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Item Open Access Weak Type Estimate of Singular Integral Operators on Variable Weak Herz–Type Hardy Spaces(2023) H. B. Boulares; D. Drihem; W. HebbacheThis paper is concerned with the boundedness properties of singular integral operators on variable weak Herz spaces and variable weak Herz-type Hardy spaces. Allowing our pa rameters to vary from point to point will raise extra difficulties, which, in general, are overcome by imposing regularity assump tions on these exponents, either at the origin or at infinity. Our results cover the classical results on weak Herz-type Hardy spaces with fixed exponentsItem Open Access REALIZATIONS OF THE HOMOGENEOUS BESOV-TYPE SPACES(2019) FARES BENSAID; MADANI MOUSSAIUsing the notion of realizations, we study the dilation commuting realizations of the homogeneous Besov-type spaces B˙ s,τ p,q (Rn), which are defined modulo polynomials of degree less than μ; the integer μ will be determined from the parameters n, s, p, q and τItem Open Access Existence And Uniqueness Of Solution For A Mixed-Type Fractional Di§erential Equation And Ulam-Hyers Stability(2021) Nora Ouagueni; Yacine AriouaIn 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.Item Open Access Global existence and blow-up of a Petrovsky equation with general nonlinear dissipative and source terms(université de msila, 2023) Mosbah Kaddour; Farid MesselmiThis work studies the initial boundary value problem for the Petrovsky equation with nonlinear damping ∂ 2u ∂t2 + ∆2 u − ∆u 0 + |u| p−2 u + αgItem Open Access Nonlinear Free Surface Flow past a Wedge in Channel(université de msila, 2023) Tahar BLIZAK; Abdelkader GASMI: In this paper, the two-dimensional problem of irrotational flow past a wedge located in the center of the channel is considered. Assuming that the fluid is incompressible and non-viscous, the influence of gravity is ignored but the surface tension is considered. The problem which is characterized by the nonlinear boundary conditions on the free surface of the unknown equation is solved numerically by the series truncation technique. The results show that for all given wedge configurations, there is a critical value for the Weber number, for which there is no solution for every Weber number value smaller than this. In addition, the obtained results extend the work done by Gasmi and Mekias [2]Item Open Access Exponential stability estimates for an axially travelling string damped at one end(université msila, 2023) Seyf Eddine Ghenimi; Abdelmouhcene SengougaWe study the small vibrations of an axially travelling string with a dashpot damping at one end. The string is modelled by a wave equation in a timedependent interval with two endpoints moving at a constant speed v. For the undamped case, we obtain a conserved functional equivalent to the energy of the solution. We derive precise upper and lower exponentially decaying estimates for the energy with explicit constants. These estimates do not seem to be reported in the literature even for the non-travelling case v = 0Item 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 BenhamidoucheThe 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.Item Open Access Variable Besov-type Spaces(Université de M'sila, 2022) Zouheyr ZEGHADIn this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the ϕ-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces. Moreover the Sobolev embeddings for these function spaces are obtainedItem Open Access On a conjecture of Heim and Neuhauser on some polynomials arising frommodular forms and related to Fibonacci polynomials(Université de M'sila, 2022) Yahia Zouareg; Moussa BenoumhaniHeim and Neuhauser investigated some polynomials related to the Dedekind function. They proved the log-concavity of these polynomials and conjectured that they have only real zeros. We prove this conjecture, and deduce some identities for Fibonacci numbers and determine the modes of another sequence related to Fibonacci polynomials.Item Open Access CLASSIFICATION OF ELEMENTS IN ELLIPTIC CURVE OVER THE RING F(Université de M'sila, 2022) Bilel Selikh; Douadi MihoubiLet 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["].Item Open Access Lipschitz p-lattice summing operators(Université de M'sila, 2022) A. Maamra; L. Mezrag; A. TallabIn this paper, we introduce and study the notion of Lipschitz p-lattice summing operators in the category of Lipschitz operators which generalizes the class of plattice summing operators in the linear case. Some interesting properties are given. Also, some connections with other classes of operators are presentedItem Open Access Dominated multilinear operators defined on tensor products of Banach spaces(Université de M'sila, 2022) Athmane Ferradi; Lahcene MezragIn 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 classesItem Open Access This paper deals with a boundary value problem for a nonlin- ear di erential equation with two conformable fractional derivatives and integral boundary conditions. The results of existence, uniqueness and stability of positive solutions are proved by using the Banach contrac- tion principle, Guo-Krasnoselskii's xed point theorem and Hyers-Ulam type stability. Two concrete examples are given to illustrate the main results. Mathematics Subject Classi cation (2010): 47H10, 26A33, 34B18.(Université de M'sila, 2021) Djiab, SomiaThis paper deals with a boundary value problem for a nonlin- ear di erential equation with two conformable fractional derivatives and integral boundary conditions. The results of existence, uniqueness and stability of positive solutions are proved by using the Banach contrac- tion principle, Guo-Krasnoselskii's xed point theorem and Hyers-Ulam type stability. Two concrete examples are given to illustrate the main results.Item Open Access SOLVING NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS USING AN ACCURATE SPECTRAL COLLOCATION METHOD(Université de M'sila, 2021) Hamani, FatimaIn this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L∞ and weighted L2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.Item Open Access Commutator estimates for vector fields on variable Triebel–Lizorkin spaces(Université de M'sila, 2022) Ben Mahmoud SalahIn 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.Item Open Access THE NUMERICAL SOLUTION OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION INVOLVING THE CAPUTO-KATUGAMPOLA FRACTIONAL DERIVATIVE.(Université de M'sila, 2022) Kaouther BouchamaIn this paper, a numerical approximation solution of a space-time fractional di usion equation (FDE), involving Caputo-Katugampola fractional derivative is considered. Stability and convergence of the proposed scheme are discussed using mathematical induction. Finally, the proposed method is validated through numerical simulation results of di erent examples.Item Open Access An efficient algorithm for solving the conformable time-space fractional telegraph equations(Université de M'sila, 2021) ABDELKEBIR, SaadIn 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.Item Open Access General Decay for a Coupled System of Viscoelastic Wave Equation of Infinite Memory with Acoustic Boundary Conditions(Université de M'sila, 2022) Abdelaziz Limamcoupled system of viscoelastic wave equation of infinite memory is considered. Our system is coupled with the acoustic boundary conditions. Under a very general assumption on the relaxation function, we establish a uniform decay rate. This work substantially improves the earlier results in cases of acoustic boundary conditions. Index Terms—viscoelastic damping, convex functions, general decayItem Open Access ON THE NUMERICAL SOLUTION OF FREDHOLM INTEGRAL EQUATION OF THE FIRST KIND(Université de M'sila, 2021) AMMAR BENDJABRIIn this work we concern with the approximate solution of the linear equation Af f where A is injective and compact operator, this equation admits a unique solution in direct sense or in the least square sense provided the right-hand side f is in RA or in , R A R A respectively. Due to the nonclosed range RA the solution is not stable. Besides, if A is positive de.nite we can replace the original equation by the auxiliary one A f where its solution exist, stable and converges to the exact solution of the original equation as tends to zero.Item Open Access ANALYSIS OF A DYNAMIC ELASTO-VISCOPLASTIC FRICTIONLESS ANTIPLAN CONTACT PROBLEM WITH NORMAL COMPLIANCE(Université de M'sila, 2021) OURAHMOUN ABBESWe 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
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