M. SAADI Abderachid

MCA

Directory of teachers

Department

Mathematics Department

Research Interests

Free boundary problems Soft topology Fractional calculus

Contact Info

University of M'Sila, Algeria

Email : abderrachid.saadi@univ-msila.dz

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Recent Publications

2024-07-20

Spectral decomposition of the fractional Sturm–Liouville operator with ρ -generalized derivative

We study the ρ-generalized fractional version of the classical Sturm–Liouville operator. We establish the existence and uniqueness of a boundary value problem for this operator with homogeneous boundary conditions. Using this problem, we present a spectral decomposition of the ρ-generalized fractional Sturm–Liouville operator.
Citation

M. SAADI Abderachid, (2024-07-20), "Spectral decomposition of the fractional Sturm–Liouville operator with ρ -generalized derivative", [national] Applicationes Mathematicae , Institute of mathematics, polish academic of science

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2023-12-03

Lipschitz Continuity and Explicit Form of Solution in a Class of Free Boundary Problem with Neumann Boundary Condition

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

M. SAADI Abderachid, (2023-12-03), "Lipschitz Continuity and Explicit Form of Solution in a Class of Free Boundary Problem with Neumann Boundary Condition", [national] JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS , Global Science Press

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2023-11-06

A unidimensional p-Laplacian boundary value problem with generalized fractional operator

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

M. SAADI Abderachid, (2023-11-06), "A unidimensional p-Laplacian boundary value problem with generalized fractional operator", [international] The first Sharjah international conference of mathematical sciences , Sharjah, UAE

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2023-03-13

Fractional Sobolev spaces and Boundary Value Problems via Hadamard derivative

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

M. SAADI Abderachid, (2023-03-13), "Fractional Sobolev spaces and Boundary Value Problems via Hadamard derivative", [national] Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES , Bulletin, Institute of Mathematics, Academia Sinica

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2023

A boundary value problem with fractional derivative via the Galerkin method

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

M. SAADI Abderachid, (2023), "A boundary value problem with fractional derivative via the Galerkin method", [international] The 1st International conference on mathematical science and applications , Univrsity of 8 Mai 1945, Galma, Algeria

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FRACTIONAL SOBOLEV SPACES AND BOUNDARY VALUE PROBLEMS VIA HADAMARD DERIVATIVE

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

M. SAADI Abderachid, (2023), "FRACTIONAL SOBOLEV SPACES AND BOUNDARY VALUE PROBLEMS VIA HADAMARD DERIVATIVE", [national] Bulletin of the Institute of Mathematics , Academia Sinica (New Series)

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2022

Fractional Sobolev Space via Loiuville operator

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

M. SAADI Abderachid, (2022), "Fractional Sobolev Space via Loiuville operator", [international] 4TH INTERNATIONAL CONFERENCE IN OPERATOR THEORY , PDE AND APPLICATION DECEMBER 7 -8 2022 , جامعة الشهيد حمة لخضر، الوادين الجزائر

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Linear fractional differential equations with generalized operators

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

M. SAADI Abderachid, (2022), "Linear fractional differential equations with generalized operators", [international] 1st International Conference on Innovative Academic Studies , Konya, Turkey

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2019

On the Continuity of the free boundary in a class of two-dimensional elliptic problems with Neuman boundary condition

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

M. SAADI Abderachid, (2019), "On the Continuity of the free boundary in a class of two-dimensional elliptic problems with Neuman boundary condition", [international] TAMTAM 2019 , Université de Telemcen

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FREE BOUNDARY PROBLEMS WITH NEUMAN BOUNDARY CONDITION

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

M. SAADI Abderachid, 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", [international] Electronic Journal of Di erential Equations, , Electronic Journal of Di erential Equations, , Department of Mathematics Texas State University

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2018

16th UAE math day

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

M. SAADI Abderachid, (2018), "16th UAE math day", [national] Soft elementary connected in soft elementary topology , American university of Ras El Khaimah, UAE

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Soft elementary topology: defined and properties

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

M. SAADI Abderachid, Abdeslem Lyaghfouri, , (2018), "Soft elementary topology: defined and properties", [national] Workshop of pure and applied mathematics , Electronic journal of differential equation , Université de M'sila

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2015

CONTINUITY OF THE FREE BOUNDARY IN ELLIPTIC PROBLEMS WITH NEUMAN BOUNDARY CONDITION

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

M. SAADI Abderachid, (2015), "CONTINUITY OF THE FREE BOUNDARY IN ELLIPTIC PROBLEMS WITH NEUMAN BOUNDARY CONDITION", [national] Electronic journal of differential equation , Electronic journal of differential equation

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