ABDERACHID Saadi

Benmeddour Mohamed Ourabah

Solutions faibles des problèmes aux limites associés aux équations différentielles d’ordre fractionnaire

TOUMIAT Ahmed

Problème de la digue associé à un lois de Darcy non linéaire

NADJI Manel

Étude d’un problème non-local avec des conditions de Neumann

SADIOU Ilhem

Solution faible d’un problème associé à une équation différentielle de type de Riemann-Liouville

LAADJEL Bahriya

Méthode de sur et sous solutions pour une équation différentielle d’ordre fractionnaire

MEROUCHE Linda

Sur les espaces de Sobolev fractionnaires et le Laplacien fractionnaire

LAKEL Nadjett

Étude d’une équation de la chaleur dans des domaines plans

GHERABI Izdihar

Sur les équations différentielles linéaires d’ordre fractionnel.

شحيمة جابر

Problème de la digue avec des conditions de fuite

مهدي فاطمة الزهراء

Calcul fractionnaire et applications aux EDOs et EDPs

بوجلال بسمة

Problème de la digue

We consider a class of free boundary problems with Neumann boundary conditions. We would like to give certain results with regularity of solutions (mainly the local interior and boundary Lipschitz continuity). We will also show an explicit form of solution under well-specified conditions.

Citation

ABDERACHID Saadi , , (2023-12-03), Lipschitz Continuity and Explicit Form of Solution in a Class of Free Boundary Problem with Neumann Boundary Condition, JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, Vol:36, Issue:4, pages:331-348, Global Science Press

This research is dedicated to investigating the existence and uniqueness of solutions for fractional differential boundary value problems that involve the fractional p−Laplacian operator. Here, a and b are real numbers, p > 2, λ 2 L1(a; b), and f : [a; b] × R −! R. The operators σDα a+ and σDα b− denote the left and right fractional derivatives with respect to the increasing function σ 2 C1(a; b). These problems are formulated within bounded intervals and are subject to homogeneous boundary conditions. The solutions are sought within fractional Sobolev spaces that are associated with σ−generalized fractional operators. Additionally, a variational formulation of the system is established, enabling the application of the variational method to demonstrate the existence of solutions, with uniqueness conditions under specific additional constraints.

Citation

ABDERACHID Saadi , ,(2023-11-06), A unidimensional p-Laplacian boundary value problem with generalized fractional operator,The first Sharjah international conference of mathematical sciences,Sharjah, UAE

This paper is devoted to the existence and uniqueness of solution to a class of Hadamard fractional differential equation under fractional Sobolev spaces. A novel form of fractional Sobolev space via Hadamard fractional operator is well proposed and related properties are also proved. Furthermore, a variational formulation of considered system is established and thereby the Lax-Milgram theorem is also employed to demonstrate the existence and uniqueness.

Citation

YACINE Arioua , Mohamedourabah BENMEDDOUR , ABDERACHID Saadi , , (2023-03-13), Fractional Sobolev spaces and Boundary Value Problems via Hadamard derivative, Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES, Vol:18, Issue:1, pages:61-83, Bulletin, Institute of Mathematics, Academia Sinica

This paper is devoted to the existence and uniqueness of solution to a class of Hadamard fractional differential equation under fractional Sobolev spaces. A novel form of fractional Sobolev space via Hadamard fractional operator is well proposed and related properties are also proved. Furthermore, a variational formulation of considered system is established and thereby the Lax-Milgram theorem is also employed to demonstrate the existence and uniqueness. AMS Subject Classification: 26A33, 34A08, 34Bxx. Key words and phrases: Fractional derivative, Boundary value problem, Hadamard.

Citation

ABDERACHID Saadi , , (2023), FRACTIONAL SOBOLEV SPACES AND BOUNDARY VALUE PROBLEMS VIA HADAMARD DERIVATIVE, Bulletin of the Institute of Mathematics, Vol:18, Issue:1, pages:61-83, Academia Sinica (New Series)

This work is devoted to the existence of weak solution to a class of Riemann-Liouville fractional differential equation with boundary value problem in a bounded interval. A novel form of fractional Sobolev space via Riemann-Liouville fractional operator is used. We give a variational formulation of considered system is established and employ the Galerkin method for the existence of weak solution. 2010 AMS Classification: 26A33, 34A08, 34Bxx. Keywords: fractional derivative, Galerkin, Riemann-Liouville operator.

Citation

ABDERACHID Saadi , ,(2023), A boundary value problem with fractional derivative via the Galerkin method,The 1st International conference on mathematical science and applications,Univrsity of 8 Mai 1945, Galma, Algeria

The aim of this work is the study of linear fractional differential equations with generalized operators, represented in the initial values problems whose elements belong to the Banach space, as well as linear differential equations of the type. 𝑦^{n𝛼} (x)+ \sum_{k=0}^{n-1}𝑎_k(𝑥)𝑦^{n𝛼}(x)= 𝑓(𝑥), where 0 < 𝛼 ≤ 1 and 𝑎_k, f are continuous functions. This is through the use of ordinary linear differential equations techniques.

Citation

ABDERACHID Saadi , ,(2022), Linear fractional differential equations with generalized operators,1st International Conference on Innovative Academic Studies,Konya, Turkey

This work is devoted to Liouville fractional Sobolev spaces. A novel form of these spaces is well proposed and related properties are also proved.

Citation

ABDERACHID Saadi , ,(2022), Fractional Sobolev Space via Loiuville operator,4TH INTERNATIONAL CONFERENCE IN OPERATOR THEORY , PDE AND APPLICATION DECEMBER 7 -8 2022,جامعة الشهيد حمة لخضر، الوادين الجزائر

Abstract. In this work, we study the continuity of the free boundary in a class of elliptic problems, with a Neuman boundary condition. The main idea is the use of a change of variable that reduces the problem to the one studied in [16].

Citation

ABDERACHID Saadi , Abdeslem Lyaghfouri, American University of Ras Al Khaimah, Department of Mathematics and Natural Sciences, Ras Al Khaimah, UAE, , (2019), FREE BOUNDARY PROBLEMS WITH NEUMAN BOUNDARY CONDITION, Electronic Journal of Dierential Equations,, Vol:2019, Issue:114, pages:1-13, Electronic Journal of Dierential Equations,

In this work, we study the continuity of free boundary, in a class of elliptic problems, with Neuman boundary condition, which generalize the work of [5]. We prove that the free boundary is represented locally by a family of continuous functions.

Citation

ABDERACHID Saadi , ,(2019), On the Continuity of the free boundary in a class of two-dimensional elliptic problems with Neuman boundary condition,TAMTAM 2019,Université de Telemcen

In a recent paper, Chiney and Samanta have introduced the notion of soft toplogy by using the elementary intersection and union. In this paper, based on this notion of soft topology, we have introduced the notion of soft elementary connected in soft elementary topology. Also, we show some properties of the soft elementary connected (space and set), compact (space and set).

Citation

ABDERACHID Saadi , Abdeslem Lyaghfouri, ,(2018), Soft elementary topology: defined and properties,Workshop of pure and applied mathematics,Université de M'sila

In a recent paper, Chiney and Samanta have introduced the notion of soft toplogy by using the elementary intersection and union. In this paper, based on this notion of soft topology, we have introduced the notion of soft elementary connected in soft elementary topology. Also, we show some properties of the soft elementary connected (space and set). To that end, we investigate the relationship between soft elementary set and soft elementary sub-topological space in soft elementary topological space.

Citation

ABDERACHID Saadi , ,(2018), 16th UAE math day,Soft elementary connected in soft elementary topology,American university of Ras El Khaimah, UAE

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.

Citation

ABDERACHID Saadi , , (2015), CONTINUITY OF THE FREE BOUNDARY IN ELLIPTIC PROBLEMS WITH NEUMAN BOUNDARY CONDITION, Electronic journal of differential equation, Vol:2015, Issue:160, pages:1-16, Electronic journal of differential equation