila, 2015) SAADI, ABDERACHID
We show the continuity of the free boundary in a class of two dimensional free boundary problems with Neuman boundary condition, which includes the aluminium electrolysis problem and the heterogeneous dam problem with leaky boundary condition
Open Access
Corporis excepturi qui quidem facilis maxime odio.
(sint neque dolorem, 2020-02-27) Renard, Neal
Aliquam ut doloribus nesciunt esse. At iusto sit eveniet et molestiae ipsam et. At omnis officia. Nemo laboriosam eum sed. Facilis neque dolor. Aut facere nihil occaecati exercitationem ex aliquid qui et nesciunt. Voluptate repellendus est cum. Sed ut qui doloremque soluta ut ab. Provident qui possimus. Corporis quia dolor magni est quia. Deleniti aut unde hic ut ipsam quis vitae unde error. Quia suscipit vitae facilis. Ut ipsum aliquam expedita magni. Quia eos qui explicabo sunt reprehenderit non voluptatem. Quidem doloribus cum optio libero. Magnam optio dolor deleniti necessitatibus ipsum vel officia ipsa voluptas.
Open Access
Dominated multilinear operators defined on tensor products of Banach spaces
(Université de M'sila, 2022) Athmane Ferradi; Lahcene Mezrag
In this paper, we introduce and study new classes of dominated multilinear operators, which we call ðp; p1; . . .; pn;G1; . . .;GnÞ-dominated and ð ~ p; p1; . . .; pn;G1; . . .;GnÞ-dominated multilinear operators defined on the tensor product of Banach spaces. Some characterizations of this type of operators are given and we prove some important coincidence results. As an application, we characterize ðp; p1; . . .; pnÞ-dominated multilinear operators on CðK;GÞ and ðp; p1; . . .; pnÞdominated multilinear operators in the sense of Dinculeanu on CðK;GÞ, where K is a compact Hausdorff space and G a Banach space. We also treat the connection between an operator T and its associated operators Tt; T~ and T# for certain classes
Open Access
An efficient algorithm for solving the conformable time-space fractional telegraph equations
(Université de M'sila, 2021) ABDELKEBIR, Saad
In this paper, an efficient algorithm is proposed for solving one dimensional time-space-fractional telegraph equations. The fractional derivatives are described in the conformable sense. This algorithm is based on shifted Chebyshev polynomials of the fourth kind. The time-space fractional telegraph equations is reduced to a linear system of second order differential equations and the Newmark’s method is applied to solve this system. Finally, some numerical examples are presented to confirm the reliability and effectiveness of this algorithm.
Open Access
Efficient spectral-collocation methods for a class of linear Fredholm integro-differential equations on the half-line
(Université de M'sila, 2021) Soufiane Benyoussef
In this paper, an extension of the Legendre spectral collocation method has been proposed for the numerical solution of a class of linear Fredholm integro-differential equation on the half-line. The properties of mapped Legendre functions are first presented. These properties together with the Legendre–Gauss points are then utilized to reform the Fredholm integro-differential equation in semi-infinite interval into a singular equation in finite interval and to reduce it to the solution of a simple matrix equation. Besides, in order to show the efficiency and accuracy of the proposed method, some numerical examples are considered and solved through a survey of three approaches, namely: Exponential, rational and logarithmic Legendre functions collocation methods. Furthermore, a comparison of the results, shows that using exponential functions, leads to more accurate results and faster convergence.
Open Access
ESSENTIAL APPROXIMATE POINT AND ESSENTIAL DEFECT SPECTRUM OF A SEQUENCE OF LINEAR OPERATORS IN BANACH SPACES
(Université de M'sila, 2019) TOUFIK, HERAIZ
This paper is devoted to an investigation of the relationship between the essential approximate point spectrum (respectively, the essential defect spectrum) of a sequence of closed linear operators (Tn)n2N on a Banach space X, and the essential approximate point spectrum (respectively, the essential defect spectrum) of a linear operator T on X, where (Tn)n2N converges to T, in the case of convergence in generalized sense as well as in the case of the convergence compactly
Open Access
Existence And Uniqueness Of Solution For A Mixed-Type Fractional Di§erential Equation And Ulam-Hyers Stability
(2021) Nora Ouagueni; Yacine Arioua
In this paper, we have discussed a special type of nonlinear boundary value problems (BVPs) which involves both the right-sided Caputo-Katugampola (CK) and the left-sided Katugampola fractional deriv atives (FDs). Based on some new techniques and some properties of the Mittag-Le er functions, we have introduced a formula of the solution for the aforementioned problem. To study the existence and uniqueness results of the solution for this problem, we have applied some known Öxed point theorems (i.e., Banachís contraction principle, Schauderís Öxed point theorem, nonlinear alternative of Leray-Schauder type and Schaeferís Öxed point theorem). We have also studied the Ulam-Hyers stability of this problem. To illustrate the theoretical results in this work, we have given two examples.
Open Access
Existence of traveling wave solutions for a free boundary problem of higher-order space-fractional wave equations∗
(université msila, 2021) Rabah Djemiat; Bilal Basti; Noureddine Benhamidouche
The fractional wave equation of higher order is presented as a generalization of the higher-order wave equation when arbitrary fractional-order derivatives are involved. This paper investigates the problem of existence and uniqueness of solutions under the traveling wave forms for a free boundary problem of higher-order space-fractional wave equations. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.
Open Access
EXISTENCE RESULTS FOR A SUBLINEAR SECOND ORDER DIRICHLET BOUNDARY VALUE PROBLEM ON THE HALF-LINE
(Université de M'sila, 2021) Dahmane Bouafia; Toufik Moussaoui
In this paper we study the existence of nontrivial solutions for a boundary value problem on the half-line, where the nonlinear term is sublinear, by using Ekeland’s variational principle and critical point theory